Ph.D. thesis

Università degli Studi di Milano-Bicocca
Facoltà di Scienze Matematiche Fisiche e Naturali
Scuola di Dottorato di Scienze
Corso di Dottorato di Ricerca in Fisica e Astronomia
CMS Tracking Performance and
/T
Sesnsitivity for the MSSM A→τ τ →eµE
decay.
Coordinatore:
Prof. Claudio Destri
Tutore:
Dott. Sandra Malvezzi
Tesi di Dottorato di
Giuseppe B. Cerati
Matricola 700084
XXI ciclo
Anno Accademico 2007 − 2008
Contents
Introduction
1
1 The CMS Experiment
1.1 The LHC accelerator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 The CMS detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
5
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2 Tracking in CMS
2.1 Overview of Tracking in CMS
2.2 Definition of Track . . . . . .
2.3 Combinatorial Kalman Filter
2.4 Road Search . . . . . . . . . .
2.5 Cosmic Track Finder . . . . .
2.6 The Final Track Fit . . . . .
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3 Tracking Validation Tools in CMSSW
3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Tracking Performance with Simulated Data . . . . . . . . . . . . . . . . . . .
3.3 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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4 Outlier Rejection in the Final Track Fit
4.1 Implementation of the Algorithm . . . .
4.2 Characterization of the Rejected Hits . .
4.3 Impact on Tracking Performance . . . .
4.4 Conclusions . . . . . . . . . . . . . . . .
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5 Tracking Efficiency with Cosmic Data during Commissioning
5.1 CRUZET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Efficiency Estimate using Tracker Data only . . . . . . . . . . . . . . . . . . .
5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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6 Summary on Tracking
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7 Motivations for the Minimal Supersymmetric Standard
7.1 Open Problems of the Standard Model . . . . . . . . . . .
7.2 A brief introduction to Supersymmetry and MSSM . . . .
7.3 Higgs particles in the MSSM . . . . . . . . . . . . . . . .
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Model
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67
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74
i
8 Search for the Heavy Neutral CP-odd Higgs Boson A
8.1 Exclusion limits from LEP and CDF . . . . . . . . . . . . . . . . . . . . . . .
8.2 Production at LHC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
/ T decay
9 Sensitivity for the MSSM A → τ τ → eµE
9.1 Introduction . . . . . . . . . . . . . . . . . . . . .
9.2 Event reconstruction . . . . . . . . . . . . . . . .
9.3 Signal and Background samples . . . . . . . . . .
9.4 Crucial issues . . . . . . . . . . . . . . . . . . . .
9.5 Event selection . . . . . . . . . . . . . . . . . . .
9.6 Results . . . . . . . . . . . . . . . . . . . . . . . .
in CMS
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79
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Conclusions
122
Bibliography
124
Acknowledgements
129
ii
Introduction
At the end of the 20th century, high energy physicists have developed the Standard Model
(SM), a powerful theory capable to describe with great precision the behavior of the fundamental particles (matter constituents and force carriers) from the M eV scale up to the order
of 100 GeV . The predictions of the Standard Model have been successfully tested for about
thirty years at many colliders, like LEP, HERA and TEVATRON. In particular, the mass
and width of the Z and W bosons were measured at LEP, the parton distribution functions in
the proton have been studied at HERA, while at TEVATRON the last piece of the fermionic
picture of the SM was discovered: the top quark.
Besides explaining the dynamics and the interactions between the elementary particles,
the SM has arisen some more fundamental problems that are being addressed at the 21st
century experiments. The most important questions are what the origin of the particles’
mass is, what is the unobserved part of the universe made of, why matter has overcome
antimatter, what happened during the Big Bang, if there are hidden dimensions and if there
is a symmetry between fermions and bosons.
The puzzle to which the largest number of physicists have been researching a solution
is the origin of the mass. According to the Higgs Theory, particles are massive because
of their interaction with a new field, called the Higgs field. In the simplest model of the
Higgs Theory just one new particle is foreseen, the Higgs boson. A more complex Higgs
particle spectrum is predicted by other theories that extend the Standard Model, such as the
Minimal Supersymmetric Standard Model (MSSM). The search for MSSM Higgs bosons is an
extremely important topic, because their discovery would address not only the question about
the origin of the mass, but it would also reveal the presence of a fermion-boson symmetry
(SUSY) in nature. Furthermore, as the MSSM predicts the existence of a weakly interacting
massive particle called neutralino, it would give a clue about the nature of dark matter.
All these issues will be investigated at LHC, the Large Hadron Collider built in the LEP
tunnel, where proton beams will collide at the unprecedented center of mass energy of 14 T eV
and at the luminosity of 1034 cm−2 s−1 . The experiments built at the LHC are ATLAS, CMS,
LHC-b and ALICE. LHC-b and ALICE are dedicated to the physics of the b-quark and to the
study of heavy ion collisions respectively. Their researches focus on the matter-antimatter
asymmetry and a new state of matter, the quark-gluon plasma. ATLAS and CMS, the socalled “general purpose” experiments, will look for answers to all the open questions in high
energy physics and, among many new particles, will seek the MSSM Higgs bosons.
ATLAS and CMS have different designs and different approaches, mostly due to the choice
of the magnetic field: toroidal for ATLAS (plus a small inner solenoidal field), solenoidal for
CMS. The CMS solenoid is the largest ever built, reaching a field of almost 4 T and containing
both the tracker and the calorimeters. The tracker, being the biggest all-silicon detector in
the world, is expected to be extremely efficient and precise also in a very hostile environment
3
such as that of the LHC collisions. The identification and the precise measurement of leptons
and conversion photons, the tagging of b and τ jets, the primary and secondary vertex reconstruction and the track-based correction to calorimeter measurements are the key feature
necessary to achieve the CMS physics goals. The track reconstruction is the basis for all
these tasks and thus, the improvement of tracking performance and the development of tools
needed to estimate it are fundamental for the outcome of the whole experiment.
Therefore, CMS is an experiment on the cutting edge of the detector technology and
pioneers the mysteries of contemporary science. Focusing on the track reconstruction and the
discovery potential of MSSM Higgs bosons, this thesis addresses some of the most important
topics both from the detector and the physics analysis point of of view.
First, in the context of the CMS tracking, the Track Validation Tool has been developed.
This tool analyzes simulated data and produces a fully configurable set of plots in order to
estimate the tracking performance and compare tracks reconstructed with different algorithms
or software releases. It has proven that the CMS tracking has full efficiency, low fake rate
and high resolution both for momentum and impact parameter measurements. Then, an
algorithm that removes biased and incorrect hits from the reconstructed tracks has been
implemented. The effect of this algorithm is to enhance the track quality by correcting the
track parameters, reducing the track χ2 and improving the track purity. Finally the tracking
performance has been evaluated with the first real data collected by the full tracker detector
in its final configuration: a method to evaluate the cosmic ray tracking efficiency using tracker
information only has been developed, leading to very good results (∼ 90%) matching Monte
Carlo predictions.
The second part of the thesis is dedicated to the discovery potential of the MSSM Heavy
/ T in CMS. The τ decay
Neutral CP -odd Higgs boson in the decay channel A → τ τ → eµE
channel is particularly favored in the MSSM because the coupling to A is enhanced by a
factor tan β with respect to the SM. The two main production processes of A at the LHC
are considered, namely the b quark associated and the direct gluon fusion processes. The
main backgrounds are Z/γ ∗ → τ τ and tt̄ events, but also W t, W W and bbll events provide
a non-negligible contribution after the selection criteria are applied. A key feature of this
analysis is the tagging of b jets: several strategies are considered on the basis of the request
or the veto on the number of b-tags, leading to significant results for each strategy, but with
different signal and background contributions. RThe analysis is performed for tan β = 30 and
mA = 160 GeV at an integrated luminosity L = 10 f b−1 ; this channel is shown to be
promising for the discovery of A and for the measurement of its mass and width. Finally, a
mass scan for the same values of tan β and luminosity has been performed: CMS is sensitive
to the A search in the mass range 140 ≤ mA ≤ 300 GeV .
4
Chapter 1
The CMS Experiment
1.1
The LHC accelerator
The Large Hadron Collider (LHC) [1] is the proton-proton (p − p) collider at CERN. It
√
will collide protons with a center of mass energy s = 14 T eV with a design luminosity
L = 1034 cm−2 s−1 . The first LHC single beams successfully circulated through the whole
collider in the morning of the 10th September 2008. Although the initial beam commissioning
was progressing extremely well, during the commissioning of the main dipole circuit in sector
34 on the 19th September (without beam), a number of magnets were damaged in an incident
that saw a large amount of Helium released into the tunnel. Due to the repair of the damaged
region and the planned winter shutdown, the next circulating beam in the LHC are foreseen
for Spring 2009 at the earliest. During the first 3 years of data taking, the luminosity is
expected to be 2 × 1033 cm−2 s−1 (the so called “low luminosity” phase), while at the start
up LHC is foreseen to run at L = 1031 -1032 cm−2 s−1 .
LHC is installed in the LEP tunnel and the available CERN accelerators are employed in
the injection chain: the proton beam exiting a small linear accelerator at 50 M eV , will be
injected in the PS at 1.4 GeV , then in the SPS at 25 GeV , and finally in the LHC ring at
450 GeV (Fig. 1.1).
One of the critical aspects in accelerating the protons up to an energy of 7 T eV is the
required bending magnetic field which, for the LHC bending radius (R ∼ 2780 m) is about
8.4 T . This magnetic field will be provided by the 1232 LHC superconducting 14.2 m long
dipole magnets, placed in the eight curved sections which connect the straight sections of the
LHC ring. The super-conducting magnets use a Ni-Ti conductor, cooled down to 1.9 K, by
means of super-fluid Helium. The choice of a p − p collider obliges to install two separate
magnetic chambers which, for economical reasons, will lay in the same mechanical structure
and cryostat.
The high luminosity of the LHC is obtained by a high frequency of bunch crossing and
by a high number of protons per bunch: two beams of protons with an energy of 7 T eV ,
circulating in two different vacuum chambers, will contain each 2808 bunches filled with about
1.15 × 1011 protons. The beams will cross at the rate of 40 M Hz, at the interaction point,
with a spread of 7.5 cm along the beam axis and 15 µm in the transverse directions. The
main machine parameters are summarized in Table 1.1.
The operating conditions at the LHC are extremely challenging for the experiments. The
√
p − p total inelastic cross section at s = 14 T eV is about 80 mb, several orders of magnitude
larger than the typical cross section for events with large momentum transfer. Most of the
5
Figure 1.1: Scheme of the LHC injection chain.
inelastic events consist of soft p − p interactions characterized by outgoing particles with a
low transverse momentum. These events are referred to as minimum bias. It is expected that
each bunch crossing will produce about 20 minimum bias events in the high luminosity phase
and 5 minimum bias events in the low luminosity phase. Hence, each interesting event will be
readout entangled with a large number of minimum bias events, which constitute the pile-up.
The high interaction rate (∼ 109 events/s) and the high bunch crossing frequency impose
stringent requirements on the data acquisition and trigger systems and on the detectors. The
trigger has to provide an high rejection factor, maintaining at the same time a high efficiency
in selecting the interesting events. The detectors has a fast response time (25-50 ns) and
a fine granularity (and therefore a large number of readout channels) in order to minimize
the pile-up effect. Furthermore, the high flux of particles coming from the p − p interactions
implies that each component of the detector, including the read-out electronics, has to be
radiation resistant.
1.2
The CMS detector
The Compact Muon Solenoid[2, 3, 4] is the general purpose experiment installed at Point 5 of
the Large Hadron Collider; it is currently under commissioning and waiting for the first beam
collisions foreseen in 2009. The CMS structure is a typical one for experiments at colliders: a
6
Beam parameters
Beam energy
Maximum luminosity
Time between collisions
Bunch length
RMS beam radius at the interaction point
7 T eV
1034 cm−2 s−1
25 ns
7.7 cm
16.7 µm
Technical parameters
Ring length
Radiofrequency
Number of bunches
Number of dipoles
Dipole magnetic field
26658.9 m
400.8 M Hz
2808
1232
8.33 T
Table 1.1: The relevant LHC parameters for p − p collisions.
cylindrical central section (the barrel) closed at its end by two caps (the endcaps), as sketched
in Fig. 1.2.
Superconducting Solenoid
Silicon Tracker
Very-forward
Calorimeter
Pixel Detector
Preshower
Hadronic
Calorimeter
Electromagnetic
Calorimeter
Muon
Detectors
Compact Muon Solenoid
Figure 1.2: CMS overview.
The main design component of CMS is its large superconducting magnet producing a
3.8 T field and allowing for a compact structure: within the solenoid the inner tracking
7
system and both the electromagnetic and the hadron calorimeters are installed, while the
muon chambers are interleaved with the iron return yoke.
The coordinates system in CMS are chosen with the z axis along the beam direction, the x
axis directed toward the center of the LHC ring and the y axis directed upward, orthogonally
to the z and x axes. Given the cylindrical structure of CMS, a convenient and commonly
used coordinate system is r, φ, η, where r is the distance from the z axis, φ is the azimuthal
angle in the xy plane and η is the pseudorapidity defined as
θ
(1.1)
η = − ln tan
2
where θ is the angle with respect to the beam axis. The use of pseudorapidity instead of
the polar angle is motivated by the fact that the difference in pseudorapidity between two
particles is invariant under Lorentz boosts along the beam axis. CMS is characterized by
high hermeticity with a full φ coverage and up to η = 5 in pseudorapidity.
1.2.1
The Magnet
A key feature of the CMS experiment is its axial high magnetic field. The magnet system
of CMS [5] is composed of three main parts: the superconducting solenoid, the barrel return
yoke and the endcap return yoke. The 3.8 T magnetic field allows to measure efficiently the
muon momentum up to a pseudorapidity of 2.4. The return yoke is made of iron and contains
the muon detectors. It is a 12-sided cylindrical structure, with a total length is about 11 m
and it is divided into five rings of about 2.5 m each. It has an outer diameter of 14 m and a
total weight of about 7000 tons. Each ring is divided into three iron layers where the muon
detectors are inserted. The thickness of the border layers is 630 mm and the middle layer
is 295 mm thick. Each endcap is composed by three independent disks; the outermost is
300 mm thick, the others 600 mm.
The superconductive coil is housed into a vacuum tank and kept at the temperature of
the liquid helium. The vacuum tank is supported only by the central barrel ring of the yoke
and in its turn supports the calorimeter system (ECAL and HCAL) and the tracker.
1.2.2
The Tracker
The CMS tracker [6] is the subdetector closest to the interaction point, placed in the 3.8 T
magnetic field of the superconductive solenoid. It is designed to determine the interaction
vertex, measure with high precision the momentum of the charged particles, identify the
presence of secondary vertices. The tracker must be able to operate without degrading its
performances in the hard radiation environment of LHC.
The CMS collaboration has adopted silicon technology for the whole tracker. Three regions can be defined according to the charged particle flux at different radii at high luminosity:
• Closest to the interaction vertex where the particle flux is highest (∼ 107 s−1 at r ∼
10 cm) pixel detectors are placed. The size of the pixel-cells is ∼ 100 × 150µm2 , leading
to an occupancy < 10−4 per pixel per LHC crossing.
• In the intermediate region (20 < r < 55 cm) the particle flux lowers, allowing for the
use of silicon microstrip detectors with a minimum cell size of ∼ 10 cm × 80 µm and
resulting in an occupancy of 2-3% per LHC crossing.
8
• The outermost region is characterized by sufficiently low fluxes which enable to adopt
larger-pitch silicon microstrips with a maximum cell size of ∼ 25 cm × 80 µm, keeping
the occupancy to ∼ 1%.
The pixel detector consists of three barrel layers and two endcap disks at each side
(Fig. 1.3). The barrel layers are located at 4.4 cm, 7.3 cm and 10.2 cm and are 53 cm
long. The two end disks, extending from 6 to 15 cm in radius, are placed on each side at
|z| = 34.5 cm and 46.5 cm. The pixel bulk is 270 µm thick. This design allows to obtain
at least three 3D measurement points per track in the |η| < 2.4 region for tracks originating
from the central interaction point. The total number of cells is about 66 millions, organized
in about 16000 modules of 52 columns and 80 rows. The total active area is close to 1 m2 .
The pixels resolution is improved thanks to the charge sharing due to the Lorentz drift and
the non-zero incident angle with respect to the module surface:
• as far as the barrel is concerned, the resolution in r is improved thanks to a Lorentz
angle of about 32◦ (cluster size ∼ 2), while the the cluster size along the z-coordinate
is 1-7 depending on the incident angle.
• for the forward pixels, a turbine geometry of 20◦ was chosen to improve the resolution in
r thanks to the Lorentz effect and in rφ thanks to the non-zero incident angle (average
cluster size 2)
The expected resolutions for unirradiated sensors are less than 15 µm in the transverse
direction for the barrel and between 15-30µm for the barrel longitudinal direction and for
the endcap disks. Test beam data proved that, even after an irradiation dose greater than
40 M Rad (3 years of LHC at design luminosity), the detector performance, both in terms of
efficiency and resolution, remains remarkable.
Figure 1.3: The inner pixel detector. The three barrel layers and the two disks of the
endcap with blades disposed in a turbine-like shape are visible.
The strip tracker is divided into four sub-detectors: the Tracker Inner Barrel (TIB), the
Tracker Outer Barrel (TOB), the Tracker Inner Disks (TID) and the Tracker End Cap (TEC).
9
In the barrel, strips are parallel to the beam axis, while, in the endcaps, they have a radial
orientation. On the whole the strip tracker is made of about 10 millions of channels for an
active area close to 198 m2 .
The TIB is made of four layers with about 25 < r < 50 cm and |z| < 65 cm. The
first two layers are double-sided (stereo) modules with a tilt angle of 100 mrad and provide
a measurement in both r-φ and r-z coordinates. The TOB is composed of six layers from
r ∼ 55 cm to r ∼ 110 cm and with |z| <
∼ 110 cm. Also for TOB the innermost two layers
are stereo. The TIB single-point resolution is 23-34 µm in the r-φ and 230 µm in the r-z
coordinate; TOB resolutions are 35-52 µm in r-φ and 530 µm in z. The three TID and the
nine TEC disks extend in the regions with 75 < |z| < 110 cm and 125 < |z| < 280 cm
respectively. The two innermost TID and TEC and the fifth TEC rings are stereo. TIB,
TID and three innermost TEC ring sensors are 320 µ thick, while TOB and outer TEC ring
sensors 500 µm.
The CMS tracker, therefore, provides a full coverage for |η| < 2.4 with more than 10
high-resolution measurement points among which at least 5 provide a 3-dimensional position
measurement.
Figure 1.4: Pseudorapoidity coverage of the CMS tracker. 2D measurement layers are
displayed in red, 3D in blue.
Main drawback for the all-silicon CMS tracker is the large amount of material due to
detector modules, support structure, cooling plant, cables and electronic devices. The total
material budget in terms of radiation length is estimated to raise up to 1.8 for η ∼ 1.5,
corresponding to about 0.5 interaction lengths (Fig. 1.5).
1.2.3
The Electromagnetic Calorimeter
The electromagnetic calorimeter (ECAL) measures the energy of the electrons and photons.
The design of the CMS ECAL [7] was driven by the requirements imposed by the search
of the Higgs boson in the channel H → γγ, where a peak in the di-photon invariant mass
placed at the Higgs mass, has to be distinguished from a continuous background. A good
resolution and a fine granularity are therefore required: both of them improve the invariant
mass resolution on the di-photon system by improving respectively the energy and angle
measurement of the two γs. The fine granularity also helps to obtain a good π 0 /γ separation.
10
x/λ0
Material Budget Tracker
x/X0
Material Budget Tracker
Support
Sensitive
Cables
Cooling
Electronics
Other
Air
1.8
1.6
Support
Sensitive
Cables
Cooling
Electronics
Other
Air
0.5
1.4
0.4
1.2
0.3
1
0.8
0.2
0.6
0.4
0.1
0.2
0
-5
-4
-3
-2
-1
0
(a)
1
2
3
4
5
η
0
-5
-4
-3
-2
-1
0
1
2
3
4
5
η
(b)
Figure 1.5: Material budget as a function of η expressed in terms of radiation length X0 (a)
and in terms of interaction length λ0 (b). The peak around η=1.5 corresponds to the cables
and services of the tracker.
In order to provide high energy resolution, ECAL is placed inside the solenoid: hence
a compact calorimeter is required. ECAL is a hermetic, homogeneous calorimeter made of
lead tungstate (PbWO4 ) crystals, 61200 crystals mounted in the central barrel part, and 7324
crystals in each endcap (Fig. 1.6). The choice of lead tungstate scintillating crystals was driven
by the characteristics of these crystals, having a short radiation length (X0 = 0.89 cm) and a
small Moliere radius (RM = 2.2 cm), being fast (80% of the scintillation light is emitted within
25 ns) and also radiation hard. However, the relative low light yield (30 γ/MeV) requires the
use of photodetectors with intrinsic gain that can operate in a magnetic field. In the barrel,
silicon avalanche photodiodes (APDs) are used as photodetectors, while vacuum phototriodes
(VPTs) have been chosen for the endcaps. In addition, the sensitivity of both the crystals
and the APDs response to temperature changes requires temperature stability. In order to
preserve the ECAL energy resolution performances, a water cooling system guarantees a long
term stability at the 0.1◦ C.
The barrel region has a pseudorapidity coverage up to |η| < 1.479. It has an inner radius of 129 cm and is structured in 36 supermodules, each containing 1700 crystals, covering
half the barrel length and covering a 20◦ angle in φ. Each supermodule is divided along η
into four modules which in their turn are made of submodules, the basic assembling alveolar units, containing 5×2 crystals each. The barrel crystals have a front face cross-section
of ∼ 22× 22 mm2 and have a length of 230 mm, corresponding to 25.8X0 . In order to
avoid that particles escape through the dead regions between the crystals, their axes are
oriented with a 3◦ tilt with respect to the pointing geometry. The granularity of the barrel
is ∆φ × ∆η = 0.0175 × 0.0175 and the crystals are grouped, from the readout point of view,
into 5×5 arrays corresponding to the trigger towers.
The encaps cover the pseudorapidity region 1.48 < |η| < 3.0, ensuring precision measurements up to η < 2.5. The endcap crystals have dimensions of 28.6×28.6×220 mm2 . Each
endcap is structured in two “Dees” consisting of semi-circular aluminum plates from which
11
Figure 1.6: Scheme of the barrel and of the endcaps of the CMS ECAL.
are cantilevered structural units of 5×5 crystals, known as “supercrystals”.
A preshower device, whose principal aim is to identify neutral pions in the endcaps within
1.653 < |η| < 2.6, is placed in front of the crystal calorimeter. The active elements are two
planes of silicon strip detectors which lie behind disks of lead absorber at depths of 2X0 and
3X0 .
1.2.4
The Hadronic Calorimeter
The hadron calorimeter (HCAL) [8], placed just outside the electromagnetic calorimeter,
plays a major role in the reconstruction of jets and missing energy. Its resolution has to guarantee a good reconstruction of the di-jets invariant mass and an efficient measurements of the
missing energy which represent an effective signature in many channels of physics beyond the
Standard Model. Similarly to the other subdetectors, HCAL has to provide a good hermeticity, which is critical for determining the missing energy, and a fine granularity to allow for a
clear separation of di-jets from resonance decays and improve the resolution in the invariant
mass of the di-jets. Moreover, it has to provide a number of interaction lengths sufficient to
contain the energetic particles from high transverse momentum jets. The dynamic range has
to be large in order to detect signals ranging from the signal of a single minimum ionizing
muon up to an energy of 3 TeV.
The pseudorapidity region |η| < 3 is covered by the barrel (up to |η| < 1.74) and the two
endcaps. The HCAL is composed by brass layers as absorbers interleaved by plastic scintillator layers, 4 mm thick, used as active medium. The absorber layers thickness is between
60 mm thick in the barrel and 80 mm in the endcaps, while the scintillators layers are 4 mm
thick. In terms of interaction lengths λ, the barrel ranges from 5.46λ at |η| =0 up to 10.82λ
at |η| =1.3; the endcaps correspond on average to ∼ 10λ. The scintillator in each layer is
divided into tiles with a granularity matching the granularity of the ECAL trigger towers
(∆η × ∆φ = 0.0875 × 0.0875) and the light is collected by wavelength shifters.
The two hadronic forward calorimeters improve the HCAL hermeticity, covering the pseudorapidity region 3< |η| <5. It is placed at 11.15 m from the interaction point outside
the magnetic field. Due to the extremely harsh radiation environment a different detection
technique is used: a grid of quartz (radiation hard) fibers is embedded in a iron absorber.
12
1.2.5
The Muon System
In CMS, the muon detectors are placed beyond the calorimeters and the solenoid. The
muon system [9] consists of four active stations interleaved by the iron absorber layers which
constitute the return yoke for the magnetic field. The muon system has three functions: muon
identification, momentum measurement, and triggering. Good muon momentum resolution
and trigger capability are enabled by the high field solenoidal magnet and its flux-return
yoke. The latter also serves as a hadron absorber for the identification of muons.
Three different typologies of detectors are employed: drift tubes (DT) in the barrel region,
cathode strip chambers (CSC) in the endcaps and, in addition to DT and CSC, resistive plate
chambers (RPC) in both regions.
In the barrel region, where the neutron-induced background is small, the muon rate is low,
and the magnetic field is uniform and mostly contained in the steel yoke, drift chambers
with standard rectangular drift cells are used. The barrel drift tube (DT) chambers cover
the pseudorapidity region |η| < 1.2 and are organized into 4 stations interspersed among the
layers of the flux return plates. The first 3 stations each contain 8 chambers, in 2 groups
of 4, which measure the muon coordinate in the r-φ bending plane, and 4 chambers which
provide a measurement in the z direction, along the beam line. The fourth station does not
contain the z-measuring planes.
In the two endcap regions of CMS, where the muon rates and background levels are high and
the magnetic field is large and non-uniform, the muon system uses cathode strip chambers
(CSC). With their fast response time, fine segmentation, and radiation resistance, the CSCs
identify muons between |η| values of 0.9 and 2.4. There are 4 stations of CSCs in each
endcap, with chambers positioned perpendicular to the beam line and interspersed between
the flux return plates. The cathode strips of each chamber run radially outward and provide
a precision measurement in the r-φ bending plane. The anode wires run approximately
perpendicular to the strips and are also read out in order to provide measurements of η and
the beam-crossing time of a muon. Each 6-layer CSC provides robust pattern recognition for
rejection of non-muon backgrounds and efficient matching of hits to those in other stations
and to the CMS inner tracker.
A crucial characteristic of the DT and CSC subsystems is that they can each trigger on the pT
of muons with good efficiency and high background rejection. A complementary, dedicated
trigger system consisting of resistive plate chambers (RPC) was added in both the barrel and
endcap regions. The RPCs provide a fast, independent, and highly-segmented trigger with a
sharp pT threshold over a large portion of the rapidity range (|η| < 1.6) of the muon system.
The RPCs are double-gap chambers, operated in avalanche mode to ensure good operation
at high rates. They produce a fast response, with good time resolution but coarser position
resolution than the DTs or CSCs. They also help to resolve ambiguities in attempting to
make tracks from multiple hits in a chamber.
1.2.6
The Trigger
At the nominal LHC luminosity, the expected event rate is about 109 Hz. Given the typical
size of a raw event (∼ 1 MB) it is not possible to record the information for each event.
Indeed, the event rate is largely dominated by soft p − p interactions with particles of low
transverse momentum. The triggering system must have a large reduction factor and maintain
at the same time high efficiency on the potential interesting events, reducing the rate down
to 100 Hz, which is the maximum sustainable rate for storing events. The trigger system
13
consists of two main steps: a Level 1 Trigger and a High Level Trigger. The basic concepts
will be described in the following.
The Level 1 trigger
The Level 1 trigger [10] (L1) reduces the rate of selected events down to 50 (100) kHz for the
low (high) luminosity running. The full data are stored in pipelines of processing elements,
while waiting for the trigger decision. The L1 decision has to be taken in 3.2 µs. If the L1
accepts the event, the data are processed by the High Level Trigger. To deal with the 25 ns
bunch crossing rate, the L1 trigger has to take a decision in a time too short to read data
from the whole detector, therefore it employs calorimetric and muon data only, since the
tracker algorithms are too sophisticated for this purpose. The Level-1 trigger is organized
into a Calorimeter Trigger and a Muon Trigger whose information is transferred to the Global
Trigger which takes the decision.
The Calorimeter Trigger is based on trigger towers, arrays of 5 crystals in ECAL, which
match the granularity of the HCAL towers. The trigger towers are grouped in calorimetric
region of 4 × 4 trigger towers. The Calorimeter Trigger identifies, from the calorimetric
region information, the best four candidates of each of the following classes: electrons and
photons, central jets, forward jets and τ -jets identified from the profile of the deposited
energy. The information of these objects is passed to the Global Trigger, together with the
measured missing ET . The Muon trigger is performed separately for each muon detector.
The information is then merged and the best four muon candidates are transferred to the
Global Trigger.
The Global Trigger takes the accept/reject decision exploiting both the characteristic of
the single objects and of combination of them.
The High Level Trigger
The High Level Trigger [11] reduces the output rate down to 100 Hz. The idea of the HLT
trigger software is the regional reconstruction on demand, that is only those objects in the
useful regions are reconstructed and the uninteresting events are rejected as soon as possible.
This leads to the development of three “virtual trigger” levels: at the first level only the
full information of the muon system and of the calorimeters is used, in the second level
the information of the tracker pixels is added and in the third and final level the full event
information is available.
14
Chapter 2
Tracking in CMS
Tracking is one of the most important tasks for CMS because most of the reconstructed
physics object depend on it: tracks not only provide the momentum measurement for charged
particles (muons, electrons and charged hadrons), but also they are the input for primary
and secondary vertex reconstruction and for b- and τ -tagging algorithms, they are used to
reconstruct the photons converted into e+ e− pairs in the tracker volume and are fundamental
for some jet-energy correction algorithms.
On the other hand, tracking in CMS is also a very complex task, because LHC collisions will
produce thousand tracks every bunch crossing, corresponding to about 2.5 tracks/cm2 every
25 ns at R = 4 cm, where the first pixel barrel layer is placed. In addition, the large material
budget provided by the all-silicon tracker makes even tougher the reconstruction of tracks
from particles that can suffer from bremsstrahlung (e.g. electrons) or nuclear interactions
(e.g. pions). Therefore, to obtain the best results in each physics analysis in CMS, an efficient
and precise tracking in different kind of events in needed.
2.1
Overview of Tracking in CMS
The CMS tracking group has developed a complex tracking strategy that leads to optimal
track reconstruction performance for any physics object use case.
In particular, this is achieved by a modular approach that divides the track reconstruction
process into three steps [12, 13, 14]:
• Seeding: hit pairs or triplets are selected, providing an initial estimate of the track
parameters.
• Pattern Recognition: starting from the track seed, the hits corresponding to that
track are searched for in the whole tracker.
• Final Fit: once all the track hits have been found, they are fitted to extract the best
estimate of the track parameters.
Currently, in CMS several tracking algorithms are available. Each algorithm defines its own
seeding and pattern recognition procedures, while, to provide a coherent track definition,
the final fit is the same for all the algorithms. Two “general purpose” algorithms have been
developed, namely the Combinatorial Kalman Filter and the Road Search. Other algorithms
are instead dedicated to the reconstruction of special kind of tracks: the Cosmic Track
15
Finder for the reconstruction of cosmic-rays, the Gaussian Sum Filter for electrons and the
Deterministic Annealing Filter for tracks in high energy jets.
After the tracks are produced, a set of quality filters [15] are applied, providing a quality
label to each reconstructed track. These filters apply cuts based on the track transverse
compatibility with the beam line, the longitudinal compatibility with the interaction vertices
and the track χ2 . The cut strength depends on the track pT , η and mostly on the number of
hits: basically no quality cuts are needed for tracks with many hits (at least 10 crossed layers),
while tighter cuts are applied for tracks with lower number of hits. The quality flags are Pre
Filter, Loose Quality, Tight Quality and High Purity, the first being the label for tracks before
any filtering is applied, the last being the most severe quality selection (Table 2.1).
Table 2.1: Examples of High Purity quality cuts for three different reconstructed tracks.
σ(α) is the expected resolution on the parameter α for that track. For the definition of the
track parameters, see §2.2
χ2 /ndof
|dxy| [cm]
|∆z| [cm]
|dxy|/σ(dxy)
|∆z|/σ(z)
pT = 0.7 GeV
η = 0.8
nhits = 5
<4,5
<0,02
<0,04
<16
<16
pT = 3 GeV
η = 0.8
nhits = 7
<6,3
<0,06
<0,15
<62
<62
pT = 3 GeV
η = 0.8
nhits = 15
<13,5
<1,2
<3,1
<1300
<1300
Also, in order to reconstruct low momentum and secondary particle tracks, an iterative
tracking [16] approach has been developed. After a first reconstruction step, severe cuts are
applied in order to keep the fake rate at a very low level, the hits attached to the track
collection are removed and a second track reconstruction is performed with the remaining
hits and looser tracking cuts. This procedure can be further iterated (the default sequences
performs three step).
Finally, to complete this introduction to CMS tracking, it is worth recalling that tracks are
also used during the High Level Trigger (HLT). For this purpose, tracks can be reconstructed
very fast using pixel hits only or using both pixels and strips but in a limited region of the
tracker (usually a region pointed by calorimeter towers of tracks is the muon chambers).
In the following, the most relevant items for this thesis are reviewed more in detail.
2.2
Definition of Track
A track is defined as a set of measurement points (hits) in the tracker that, once properly
fitted, provide an estimate (with corresponding errors) of a charged particle trajectory. The
trajectory of a charged particle in a magnetic field is a helix and can be geometrically described by five parameters. These parameters are evaluated at a given reference position
v = (vx, vy, vz) along the track, which, for tracks from LHC collisions, is the point of closest
approach to the beam axis. In addition, some of them are evaluated as distances with respect
to another point, the beam spot [17] bs = (bsx, bsy, bsz).
The choice of the parameters currently made in CMSSW is the following [18]:
16
1. qoverp = q/|~
p| = signed inverse of momentum [1/GeV].
2. λ = π/2 − θ where θ is the polar angle at the point v.
3. φ = azimuthal angle at v.
4. dxy = −(vx − bsx) ∗ sin φ + (vy − bsy) ∗ cos φ [cm]. Geometrically, dxy is the signed
distance in the XY plane between the straight line passing through (vx, vy) with azimuthal angle φ and the point (bsx, bsy).
5. dsz = (vz − bsz) ∗ cos λ − ((vx − bsx) ∗ cos φ + (vy − bsy) ∗ sin φ) ∗ sin λ [cm]. The dsz
parameter is the signed distance in the SZ plane between the straight line l passing
through (vx, vy, vz) with angles (φ, λ) and the projection of the bs point on the SZ
plane. The S axis is defined by the projection of l on the XY plane.
Other important quantities are the transverse impact parameter d0 , the longitudinal impact
parameter dz and the transverse momentum pT , which can be expressed as a function of the
above parameters as d0 = −dxy, dz = dsz/ cos λ and pT = |p| sin θ.
2.3
Combinatorial Kalman Filter
The Combinatorial Kalman Filter (CKF), also known as Combinatorial Track Finder (CTF),
is the default CMS track reconstruction algorithm as it provides the best performance both
in terms of physics results and computing time.
The CKF seeding looks for hit pairs and triplets on consecutive tracker layers or, to
account for hit reconstruction and detector acceptance inefficiencies, layers with only another
layer with no hits in between. Pairs and triplets have to be compatible with tracks coming
from the beam interaction region and with a minimum pT value. By default, both the
innermost pixel and strip layers are considered: even if the track density is higher in the
inner tracker layers, the pixel hits are particularly useful since their high granularity leads
to low occupancy and they provide a 3-D measurement; strip hits, instead, are useful to
maximize the seeding efficiency at large η thanks to the bigger geometrical acceptance of the
strip detector.
The pattern recognition proceeds iteratively starting from the track parameter estimate
on the seed layer and including the information of the successive detection layers one by one.
First, the layers which are compatible with the initial seed trajectory are determined. The
trajectory is then extrapolated to these layers, accounting for magnetic field, multiple scattering and energy loss in the traversed material. Several hits on the new layer may be compatible
with the predicted trajectory, and thus one new trajectory candidate per compatible hit is
created. In addition, one further trajectory candidate is created, without any reconstructed
hit in that layer, but with a fake hit, called invalid hit, used to account for the material effects
in a layer where the track has fired no hits. Each trajectory is then updated with the corresponding hit according to the Kalman filter formalism by combining the predicted trajectory
parameters and the hit measurement as a weighted mean. This procedure is repeated until
the outermost layer of the tracker is reached.
Several parameters are tunable to properly configure the CKF algorithm; for example,
the maximum number of candidates that are propagated at each step, the maximum number
of invalid hits and the minimum transverse momentum.
17
(a)
(b)
Figure 2.1: Schematic view of the CKF seeding with hit pairs(a): considering two inner
tracker layer, starting from a hit in the outer layer, hits in a φ window corresponding to
a minimum pT and compatible with the beam spot are searched for in the inner layer.
Schematic view of the CKF pattern recognition(b): starting from the seed estimate, the
compatible hits are iteratively processed, each leading to trajectory candidate. The candidate
on the left is stopped because no more compatible hits are found, the one on the right is
stopped because, after adding the last hit, its χ2 is too high. Red dots are compatible
measurements, black are not compatible.
18
The default CKF behavior is optimized to reconstruct tracks in collision events. In order
to be able to reconstruct also cosmic tracks during commissioning runs, a customized version
of it has been implemented. In particular, this adapted algorithm makes use of seeding from
outer top layer (global y coordinate > 0) and of loose cuts on the number of invalid hits per
track.
2.4
Road Search
Road Search (RS) is the other general purpose tracking algorithm in CMS. The algorithm
treats the CMS tracker in terms of rings, where a ring contains all tracker modules at a given
r − z position, spanning 360 degrees in phi. Its approach differs from CKF since the seeding
step: in this case, the seed hits are not searched for in consecutive layers, but in the inner
and in the outer rings of the strip detector.
The pattern recognition is based on a predetermined set of roads, which are lines in
the r − z plane consistent with the trajectory of particles from the beam spot. The roads
connecting the seed hits are considered and all the hits along the road are collected in a
cloud. Then, starting from the low occupancy layers, the most compatible hits in the cloud
are selected.
(a)
(b)
Figure 2.2: Schematic view of the RS seeding regions(a): inner (red) and outer (blue)
rings. Schematic representation of the Road Search algorithm(b): in (a) a trajectory is
drawn through the two circled seed hits. All hits within a window around the trajectory
(shaded region) are collected in the cloud. In (b) a new trajectory is built inside-out using
only hits on the low occupancy layers of the cloud, resulting in the fitted trajectory in (c).
This trajectory is extrapolated back to the innermost layer and then hits on the higher
occupancy layers are tested (d). The best hit on each layer is used to yield the fitted track
(e).
The RS algorithm has been also customized for cosmic ray tracking. By construction, RS
reconstructs tracks in one half only (top or bottom) of the tracker; a cosmic muon may cross
the two tracker halves and lead to two different RS tracks: these two tracks are merged into
a single track if they match.
19
2.5
Cosmic Track Finder
The Cosmic Track Finder (CosmicTF) is an algorithm specialized for the reconstruction of
cosmic ray tracks. It is designed to work for low hit multiplicity and single track events.
All pair of hits (triplets in case of cosmic run with magnetic field) in the outer tracker
layers (both with y < 0 and y > 0) are considered as seeds, each corresponding to a trajectory
candidate.
The trajectory candidate is iteratively propagated to every hit in the tracker according to
their order with respect to the vertical (y) direction. If a hit is compatible, then it is added
to the trajectory. Once all the hits have been considered, the final fit is performed on the
trajectory candidate.
(a)
(b)
Figure 2.3: Schematic view of the CosmicTF seeding(a): all the hit pairs in the outer
tracker layer are seeds; in the example the outer bottom pair is the seed. Schematic view of
the CosmicTF pattern recognition(b):the hits are sorted in the y direction, the compatible
ones (red) are added to the trajectory, while the not compatible ones (green) are disregarded.
After all seeds have been processed, the found tracks are analyzed and only the best track
is kept according to the highest number of crossed layers, the highest number of hits and the
lowest track χ2 .
2.6
The Final Track Fit
The final fit represents the first commitment for this thesis work. The initial task was the
porting from the old CMS reconstruction software framework (ORCA [20]) to the new one
(CMSSW [19]); afterwards it converted into the maintenance of this code and the development
of new features related to the final fit.
The final fit is based on the Kalman filtering technique and is the last step, common
to all the CMS tracking algorithms, of the track reconstruction process, providing the most
accurate measurement of the track parameters after the seeding and the pattern recognition
procedures.
For each trajectory, the pattern recognition step results in a collection of hits and an
estimate of the track parameters. At this stage, the determination of the track parameters is
still not optimal since it is accurate only at the last hit of the trajectory and since the estimate
20
can be biased by constraints applied during the seeding stage. Therefore the trajectory is
refitted using a least-squares approach, implemented as a combination of a standard Kalman
filter and smoother.
The final fit starts on the first seed hit layer, usually the innermost, with the estimate of
the track parameters obtained during the pattern recognition. The corresponding covariance
matrix is scaled by a large factor in order to avoid any bias.
This estimate is updated with the measurement provided by the first hit. The trajectory
is then propagated (outwards in the case of inner seeding) to the next hit surface, taking into
account both the energy loss and the multiple scattering. For each valid hit, the position
estimate is re-evaluated using the current values of the track parameters: the information on
the incidence angle increases the precision of the measurement especially in the pixel modules.
The predicted track parameters on this surface and their covariance matrix are updated with
the hit measurement. This sequence is repeated until the last hit has been reached.
At this point, a new Kalman filter fit (called smoothing) is initialized with the result of
the first one - except for the covariance matrix, which is scaled by a large factor - and is
performed in the opposite direction. During the smoothing, for each hit, seven different track
parameter estimates are available:
• Forward predicted state: track parameter estimate obtained during the first fit
propagating the information from the first (n − 1) hits on the n-th hit surface.
• Backward predicted state: track parameter estimate obtained during the smoothing
step propagating the information from the last (N − n + 1) hits on the n-th hit surface.
• Combined predicted state: weighted mean combination of forward and backward
predicted states. This is most precise estimate of the track parameters on the n-th hit
surface without taking into account the n-th hit measurement.
• Forward updated state: estimate obtained updating the forward predicted state
with the hit measurement.
• Backward updated state: estimate obtained updating the backward predicted state
with the hit measurement.
• Combined forward updated state: weighted mean combination of forward updated
and backward predicted states.
• Combined backward updated state: weighted mean combination of backward updated and forward predicted states.
The hit position is re-evaluated using the combined predicted state, thus leading to the best
hit position estimate. In addition, a hit χ2 , evaluating the compatibility of the hit position
with the predicted state position, can be computed between the hit measurement and the
combined predicted state.
This filtering and smoothing procedure yields optimal estimates of the parameters at the
surface associated with each hit and, specially, at the first and the last hit of the trajectory.
Estimates on other surfaces, are then derived by extrapolation from the closest hit. In
particular, an extrapolation of the track parameters from the innermost hit to the point of
closest approach to the beam line is performed in order to evaluate them according to the
track definition (§2.2).
21
2.6.1
Track Refitting
Some use cases require performing a new final fit over already reconstructed Tracks to reevaluate the track parameters after some conditions have changed, but without performing
the whole track reconstruction sequence again. The most typical example are alignment
studies, where tracks are refitted after modifying the geometry of detectors.
The only difference between a “standard” final fit and a refit is the initial evaluation of
the track parameters. The pattern recognition output is a TrackCandidate object, which
stores a starting trajectory state on the surface of the first hit; this estimate has enlarged
track parameter errors in order to unbias the fit. A reconstructed track, instead, loses this
information. Therefore, a new starting state is built propagating the track parameters, defined
at the point of closest approach to the beam line, to the surface of the first hit and then
rescaling errors. This new state is very close to the TrackCandidate one: in fact, running the
Refitter with the same conditions (e.g. same geometry) of the first final fit the differences
between any parameter of the produced Tracks are orders of magnitude smaller than the
estimated errors on that parameter.
Refitting with Constraints
The possibility to refit a track using additional constraints is very important in many situations: for example it can be used to set the momentum of the track in such cases when the
refitted hits are too few to properly determine it. Other application could be a beam-spot or
generic vertex constraint. Therefore, the possibility to add constraints to the track refitter
has been provided. An important feature of this implementation is that it does not simply
add the constraint at the end of the fit, but it takes into account the constraint as an additional ordinary hit: in this way all the measurement points are affected by the presence of
the constraining hit.
The main idea is that the constraint is a new kind of hit with user defined values of
parameters and associated errors. At the moment there are 2 different kind of constraints
that can be applied:
• the momentum magnitude constraint
• the vertex constraint.
The user has to specify the constraint to apply by producing an association map between
the track to be refitted and the constraint to be applied. Once this map is provided to the
refitter, it finds the correct position in the hit vector for the constraining hit, computes a
proper starting state and then performs a new final fit in the usual way. This approach
is optimal because, as the constraints are completely defined by the user, it provides the
maximum flexibility.
22
Chapter 3
Tracking Validation Tools in
CMSSW
3.1
Overview
Goal of the CMS Track Validation Tool is to provide an official evaluation of the tracking performance. For this purpose, an analysis program has been written that, given the collections
of reconstructed and simulated tracks in the event, provides a set of plots which summarizes
the performance of track reconstruction. A set of macros compares the histograms produced
by the validation tool on different samples, with different reconstruction algorithms or with
different releases. A comparison of the tracking performance under different conditions is
very useful to monitor it for every new software release and evaluate the impact of new reconstruction algorithms on track reconstruction.
The Track Validation Tool is composed by three elements:
• Track Associators: they are used in order to establish if a reconstructed track matches
a simulated track. The association is performed according to different criteria that can
be divided in methods that compare the parameters of reconstructed and simulated
tracks (association by χ2 ) or check the provenance of the track hits (association by
hits). Two kinds of association are possible: the association of reconstructed to simulated tracks (RecoToSim) and the association of simulated to reconstructed tracks
(SimToReco). RecoToSim and SimToReco may have different association requests.
• Track Filters: the input collection can be selected with three different filters: a
reconstructed track filter and two simulated track filters, one for efficiency and one for
the fake rate studies. The filter for the reconstructed tracks can be used to study tracks
with a particular topology, a particular pT or according to the tracking algorithm and
the quality label used. The default cuts are reported in Table 3.1: in this case, all the
other cuts are dummy because the request for High Purity tracks is already a severe
selection. For the evaluation of the efficiency the filter has to select the simulated tracks
which are expected to be reconstructed by the tracking algorithm under test. As an
example, the filter cuts for the default CMS tracking are reported in Table 3.2. For the
fake rate estimate, instead, the simulated track collection does not need to pass severe
cuts, so the cuts used for the efficiency are loosened or no filter at all is applied.
23
• MultiTrackValidator: it is the analysis program itself. The analysis performed in
the MultiTrackValidator is divided in four steps.
First, the track collections are selected with the dedicated filters. They apply the selection cuts either before or during the MultiTrackValidator program execution.
The second step consists in the association of the reconstructed and simulated tracks
(in case the association map is not already provided as external input). For each specified track associator, the SimToReco association is performed between the collection of
simulated tracks, filtered for efficiency studies, and the reconstructed tracks, while the
RecoToSim is performed between the reconstructed and the simulated tracks for fake
rate studies.
Then, for each simulated track selected for the efficiency studies the SimToReco association map is scanned looking for the matching reconstructed track: the efficiency is
computed as the number of matched tracks divided by the number of simulated tracks
per (η, pT or number of hits) bin.
Finally, for every reconstructed track in the input collection, the RecoToSim association
map is scanned looking for the matching simulated track: the fake rate is computed as
the number of matched tracks divided by the number of reconstructed tracks per bin.
In addition, when a reconstructed track is associated to a simulated one, their parameters are compared, providing the input for residue distribution plots. The resolutions
are computed by fitting each x axis bin of the residue vs (η, pT or number of hits) 2D
plots with a Gaussian function and filling new 1D histograms, defined with the same x
axis binning, with the corresponding fit width.
Table 3.1: Default selection cuts for the reco::Tracks.
algorithm
any
η
−5 < η < 5
quality
High Purity
pT
> 0.1 GeV
χ2
< 104
dxy
< 120 cm
n hits
≥3
dz
< 300 cm
Table 3.2: Default selection cuts for the TrackingParticles used for efficiency studies. Only
signal means that the TrackingParticle is not from a pile-up event and V is the particle
production point.
only signal
true
η
−2.4 < η < 2.4
q 6= 0
true
pT
> 0.9 GeV
particle type
all
Vxy
< 3.5 cm
n hits
≥0
Vz
< 30 cm
In this chapter, the tracking performance with simulated data are first reviewed, and then,
the details about the implementation of the track associators and the validation program are
presented.
24
3.2
Tracking Performance with Simulated Data
For each new software release, a set of reference samples is produced to monitor the reconstruction performance with that release (RelVal samples). Every time new RelVal samples are
available, the CMS tracking group uses the MultiTrackValidator program to analyze them,
thus book-keeping the tracking performance with respect to the new software and algorithmic
developments and providing and “official” estimate of the expected tracking performance for
various kind of events.
The most important variables and distributions, taken as benchmark for the tracking
performance, are here introduced and discussed. In Fig. 3.1, the efficiency for particle gun
events is presented: for single muons the efficiency is close to 100% over the whole Tracker
acceptance range, while, because of nuclear interactions, about 10% of single pions yield too
few tracker measurements and thus can’t be reconstructed.
efficiency vs η
efficiency vs η
1
1
0.95
0.95
0.9
0.9
0.85
0.85
0.8
0.8
µ pt=1 GeV
µ pt=10 GeV
µ pt=100 GeV
0.75
0.7
-2.5
-2
-1.5
-1
-0.5
0
(a)
0.5
1
1.5
0.75
2
2.5
η
0.7
-2.5
-2
-1.5
-1
-0.5
0
π pt=1 GeV
π pt=10 GeV
π pt=100 GeV
0.5
1
1.5
2
2.5
η
(b)
Figure 3.1: Single particle gun events efficiency: muons(a) and pions(b).
The track parameter resolutions for single muon events are reported in Fig. 3.2. In
the central region, the pT resolution (Fig. 3.2(e)) is better than 1% for single muons with
pT ≤ 10 GeV , while for large |η| values it worsens because of material effects, reduced lever
arm and lower hit resolution. The resolution on the transverse (Fig. 3.2(a)) and longitudinal
(Fig. 3.2(b)) impact parameter is at the level of or below a few tens of µm for pT ≥ 10 GeV .
The efficiency and fake rate for tt̄ events without and with low luminosity pile-up are
reported in Fig. 3.3. The efficiency vs η (Fig. 3.3(a)) is consistent with that obtained for single
pion events (Fig. 3.1(b)) and is about 90%, while the fake rate is below 5% (Fig. 3.3(b)).
The effect of low luminosity pile-up on the efficiency leads to a small reduction, while it
increases the fake rate of about a factor two. Most inefficiencies and fakes are due to wrongly
reconstructed low momentum tracks (Fig. 3.3(c) and (d)) and tracks with a small number of
hits (Fig. 3.3(e) and (f)).
Summarizing, the expected performance of CMS tracking is characterized by a high efficiency (above 99% for single muons, around 90% for tt̄ events), a low fake rate (smaller
than 10% in tt̄ events with low luminosity pile-up) and great precision in the track parameter
measurement (impact parameter resolution smaller than 10 µm at high momenta and pT
resolution at the order of 1%).
25
σ(δ dxy) vs η
σ(δ dz) vs η
µ pt=1 GeV
µ pt=10 GeV
µ pt=100 GeV
σ(∆dz)[µ m]
σ(∆dxy)[µ m]
µ pt=1 GeV
µ pt=10 GeV
µ pt=100 GeV
103
2
10
102
10
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σ(δ cot(θ)) vs η
µ pt=1 GeV
µ pt=10 GeV
µ pt=100 GeV
µ pt=1 GeV
µ pt=10 GeV
µ pt=100 GeV
-3
10
σ(∆cot(θ))[10 ]
σ(∆φ)[mrad]
0
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σ(δp /p ) vs η
t
T
T
σ(∆p /p )[%]
t
10
1
µ pt=1 GeV
µ pt=10 GeV
µ pt=100 GeV
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
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(e)
Figure 3.2: Resolution of track parameters for single muon events with pT = 1, 10, 100 GeV :
dxy(a), dz(b), φ(c), cot θ(d) and pT (e).
26
efficiency vs η
fake rate vs η
0.5
tt, no PileUp
1
0.45
tt, LowLumi PileUp
0.4
0.95
0.35
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0.3
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fake rate vs pT
0.5
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p [GeV]
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T
(c)
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effic vs hit
fake rate vs hit
0.8
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0.9
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0.6
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5
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(e)
20
25
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35
number of hits
0
0
5
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15
20
25
30
35
number of hits
(f)
Figure 3.3: Validation plots for tt̄ events without and with low luminosity pile-up for high
purity tracks with pT > 0.9 GeV : efficiency and fake rate vs η(a)-(b), vs pT (c)-(d) and vs
number of hits(e)-(f)
27
3.3
Implementation
3.3.1
Track Associators
In order to evaluate the performance of tracking algorithms, it is necessary to define if a
reconstructed track is produced by the passage of a charged particle trough the tracker
detector or it is due to a combinatorial effect of randomly positioned hits (fake track ). For
simulated data this task corresponds to check if a reconstructed track is associated to a
simulated track.
Within the CMS software framework, the association between a reconstructed track
(reco::Track ) and a simulated track object (TrackingParticle) is performed by the TrackAssociators. In the base track associator class (TrackAssociatorBase), two pure virtual method
are defined:
• associateRecoToSim: associates reco::Tracks to TrackingParticles, returning a RecoToSimCollection.
• associateSimToReco: associates TrackingParticles to reco::Tracks, returning a SimToRecoCollection.
For each reco::Track (TrackingParticle), the RecoToSimCollection (SimToRecoCollection)
association map stores the vector of associated TrackingParticles (reco::Tracks) and the quality of the association. The vector is ordered from the element with the best quality to the
element with the worst.
The association methods are implemented with a general interface such that any concrete
track object that inherits from reco::Track (e.g. reco::GsfTrack ) can be used in the association
methods1 .
Concrete track associator classes has to implement these methods.
TrackAssociatorByHits
The TrackAssociatorByHits associates reco::Tracks and TrackingParticles on the basis of the
number of hits they share. Thus, it basically checks that the hits found during the pattern
recognition correspond to a unique simulated track.
The hit level association is performed by the TrackerHitAssociator. Given a reconstructed
hit, it provides the vector of simulated hits that merged into the reconstructed hit and the
ids of the simulated tracks that fired the simulated hits. Within this context, a simulated hit
is defined by the entry point of the simulated track in the detector, the energy loss by the
particle, its id, its particle type and the process that generated it. The number of hits shared
between a reco::Track and a TrackingParticle correspond to the number of reconstructed hits
from that track which, according to the TrackerHitAssociator, are associated to the id of that
TrackingParticle.
The TrackAssociatorByHits is a configurable object that can be adapted to any usecase by changing the configuration file parameters. These parameters can be grouped into
two categories: the parameters tuning the association criteria and those specifying how the
number of simulated hits is computed.
The first set of parameters are:
1
This is accomplished by defining two version for the association methods, one that takes as input an
edm::Handle<edm::View<reco::Track> > and an edm::Handle<TrackingParticleCollection>, the other taking
an edm::RefToBaseVector<reco::Track> and an edm::RefVector<TrackingParticleCollection>.
28
• AbsoluteNumberOfHits: false (default) means that the association quality is the
fraction of hits shared, true means that the association quality is the absolute number
of shared hits.
• Purity SimToReco: Purity cut for SimToReco association. The purity is defined as
the number of shared hits divided by the number of TrackingParticle hits. The default
value is 0.75.
• Quality SimToReco: Quality cut for SimToReco association. If AbsoluteNumberOfHits
is false, the quality is defined as the number of shared hits divided by the number of
TrackingParticle hits (default value 0.5) and a TrackingParticle is associated if the quality is greater than Quality SimToReco and the purity is greater than Purity SimToReco.
If AbsoluteNumberOfHits is true the quality is defined as the number of shared hits,
the purity cut has no effect and a TrackingParticle is associated if the quality is greater
than Quality SimToReco.
• Cut RecoToSim: Quality cut for RecoToSim association (default value 0.75). The
value of RecoToSim quality is defined as the number of shared hits divided by the number of TrackingParticle hits, the same as SimToReco purity. A reco::Track is associated
if the quality is greater than Cut RecoToSim.
• SimToRecoDenominator: by default, for the SimToReco association the minimum
fraction is defined as the number of shared hits divided by the number of TrackingParticle hits (SimToRecoDenominator = ”sim”). If SimToRecoDenominator = ”reco”, the
fraction is defined as the number of shared hits divided by the number of reco::Track
hits.
The track reconstruction algorithms have been designed as flexible, easily configurable
processes: in particular, several of the available features lead to different number and type
of reconstructed hits per track. Therefore, in order to correctly compute the number of
TrackingParticle hits expected to be reconstructed by any tracking configuration, the TrackAssociatorByHits has to account for all these options and provide a complete set of parameters
to handle them:
• UseGrouped: during the track pattern recognition two different behaviors are possible: consider at most one hit per tracker layer (TrajectoryBuilder ) or all the hits in
case of overlapping layers (GroupedTrajectoryBuilder, default). If UseGrouped is true,
the number of TrackingParticle hits is computed counting all its simulated hits in the
tracker, if it is false, only one simulated hit per layer is computed,.
• UseSplitting: for timing purposes, during the pattern recognition the hits in the
double sided strip layer are merged into one matched hit. Before the final fit, these
hits can be again splitted in the two (mono and stereo) contributions (default). If
UseSplitting is false, only one simulated hit in the double sided strip layers counts for
the number of TrackingParticle hits; if true, both mono and stereo hits contribute.
• UsePixels: the track reconstruction can optionally be performed considering only strip
hits (pixel-less tracking). If UsePixels is true the pixel hits are counted for the number
of TrackingParticle hits, if false they are not.
29
• ThreeHitTracksAreSpecial: if true (default) the tracks with a number of hits equal
to three are associated only if all their hits are shared with the correct TrackingParticle.
TrackAssociatorByChi2
The TrackAssociatorByChi2 associates tracks and TrackingParticles on the basis of the χ2
(per degree of freedom) computed between the track parameters of the reco::Track and those
of the TrackingParticle. If the χ2 value is below the cut value they are associated. The
TrackAssociatorByChi2 essentially evaluates the compatibility of the reconstructed track parameters with the simulated ones and provides an estimate of the reconstructed track quality.
The χ2 is stored in the association map as −χ2 because the association map is sorted for
decreasing association quality values: in this way the first element in the map is still the one
with the best quality, i.e. the lowest χ2 .
The following settings can be specified via configuration file:
• chi2cut: value of the applied cut (default=25).
• onlyDiagonal: false by default. Turn it to true to use only the diagonal terms of the
track parameters covariance matrix.
• beamSpot: name of the module that produced the BeamSpot (default: offlineBeamSpot).
The BeamSpot is needed by the TrackAssociatorByChi2 because the TrackingParticle
contains the information about the position and the momentum at the point where the particle
is created, while the reconstructed track parameter are defined at the point of closest approach
to the beam line. Thus, the BeamSpot is used for the propagation of the TrackingParticle
parameters from the production point to the point of closest approach to the beam line (note
that a similar propagation is used also in TrackProducer, see §2.6).
Seed Association
In order to allow for performance studies of the first two steps of the track reconstruction
process, seeding and pattern recognition, the TrackAssociatorBase class allows also the association of TrajectorySeeds and TrackCandidates to TrackingParticles: it defines the corresponding association maps and the associateSimToReco (RecoToSim) methods. These methods have dummy virtual implementations in the TrackAssociatorBase class, so the concrete
TrackAssociators can implement their own TrajectorySeed or TrackCandidate association.
At the moment, only the TrackAssociatorByHits implements the seed association.
The association algorithm is the same as in the track association, with only the following
differences:
• The input and output collections, which accounts for TrajectorySeeds instead of reco::Tracks.
• Not only the RecoToSim, but also the SimToReco association fraction is always defined
as the number of shared hits divided by number of reconstructed track hits.
• No request is made on the purity.
Note that, as the seeds have two or three hits, the default settings (AbsoluteNumberOfHits
= false, MinHitCut = 0.5, ThreeHitTracksAreSpecial = true) allow the association only if
100% of the seed hits are shared with the same TrackingParticle.
30
3.3.2
Track Validation
The MultiTrackValidator analysis program is fully configurable as it allows for the choice of
the input collection, of the track associator to be used and of several other options.
As the TrackAssociators, also the Track Validation Tool makes use of an interface that
allows to take as input for the validation not only the standard reco::Tracks, but also the
electron reco::GsfTracks.
MultiTrackValidator takes as input one or more .root files containing previously reconstructed tracks and produces an output file containing the plots. The main configurable
parameters of the MultiTrackValidator are:
• label, label tp effic and label tp fake are the names of the of input collections. The
first is the vector of the reconstructed track collections to analyze, the others are the
collection of TrackingParticles used for efficiency studies and for the fake rate evaluation
respectively.
• beamSpot is the module that produced the beam spot which the track parameters are
referred to.
• UseAssociators is a flag to control how the association between reco::Track and TrackingParticles is performed. If the association has already been done, and the association
map is already stored in the input file UseAssociators has to be set to false, otherwise,
to perform a new association during the validation process, it has to be set to true.
• associatormap is the name of the module that produced the association map stored
in the input file.
• TrackingParticleSelectionForEfficiency is a filter used to select the TrackingParticles for the evaluation of tracking efficiency in case UseAssociators is false.
• associators is the list of the associators to be used.
• min and max is the pseudorapidity range you want to explore while nint is the number
of intervals you want to divide it in, minpT, maxpT, nintpT and minHit, maxHit,nintHit are the same of min, max, nint but for studies vs pT and vs the number
of hits.
• useFabsEta is a flag to fill plots vs the absolute value of pseudorapidity of vs the
signed value.
• useInvPt is a flag to fill plots vs the inverse of the transverse momentum.
• outputFile is the name of the output file containing the performance histograms.
As many different track collections can be processed with different track associators during
the same program execution, in order to separate the plots corresponding to each case, the
output file is organized as follows: several directories are created according to the names in
the label and in the associators configuration file vector parameters. Every directory contains
the same set of histograms, but filled using a different track collection and a different track
associator. For example, a directory named general AssociatorByHits contains the validation
plots obtained with the default CMS track collection, labeled as “generalTracks”, and the
TrackAssociatorByHits.
The plots created by the validation tool can be grouped into different categories:
31
• Global tracking performances:
– Number of associated and fake reconstructed tracks per event.
– Number of total reco::Tracks, of associated tracks (simToReco and recoToSim)
and of simulated tracks vs η, vs pT and vs number of hits.
– Efficiency vs η, vs pT and vs number of hits.
– Fake rate vs η, vs pT and vs number of hits.
– Number of reconstructed vs number of simulated tracks (2D plot).
• Number of hits, χ2 and charge distributions:
– Track χ2 /ndof and χ2 /ndof probability distributions.
– Average track χ2 /ndof vs η and χ2 /ndof vs η 2D plot.
– Number of valid and lost hit per track total distributions and vs η.
– Track χ2 /ndof vs number of hits, number of valid hits vs η and number of lost
hits vs η (2D plots).
– Track charge distribution.
• Pulls and residues:
– η residue.
– Pull plots of track pT and θ, φ, dxy, dz and q/p parameters.
– Average width of Gaussian fits to the track parameter pull plots vs η.
– Width of Gaussian fits to the track parameter pull plots vs η (2D plots).
– Average ∆pT /pT vs η.
• Resolution of track parameters:
– Average width of Gaussian fits to ∆η, ∆pT /pT , ∆ cot θ, ∆φ, ∆dxy and ∆dz
distributions vs η and vs pT .
– ∆η, ∆pT /pT , ∆ cot θ, ∆φ, ∆dxy and ∆dz distributions vs η and vs pT (2D plots).
• Track association:
– Fraction of shared hits and number of shared hits distributions (TrackAssociatorByHits only)
– Track association χ2 and probability of association χ2 distributions (TrackAssociatorByChi2 only)
• cross checking with simulation:
– pT and η distributions of simulated tracks.
– Number of simulated tracks per event.
– Transverse position of production vertices of simulated tracks.
32
Seed Validation
The TrackerSeedValidator is a tool that produces a set of histograms useful to test, validate
and debug the track seeds. The seed validator probes the seeding performance by comparing
every TrajectorySeed with the corresponding TrackingParticle. TrajectorySeeds are matched
to TrackingParticles using the seed association provided by the TrackAssociatorByHits.
The evaluation of the efficiency and the purity at the seeding level is very important since
most of the fake reconstructed tracks correspond to badly reconstructed seeds, and because
a high number of fake or duplicated seeds heavily degrades the global timing of the track
reconstruction process.
The TrackerSeedValidator is a branch that originates from the MultiTrackValidator. They
inherits from the same base class (MultiTrackValidatorBase), where the common functionalities are stored.
A seed object is mainly constituted by a vector of reconstructed hits (two or three) and
a rough estimate of the track parameters on the surface of the outermost hit. In order to
compare the seed track parameters and the TrackingParticle ones, also the seed parameters
are propagated to the point of closest approach to the beam line.
The TrackerSeedValidator works in the same way as the MultiTrackValidator. The only
difference is that the parameter label refers to the module that produced the seeds2 .
The output file of the SeedValidator has the same features as the MultiTrackValidator,
except the fact that the distributions refer to the the seeds instead of the tracks and that the
resolution plots are not produced as they are not meaningful in this case.
2
Actually, in the case of the TrajectorySeedValidator, an extra parameter, called TTRHBuilder, is added.
It defines the component name of the TransientTrackingrecHitBuilder to be used in the TrackerSeedValidator.
The default values of this parameter is: ”WithTrackAngle”.
33
Chapter 4
Outlier Rejection in the Final Track
Fit
As discussed in §3.2, tracking in CMS has excellent performance, characterized by high efficiency, purity and resolutions.
Nevertheless, the quality of some tracks can be improved: the pulls (defined as residuals
divided by their errors) of the track parameters show long non Gaussian tails. In other
words, sometimes the reconstructed tracks have parameters significantly different from the
corresponding simulated ones. This can happen for several reasons: the track can include
noise hits, hits belonging to another track or hits generated by δ rays or by other complex
processes. Such hits worsen the quality of reconstructed tracks because they provide an
incorrect or an inaccurate measurement. These hits are likely to give a large χ2 during the
final fit: if they were rejected and the fit repeated, the quality of the tracks would improve [13].
The Outlier Rejection algorithm [21] is intended to remove from the final fit the hits with
a large χ2 . The algorithm is designed to fulfill the following criteria:
• Do not worsen the tracking efficiency.
• Decrease the fake rate.
• Improve as much as possible the quality of the tracks.
• Keep the CPU time at a reasonable level.
4.1
Implementation of the Algorithm
The Outlier Rejection is performed during the Final Track Fit (§2.6). The final fit is the last
element of the track reconstruction process and is common to all the tracking algorithms in
CMS; therefore the Outlier Rejection can be used by all the algorithms.
The Outlier Rejection algorithm makes use of the hit χ2 , defined as the χ2 deviation
between the hit position and the combined track state on the hit surface. The combined
state is the weighted mean of the forward and backward predicted states: it is the best
estimate of the track parameters without taking into account the hit that is being processed.
The algorithm works as follows. After the smoothing step, the resulting track is analyzed.
If there is at least one hit that has a χ2 greater than a χ2 threshold, then the hit with
the largest χ2 is removed and the final fit is restarted. Technically, the hit is removed
35
substituting it with an invalid hit; by definition it does not provide any measurement, but
takes into account the material effects of the hit layer during the propagation. The procedure
is iterated until one of the following cases is found:
1. No hit has a χ2 above the chosen cut value.
2. The remaining number of hits falls below a minimum number of hits. In this case, the
track is rejected.
During this iteration, if a track has two or more consecutive invalid hits, the hits before the
first of the invalid hit sequence are saved, the others are dismissed. The hit order is given
by the track candidate direction. The motivation for breaking these tracks is to separate a
primary track from its products, which are expected to be reconstructed during later steps
of the iterative tracking (Fig. 4.1).
Figure 4.1: Example of a track that benefit from the breaking after two consecutive invalid
hits are found during Outlier Rejection. The two consecutive invalid hits are caused by the
decay of a primary track into one or more secondary tracks: keeping only the hits before the
first invalid correspond to reconstruct only the primary track.
At the end of this procedure the useless1 invalid hits at the beginning or at the end of
the track are removed.
The cut value on the hit χ2 , the minimum number of remaining hits, and the boolean
values - to switch off and on the breaking of the tracks with consecutive invalid hits and the
cleaning of the invalid hits at the beginning or at the end of the tracks - are parameters that
can be easily set via configuration file. If the χ2 threshold is set to -1, the Outlier Rejection
is switched off.
4.2
Characterization of the Rejected Hits
Hits rejected by the Outlier Rejection algorithm can be classified into five categories: Bad
Hits, Good Hits, δ-ray Hits, Not Shared Hits and Shared Hits. Considering a reconstructed
track, which is not fake according to the TrackAssociatorByHits, a TrackingParticle is associated to it and each hit of the track can be associated to a vector of simulated hits (SimHits)
by means of the hit level associator. The categories above correspond to the following cases:
• Good Hits: only one SimHit is associated to the reconstructed hit and it comes from
the correct simulated track (i.e. the same TrackingParticle associated to the track).
1
Actually invalid hits in the layers between the first hit and the beam line should be introduced to correctly
take into account the material during the propagation to the point of closest approach to the beam line (where
the track parameters are defined), but it’s a general issue valid for all the tracks and not only those with
outliers.
36
• Bad Hits: none of the associated SimHits is from the correct Tracking Particle.
• δ-ray Hits: more than one SimHit is associated and all of them are from the correct
TrackingParticle. All the SimHits (except the first one) are produced by an electron
ionization process.
• Not Shared Hits: also in this case more than one Sim Hit is associated and all of them
are from the correct Tracking Particle but not all are δ rays.
• Shared Hits: more than one Sim Hit is associated, at least one coming from the correct
Tracking Particle and at least one not.
Good Hits are correct and unbiased: they are by far the majority of the hits associated to
non-fake track and, in principle should not be removed. Bad Hits are wrong measurements,
and thus the Outlier Rejection is expected to reject as many as possible. The other three
categories correspond to hits that, even if for different causes, provide biased or imprecise
measurements. The convenience of rejecting them, of course, depends on how much they are
biased with respect to their ideal position.
The hit χ2 distributions for all the categories above are reported in Fig. 4.2. As expected,
Bad Hits have the broadest distribution and the highest mean value, while Good Hits have
the sharpest distribution and the lowest mean value.
As discussed in the next section, the effect of Outlier Rejection is to increase the fraction
of Good Hits and decrease the fraction of Bad Hits, while the other categories are mainly
unaffected. The fraction of hits per tracker layer corresponding to the five categories are
shown in Fig. 4.3 and Fig. 4.4.
All the results reported in this chapter have been obtained with CM SSW 2 0 X releases.
4.3
Impact on Tracking Performance
Tracking performance with Outlier Rejection are studied on various data samples.
4.3.1
Results with tt̄ sample
tt̄ events are characterized by a high multiplicity of tracks (≥ 80 tracks per event), contain jets
of different energy and also isolated tracks; tracks are produced by several types of particles,
like muons, electrons or charged pions. For these reasons, tt̄ events constitute an optimal
test-bed for Outlier Rejection.
Comparing the track collections obtained with and without Outlier Rejection, many differences can be found:
• rejected hits: the same track, reconstructed with a different cut value, differs only for
the rejected outlier hits.
• lost hits: after Outlier Rejection the track loses other hits because of fitting failures or
track breaking for consecutive invalid hits.
• gained hits: the track gains hits because, after Outlier Rejection, the fit does not fail
anymore.
• lost tracks: after Outlier Rejection, the track is not present in the collection anymore.
37
TotChi2Increment
Entries
769161
Mean
2.728
RMS
6.002
All Hits
TotChi2GoodHit
Entries
653690
Mean
2.472
RMS
5.208
Good Hits
30000
104
25000
103
20000
15000
102
10000
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χ2
(b)
TotChi2BadHit
Entries
20246
Mean
9.77
RMS
15.54
Bad Hits
350
δ-ray Hits
TotChi2DeltaHit
Entries
76568
Mean
2.878
RMS
6.528
4000
300
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250
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χ2
(d)
TotChi2NSharedHit
Not Shared Hits
Entries
Mean
RMS
140
3566
4.062
7.836
TotChi2SharedHit
Entries
15091
Mean
4.605
RMS
9.005
Shared Hits
500
120
400
100
80
300
60
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20
0
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100
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0
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χ2
(f)
Figure 4.2: Hit χ2 distributions for the hits in the associated (non-fake) tracks, reconstructed without Outlier Rejection: (a) all hits in the collection, (b) Good Hits, (c) Bad
Hits, (d) δ-ray Hits, (e) Not Shared Hits and (f) Shared Hits (sample used: tt̄, 500 events,
track quality: Pre Filter tracks).
38
(a)
(b)
(c)
Figure 4.3: Fraction of hits per category per tracker layer in the track collection without
Outlier Rejection (blue) and in the collection with χ2 cut = 20 (red): (a) Good Hits, (b)
Bad Hits, (c) δ-ray Hits (sample used: tt̄, 500 events, track quality: Pre Filter tracks).
39
(a)
(b)
Figure 4.4: Fraction of hits per category per tracker layer in the track collection without
Outlier Rejection (blue) and in the collection with χ2 cut = 20 (red): (a) Not Shared Hits,
(b) Shared Hits (sample used: tt̄, 500 events, track quality: Pre Filter tracks).
40
• gained tracks: a track that was not present in the original collection is found in the
collection after Outlier Rejection.
• lost track-association: after Outlier Rejection, a track that was associated is now not
associated.
• gained track-association: a track that was not associated is associated.
To avoid the complication of analyzing how frequently each case happen, the most convenient
approach is to look at the fraction of hits per category and at the number of associated and
fake tracks as a function of the applied χ2 cut.
The effect of Outlier Rejection is to increase the fraction of Good Hits and reduce the
fraction of Bad Hits in the track collection. The hit fractions for the other categories are not
much affected (Tables 4.1, 4.2).
Table 4.1: Fraction of the hit number per category as function of the applied χ2 cut (sample
used: tt̄, 500 events, track quality: Pre Filter tracks).
cut
-1
5
10
15
20
25
30
35
40
45
50
55
60
tot hits
769161
662279
725108
738166
744478
747813
749945
751612
752740
753603
754351
755034
755465
good [%]
85.0
86.7
86.3
86.0
85.9
85.7
85.7
85.6
85.6
85.5
85.5
85.5
85.5
bad [%]
2.6
1.1
1.5
1.7
1.8
1.9
2.0
2.0
2.1
2.1
2.1
2.1
2.1
delta [%]
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
not shared [%]
0.5
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.5
0.5
0.5
0.5
shared [%]
2.0
1.7
1.8
1.9
1.9
1.9
1.9
1.9
1.9
1.9
1.9
1.9
1.9
In the case of Pre Filter tracks, starting from ∼ 102 associated tracks and ∼ 38 fakes
per event for disabled Outlier Rejection and using the TrackAssociatorByHits, the effect of
activating Outlier Rejection is to decrease both the number of associated tracks and the
number of fake track, but the number of fakes decrease 2 − 3 times more than the number
of good tracks (Fig. 4.5). For High Purity tracks, instead, the number of associated tracks
increases for χ2 cut values above 15 and the number of fake tracks decreases for values below
25 (Fig. 4.6). The average number of associated and fake tracks per event for disabled Outlier
Rejection are 84.4 and 0.6 respectively.
The effect of Outlier Rejection on tracking performance can be estimated also using the
standard tracking validation tool for tracks reconstructed with different χ2 cut values.
The plots obtained with Pre Filter tracks are reported in Fig. 4.7. Using the TrackAssociatorByHits, the effect of Outlier Rejection is to reduce both the efficiency (less than 3% for
a cut value of 20) and the fake rate (up to 10% for the same cut). Using the TrackAssociatorByChi2, instead, the efficiency increases of a few percent, showing that the quality of the
41
Table 4.2: Fraction of the hit number per category as function of the applied χ2 cut (sample
used: tt̄, 500 events, track quality: High Purity tracks).
cut
-1
5
10
15
20
25
30
35
40
45
50
55
60
tot hits
710949
628661
693321
706079
711706
714450
715979
716970
717460
717786
717884
718107
718088
good [%]
86.6
87.7
87.2
87.0
86.8
86.7
86.7
86.6
86.6
86.6
86.6
86.6
86.6
bad [%]
1.5
0.7
1.0
1.2
1.3
1.3
1.4
1.4
1.4
1.5
1.5
1.5
1.5
delta [%]
9.8
9.8
9.8
9.8
9.8
9.8
9.8
9.8
9.8
9.8
9.8
9.8
9.8
not shared [%]
0.4
0.3
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
shared [%]
1.8
1.6
1.7
1.7
1.8
1.8
1.8
1.8
1.8
1.8
1.8
1.8
1.8
Figure 4.5: Difference on the number of associated (blue) and fake (red) tracks per event
with respect to the sample without using the Outlier Rejection as a function of the applied
χ2 cut (sample used: tt̄, 500 events, track quality: Pre Filter tracks, associator: TrackAssociatorByHits).
42
Figure 4.6: Difference on the number of associated (blue) and fake (red) tracks per event
with respect to the sample without using the Outlier Rejection as a function of the applied
χ2 cut (sample used: tt̄, 500 events, track quality: High Purity tracks, associator: TrackAssociatorByHits).
reconstructed tracks is improved by Outlier Rejection. The average χ2 /n.d.o.f. is reduced
and becomes more compatible with the expected value of one.
Of course, the effect of Outlier Rejection on High Purity tracks is less striking because
these tracks have already passed very selective quality criteria (Fig. 4.8). Nevertheless, it is
worth noting that the fake rate evaluated with the TrackAssociatorByHits is reduced of about
1% for some η values (χ2 cut equal to 20) and that the χ2 /n.d.o.f. is significantly closer to
one. The improvement in the track quality can be observed by looking at parameter pulls for
the tracks which had at least one hit rejected and were reconstructed both in case of disabled
Outlier Rejection and in case of χ2 cut value equal to 20; for all the track parameters, the
pull plot in case of Outlier Rejection shows a more Gaussian behavior (Fig. 4.9).
Plots mainly unaffected by the Outlier Rejection algorithm are those related to resolutions.
In fact, Outlier Rejection mainly improves the quality of the tracks that populate the tails
of the track parameter pulls and, when resolution values are computed, pulls are fitted with
a Gaussian: its width provides the resolution value and the pull tails have a small impact on
the results of the fit.
The impact of Outlier Rejection on the tracking computing time has also been evaluated.
Considering seeding, pattern recognition, final fit and track collection filtering, for tt̄ events,
the total computing time per event is about 7 sec. The final fit only takes about 2.5-3 sec
per event. Outlier Rejection increases the final fit time of about 20% for a χ2 cut value of 10,
11% for 20 and 4% for 50. Therefore, for a cut value of 20, the impact on the total tracking
computing time is an increase of the order of 5%.
43
efficiency vs η
fake rate vs η
cut=-1
cut=10
cut=20
0.7
cut=30
cut=40
1
0.95
cut=-1
cut=10
cut=20
cut=50
0.6
cut=60
cut=30
cut=40
cut=50
0.9
0.5
cut=60
0.85
0.4
0.8
0.3
0.75
0.7
0.2
0.65
0.1
0.6
0.55
0
0.5
1
1.5
2
0
0
2.5
|η|
0.5
1
(a)
1.5
2
2.5
|η|
1.5
2
2.5
|η|
(b)
efficiency vs η
fake rate vs η
cut=-1
cut=10
cut=20
0.7
cut=30
cut=40
1
0.95
cut=-1
cut=10
cut=20
cut=50
0.6
cut=60
cut=30
cut=40
cut=50
0.9
0.5
cut=60
0.85
0.4
0.8
0.3
0.75
0.7
0.2
0.65
0.1
0.6
0.55
0
0.5
1
1.5
2
0
0
2.5
|η|
0.5
1
(c)
(d)
mean χ2 vs η
cut=-1
cut=10
cut=20
2
cut=30
cut=40
cut=50
1.8
cut=60
1.6
1.4
1.2
1
0.8
0.6
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
2.4
|η|
(e)
Figure 4.7: Impact of the Outlier Rejection algorithm on tracking performance: (a) tracking efficiency evaluated with the TrackAssociatorByHits vs η, (b) fake rate evaluated with
the TrackAssociatorByHits vs η, (c) tracking efficiency evaluated with the TrackAssociatorByChi2 vs η, (d) fake rate evaluated with the TrackAssociatorByChi2 vs η and (e) mean
track χ2 /n.d.o.f. vs η for different χ2 cut values (sample used: tt̄, 500 events, track quality:
Pre Filter tracks).
44
efficiency vs η
fake rate vs η
cut=-1
cut=10
cut=20
1
0.05
cut=30
cut=40
cut=20
cut=30
cut=60
0.95
cut=-1
cut=10
0.045
cut=50
0.9
0.04
cut=40
cut=50
0.035
cut=60
0.03
0.025
0.85
0.02
0.8
0.015
0.01
0.75
0.005
0.7
0
0.5
1
1.5
2
0
0
2.5
|η|
0.5
1
(a)
1.5
2
2.5
|η|
1.5
2
2.5
|η|
(b)
efficiency vs η
fake rate vs η
cut=-1
cut=10
1
cut=20
0.95
cut=50
0.5
cut=30
cut=40
cut=-1
cut=10
0.45
cut=20
cut=30
cut=60
0.4
cut=40
cut=50
0.35
cut=60
0.9
0.85
0.3
0.25
0.8
0.2
0.75
0.15
0.7
0.1
0.65
0.6
0
0.05
0.5
1
1.5
2
0
0
2.5
|η|
0.5
1
(c)
(d)
mean χ2 vs η
cut=-1
cut=10
cut=20
2
cut=30
cut=40
cut=50
1.8
cut=60
1.6
1.4
1.2
1
0.8
0.6
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
2.4
|η|
(e)
Figure 4.8: Impact of the Outlier Rejection algorithm on tracking performance: (a) tracking efficiency evaluated with the TrackAssociatorByHits vs η, (b) fake rate evaluated with
the TrackAssociatorByHits vs η, (c) tracking efficiency evaluated with the TrackAssociatorByChi2 vs η, (d) fake rate evaluated with the TrackAssociatorByChi2 vs η and (e) mean
track χ2 /n.d.o.f. vs η for different χ2 cut values (sample used: tt̄, 500 events, track quality:
High Purity tracks).
45
histoD0Old
dxy pull
Entries
Mean
RMS
Underflow
Overflow
χ 2 / ndf
Constant
Mean
Sigma
250
Entries
Mean
RMS
Underflow
Overflow
χ 2 / ndf
Constant
Mean
Sigma
200
150
2976
0.006216
3.198
15
27
359.5 / 152
183.3 ± 5.2
-0.003285 ± 0.022157
1.121 ± 0.022
histoD0Out
2976
-0.009644
2.205
11
15
309.5 / 105
205.5 ± 5.8
0.00629 ± 0.01996
1.025 ± 0.021
Entries
Mean
RMS
Underflow
Overflow
χ 2 / ndf
Constant
Mean
Sigma
200
150
2976
0.04804
3.682
20
31
421 / 164
212.5 ± 6.1
-0.01182 ± 0.01879
0.9403 ± 0.0191
histoDzOut
2976
-0.07886
2.373
13
18
324.5 / 118
222.3 ± 6.3
0.005479 ± 0.018429
0.9405 ± 0.0192
100
cut=-1
0
-25
Entries
Mean
RMS
Underflow
Overflow
χ 2 / ndf
Constant
Mean
Sigma
250
100
50
histoDzOld
dz pull
cut=-1
50
cut=20
-20
-15
-10
-5
0
5
10
15
cut=20
0
-25
20
25
∆dxy/ σdxy
-20
-15
-10
-5
(a)
0
5
10
15
20
25
∆dz/ σdz
(b)
φ pull
histoPhiOld
Entries
Mean
RMS
Underflow
Overflow
χ 2 / ndf
Constant
Mean
Sigma
220
200
180
Entries
Mean
RMS
Underflow
Overflow
χ 2 / ndf
Constant
Mean
Sigma
160
140
120
2976
0.05271
2.949
3
11
309 / 136
150.6 ± 4.2
-0.002433 ± 0.027295
1.406 ± 0.029
histoPhiOut
2976
-0.02047
2.516
3
11
298.8 / 112
179.4 ± 5.1
-0.00041 ± 0.02296
1.185 ± 0.024
histoThetaOld
θ pull
Entries
Mean
RMS
Underflow
Overflow
χ 2 / ndf
Constant
Mean
Sigma
250
200
Entries
Mean
RMS
Underflow
Overflow
χ 2 / ndf
Constant
Mean
Sigma
150
2976
-0.1061
3
11
10
441.2 / 138
208.2 ± 6.2
-0.003965 ± 0.019238
0.9631 ± 0.0210
histoThetaOut
2976
0.04949
2.449
8
10
336.6 / 117
220.5 ± 6.2
-0.02098 ± 0.01858
0.9487 ± 0.0192
100
100
80
60
cut=-1
40
cut=20
cut=-1
50
cut=20
20
0
-25
-20
-15
-10
-5
0
5
10
15
20
0
-25
25
∆φ/ σφ
-20
-15
-10
-5
(c)
0
5
10
15
20
25
∆θ/ σθ
(d)
histoQoverpOld
q/p pull
Entries
Mean
RMS
Underflow
Overflow
χ 2 / ndf
Constant
Mean
Sigma
2976
0.002719
3.725
7
13
348 / 150
84.71 ± 2.61
-0.0009018 ± 0.0481770
2.457 ± 0.058
histoQoverpOut
Entries
2976
Mean
-0.07974
RMS
2.819
Underflow
6
Overflow
12
χ 2 / ndf
323.4 / 128
Constant
148.6 ± 4.3
Mean
-0.05677 ± 0.02758
Sigma
1.415 ± 0.030
180
160
140
120
100
80
60
40
cut=-1
cut=20
20
0
-25
-20
-15
-10
-5
0
5
10
15
20
25
∆(q/p)/ σq/p
(e)
Figure 4.9: Impact of the Outlier Rejection algorithm on tracking performance: comparison
of the track parameter pulls for the tracks with at least one rejected hit which are present both
in the collection without Outlier Rejection and in the collection with χ2 cut = 20 (sample
used: tt̄, 500 events, track quality: High Purity tracks, associator: TrackAssociatorByHits).
46
4.3.2
Results with 3000 − 3500 GeV QCD jets sample
The performance of the Outlier Rejection algorithm has been also analyzed on a 3000 −
3500 GeV QCD jets sample. A sample of extremely high-energy jets contains many tracks
in a very narrow cone, where the probability for the pattern recognition to select a wrong hit
is high. In this case, the best performance is obtained disabling the trajectory breaking in
case of two consecutive invalid hits because such requirement turns out to be too severe for
this kind of events and would lead to an efficiency loss. Results obtained without trajectory
breaking are reported in Fig. 4.10
Unfortunately the sample has low statistics and thus the uncertainties are large; however,
it seems clear that, mostly in the barrel region, the performance improvement thanks to Outlier Rejection is remarkable: the efficiency increase and the fake rate reduction is at the level
of a few percent both with the TrackAssociatorByHits and with the TrackAssociatorByChi2,
while the average χ2 is significantly closer to one.
4.4
Conclusions
The Outlier Rejection algorithm highly improves the performance of Pre Filter tracks and has
a positive impact also on High Purity tracks. A χ2 cut value in the range [20,35] increases the
efficiency, reduces the fake rate and the number of bad hits in the track collection. Further
developments could take into account some new features of local reconstruction, such as pixel
quality or template fit probability.
47
efficiency vs η
fake rate vs η
cut=-1
cut=10
cut=20
0.7
cut=30
cut=40
1
0.95
cut=-1
cut=10
cut=20
cut=50
0.6
cut=60
cut=30
cut=40
cut=50
0.9
0.5
cut=60
0.85
0.4
0.8
0.3
0.75
0.7
0.2
0.65
0.1
0.6
0.55
0
0.5
1
1.5
2
0
0
2.5
|η|
0.5
1
(a)
1.5
2
2.5
|η|
1.5
2
2.5
|η|
(b)
efficiency vs η
fake rate vs η
cut=-1
cut=10
cut=20
0.7
cut=30
cut=40
1
0.95
cut=-1
cut=10
cut=20
cut=50
0.6
cut=60
cut=30
cut=40
cut=50
0.9
0.5
cut=60
0.85
0.4
0.8
0.3
0.75
0.7
0.2
0.65
0.1
0.6
0.55
0
0.5
1
1.5
2
0
0
2.5
|η|
0.5
1
(c)
(d)
mean χ2 vs η
cut=-1
cut=10
cut=20
2
cut=30
cut=40
cut=50
1.8
cut=60
1.6
1.4
1.2
1
0.8
0.6
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
2.4
|η|
(e)
Figure 4.10: Impact of the Outlier Rejection algorithm on tracking performance: (a) tracking efficiency evaluated with the TrackAssociatorByHits vs η, (b) fake rate evaluated with
the TrackAssociatorByHits vs η, (c) tracking efficiency evaluated with the TrackAssociatorByChi2 vs η, (d) fake rate evaluated with the TrackAssociatorByChi2 vs η and (e) mean
track χ2 /n.d.o.f. vs η for different χ2 cut values (sample used: 3000 − 3500 GeV QCD jets,
100 events, track quality: High Purity tracks).
48
Chapter 5
Tracking Efficiency with Cosmic
Data during Commissioning
The evaluation of the track reconstruction performance on real data is crucial to check the
detector and reconstruction status, measure inefficiencies and understand detector calibration
or alignment problems. The first chance to test the track reconstruction performance with
the full tracker detector occurred during the commissioning phase at P5.
The tracker detector commissioning has been performed in several stages and in different
places for the various parts of the detector.
The integration of the four strip sub-detectors1 has been completed at the Tracker Integration Facility (TIF) at CERN in 2006 and 2007, where, the first runs on cosmic ray data
have been performed as well [22].
2161 modules, ∼ 15% of all the sub-detectors, have been sandwiched between scintillator
counters providing trigger coincidence signal. A 5 cm thick lead plate, placed on top of lower
scintillators, served as shield from tracks with momentum below 200 M eV . For completeness,
a trigger configuration is displayed in Fig. 5.1. During the runs, the operating temperature
was gradually decreased from +15◦ C to −15◦ C. At the TIF, more than 4 million events
were collected and, for the first time in CMS, processed to reconstruct tracks. The total
number of collected tracks is about 2.3M and similar performance results are obtained for
the three tracking algorithms used (CKF, RS, CosmicTF). Many analysis methods have been
developed during the TIF data-taking: as the tracker was the only detector used for these
runs, all these methods are based on the tracker data only. After the TIF operations, in
December 2007, the whole silicon strip detector has been installed at the CMS site.
The barrel pixel detector has been built, assembled and tested at PSI (Zurich), while the
forward pixel detector has been built and assembled at FNAL (Chicago) and later commissioned at the TIF. During the Summer 2008, the pixel detectors have been inserted into the
CMS experiment at P5.
Since then, the commissioning operations of the whole tracker detector with cosmic ray
data has been carried out.
1
The silicon strip modules have been produced in several parts of Europe and of the U.S., then they have
been assembled at CERN (TOB), Italy (TIB and TID)and Germany (TEC).
49
Figure 5.1: Layout of the trigger scintillator position C. The x-y view is shown on the left
side, the r-z view is shown on the right. The straight lines connecting the active areas of the
top and bottom scintillation counters indicate the acceptance region. In the x-y view, the
active TOB modules are shown in contrasting colors while the active TIB area is framed in
black.
5.1
CRUZET
CRUZET, acronym for Cosmic RUn at ZEro Tesla, is the first global run making use of full
CMS detector, trigger and Data Quality Monitor (DQM). The tracker detector joined the
CRUZET3 data-taking (7-14 July 2008) with the strip detector only, and the CRUZET4 (1825 August 2008) with both the strip and pixel detectors. The tracker operated in the same
conditions foreseen for the collision runs: the raw data from the Front-End Driver (FED)
boards are collected and promptly reconstructed; these data are then processed updating
the alignment and calibration constants and finally re-reconstructed making use of the new
conditions.
During these global runs, the tracking algorithms have been used to reconstruct tracks in
the whole tracker detector for the first time. The track parameter distributions from the three
algorithms are consistent with the related expectations. In particular, CosmicTF reconstructs
the highest number of tracks, especially in the end-cap region, while CKF and RS algorithms
have similar behaviors. RS, actually, reconstructs more tracks at dz = −100 cm because it
also uses seeds from the bottom part of the tracker (Fig. 5.2(a)). The η distributions show a
peak due to the presence of the shaft (Fig. 5.2(b)), while the φ distributions have a peak for
vertical tracks at φ = − π2 (Fig. 5.2(c)).
The CRUZET performance [23] has been evaluated using the methods developed at the
TIF for the standalone tracker analyses. New analyses, exploiting data from other detectors,
have also been performed. In particular, the tracking efficiency has been evaluated through
two different methods:
• Efficiency using StandAlone muons. Tracks are reconstructed in the muon chambers and, for those pointing to tracker volume, a matching tracker track is looked for.
• Efficiency using tracker data only. This method, based on the TIF tracking efficiency estimate, is presented in this section.
50
(a)
(b)
(c)
Figure 5.2: Distribution of the reconstructed track parameters dz(a), η(b) and φ(c) for the
three tracking algorithms used to reconstruct cosmic tracks. Some RS tracks are wrongly
reconstructed with φ > 0: for such tracks the φ value has to be corrected as φ = φ − π.
51
5.2
Efficiency Estimate using Tracker Data only
At the TIF only a slice of the strip tracker was installed; thus, the method developed to
evaluate the efficiency there considers two independently reconstructed classes of tracks:
TOB tracks, which are seeded in the outer TOB layers and tracked in the TOB only, and
TIB tracks, seeded in the inner TIB layers and tracked in the TIB only. Two efficiencies
are computed: ǫ(T IB|T OB), the probability to find a matching TIB track for a given TOB
track, and, vice versa, ǫ(T OB|T IB). The match between the two tracks is realized when
∆φ < 5σφ , where σφ is the expected azimuthal angle resolution. Only the events with just
one reconstructed track are considered.
At P5 the full tracker is installed. Therefore, two independent reconstruction processes
can be performed in the top and bottom halves of the tracker. Such approach is interesting
since, at least for the barrel region, the tracks produced by LHC collision will be reconstructed
in one half of the tracker only as well.
The work-flow of this analysis is:
• Reprocess the data to reconstruct the tracks using the hits in only one half of the
tracker.
• Select a high quality reference track.
• Look for a track matching the reference track in the opposite half.
• Evaluate the efficiency.
5.2.1
Track Reconstruction from Top/Bottom Seeds
The tracking algorithms have been customized to allow for cosmic track reconstruction in
a single half of the tracker. Tracks have to be independently reconstructed in the top half
(Top tracks) and bottom half (Bottom tracks). For this purpose, it is necessary to modify
the tracking algorithms (in the version used to reconstruct cosmic ray track, see §2.3-§2.5)
already at the seeding level. The details for each algorithm are the following.
• CKF: the CKF algorithm for cosmic tracks makes use, by default, of seeds in the outer
layers of the tracker top half (global y coordinate > 0), and then searches for other hits
moving downwards along the particle momentum. This is the correct behavior for the
reconstruction of Top tracks. Before the final fit, a filter for the bottom half hits is
added.
An option for using seed hits with y < 0 only is added to allow for the reconstruction of
Bottom tracks. Then tracks are reconstructed in the direction opposite to the particle
momentum. After the pattern recognition, the same filter is applied for hits with y > 0.
• RS: RS seeds have hits both in the top and bottom halves of the tracker. The
Top/Bottom track reconstruction is implemented by selecting the seeds with hits only
in the correct half of the tracker. The option, described in §2.4, which allows for merging the cosmic tracks in the opposite halves, is not needed in this context. The same
CKF hit filter is applied for RS tracks too.
By default, the RS algorithm reconstructs tracks, from the inner layers to the outer,
forcing the track direction to be along the particle momentum: therefore, tracks in the
52
top half, for which inside-out means opposite to momentum, have an incorrect convention for the momentum direction (the true values are φ = φ − π and η = −η). For this
study, the RS code has been modified to reconstruct tracks with the correct direction
in case of top seeding.
• CosmicTF: the CosmicTF is also seeded from both halves of the tracker. Therefore,
only seed hits in one half of the tracker are considered and, in case of bottom seeding,
tracks are reconstructed in the direction opposite to the particle momentum. Instead of
using the hit filter, hits in the other half of the tracker are discarded during the pattern
recognition.
All the three algorithms are now properly customized to reconstruct Top and Bottom tracks
with independent processes and correct momentum direction.
The dz distributions and the RS φ distributions are shown in Fig. 5.3: Top and Bottom
tracks have different dz acceptance regions, and the customized versions of the RS algorithm
always reconstruct the correct φ sign.
The hit position for Top and Bottom tracks are reported in Fig. 5.4-5.6. CKF hits are in
one half of tracker only. CosmicTF and RS hit filters, instead, are not fully efficient; however,
the hit fraction in the other half is negligible.
5.2.2
Analysis Implementation
Two efficiencies can be computed: ǫ(T |B) and ǫ(B|T ), which correspond to the probability
to find a matching Top track for a given reference Bottom track, and vice versa. Clearly,
this method relies on good quality and not fake reference tracks, pointing to the acceptance
region of the other half of the detector. Events with only one track in the reference collection
are considered. The following requests are then applied:
• Nhits ≥ 7
• χ2 /ndof ≤ 10
• Nlay ≥ 5
where Nlay is the number of silicon strip layers crossed by the projection of the track in
the opposite half of the tracker. The layer propagation can actually return more than one
compatible layer; only the first compatible layer per iteration is considered for the Nlay
computation.
Once a reference Top (Bottom) track is found, the Bottom (Top) track collection is probed
looking for a matching track. For this analysis, two tracks match if the difference between
their azimuthal angles is smaller than 0.05 rad.
53
CosmicTF
Entries
973950
Mean
-4.539
RMS
123.7
CosmicTF_Top
Entries
535588
Mean
-2.894
RMS
85.65
CosmicTF_Bot
Entries
542101
Mean
-5.813
RMS
86.3
dz
16000
14000
12000
10000
CKF
Entries
569553
Mean
-0.707
RMS
81.91
CKF_Top
Entries
549991
Mean
-0.8088
RMS
82.77
CKF_Bot
Entries
581177
Mean
-10.16
RMS
89.61
dz
14000
12000
10000
8000
8000
6000
6000
4000
4000
2000
2000
-300
-200
-100
0
100
200
300
dz[cm]
-300
-200
-100
(a)
RS
Entries
566977
Mean
-6.085
RMS
86.68
RS_Top
Entries
400972
Mean
1.462
RMS
78.96
RS_Bot
Entries
413745
Mean
-13.08
RMS
76.7
12000
10000
8000
25000
20000
4000
10000
2000
5000
0
(c)
300
dz[cm]
100
200
300
dz[cm]
RS
Entries
566977
Mean
-1.579
RMS
0.4069
RS_Top
Entries
400972
Mean
-1.586
RMS
0.3854
RS_Bot
Entries
413745
Mean
-1.571
RMS
0.377
30000
15000
-100
200
phi
6000
-200
100
(b)
dz
0
-300
0
0
-3
-2
-1
0
1
2
3
φ[rad]
(d)
Figure 5.3: dz distribution for the reconstruction algorithms in their default configuration
cosmic tracking (blue), for Top (red) and Bottom tracking (green): CosmicTF(a), CKF(b)
and RS(c). φ distribution for the RS algorithm(d).
54
hitsValidPosXYBot
3500
100
y[cm]
y[cm]
hitsValidPosXYTop
3500
100
3000
3000
50
2500
50
2500
2000
2000
0
0
1500
1500
-50
-50
1000
1000
500
500
-100
-100
-100
-50
0
50
100
x[cm]
0
-100
-50
(a)
50
100
x[cm]
35000
100
30000
80
25000
20000
60
z[cm]
hitsValidPosZRBot
120
120
35000
100
30000
80
25000
60
20000
15000
40
15000
40
10000
20
0
0
(b)
hitsValidPosZRTop
z[cm]
0
5000
-100
-50
0
(c)
50
100
r[cm]
0
10000
20
0
5000
-100
-50
0
50
100
r[cm]
0
(d)
Figure 5.4: Hit position in the XY plane for CosmicTF Top (a) and Bottom (b) tracks.
Hit position in the RZ plane for CosmicTF Top (c) and Bottom (d) tracks.
55
hitsValidPosXYBot
y[cm]
y[cm]
hitsValidPosXYTop
100
3500
100
3000
3000
2500
50
50
2500
2000
2000
0
0
1500
-50
1500
-50
1000
1000
500
500
-100
-100
-100
-50
0
50
100
x[cm]
0
-100
-50
(a)
50
100
x[cm]
35000
z[cm]
hitsValidPosZRBot
120
120
35000
100
30000
100
30000
80
25000
80
25000
20000
60
20000
60
15000
40
15000
40
10000
20
0
5000
-100
-50
0
(c)
50
100
r[cm]
0
10000
20
0
5000
-100
-50
0
50
100
r[cm]
(d)
Figure 5.5: Hit position in the XY plane for CKF Top (a) and Bottom (b) tracks. Hit
position in the RZ plane for CKF Top (c) and Bottom (d) tracks.
56
0
(b)
hitsValidPosZRTop
z[cm]
0
0
hitsValidPosXYBot
3000
100
y[cm]
y[cm]
hitsValidPosXYTop
3000
100
2500
2500
50
50
2000
0
2000
0
1500
1000
-50
1500
1000
-50
500
500
-100
-100
-100
-50
0
50
100
x[cm]
0
-100
-50
(a)
50
100
x[cm]
30000
100
z[cm]
hitsValidPosZRBot
120
120
30000
100
25000
25000
80
80
20000
20000
60
15000
40
10000
20
0
0
(b)
hitsValidPosZRTop
z[cm]
0
5000
-100
-50
0
(c)
50
100
r[cm]
0
60
15000
40
10000
20
5000
0
-100
-50
0
50
100
r[cm]
0
(d)
Figure 5.6: Hit position in the XY plane for RS Top (a) and Bottom (b) tracks. Hit
position in the RZ plane for RS Top (c) and Bottom (d) tracks.
57
5.3
Results
This method has been applied both on MC and CRUZET4 data, providing the efficiency plots
as a function of track parameters and applied cuts. The results are reported in Table 5.1,
Fig. 5.7 and Fig. 5.8.
Table 5.1: Top/Bottom and Bottom/Top efficiencies. Values are %.
ǫ(T |B)
ǫ(B|T )
CosmicTF
CRUZET4
89.7 ± 0.4
90.3 ± 0.3
CosmicTF
MC
92.8 ± 1.0
91.9 ± 0.7
CKF
CRUZET4
90.2 ± 0.5
90.8 ± 0.4
CKF
MC
93.3 ± 1.2
92.5 ± 0.9
RS
CRUZET4
86.2 ± 0.4
84.9 ± 0.4
RS
MC
87.3 ± 0.8
87.4 ± 0.8
Measured CRUZET results are essentially consistent with Monte Carlo. Some small
differences remain, which can be explained by a not yet complete commissioning of the
detector. The overall efficiency is ≥ 90% for CosmicTF and CKF and around 85% for RS.
For vertical tracks in the central region of the tracker it can reach values of ≥ 95% and ≥ 90%
respectively.
The dependence on the reference track selection cuts is further investigated (Fig. 5.9). The
efficiency increases, as expected, with the number of hits and layers crossed by the projection
of the reference track, while it decreases for increasing χ2 values. Results are quite stable in
time (Fig. 5.9(d)).
The same method is applied using Top and Bottom Tracks reconstructed with different
algorithms. Results are shown in Fig. 5.10 and Fig. 5.11, proving that the efficiencies are
almost independent on the algorithm used for the reference tracks and thus providing a good
consistency check.
58
∈(B|T) vs φ
∈(B|T) vs η
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0
-3
ckf
ckf-mc
ckf
ckf-mc
cosmic
cosmic-mc
cosmic
cosmic-mc
rs
rs-mc
rs
rs-mc
-2.5
-2
-1.5
0.2
-1
-0.5
0
φ [rad]
0
-1.5
-1
-0.5
(a)
0.5
1
1.5
η
(b)
∈(B|T) vs dxy
∈(B|T) vs dz
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0
-80
0
-60
-40
ckf
ckf-mc
ckf
ckf-mc
cosmic
cosmic-mc
cosmic
cosmic-mc
rs
rs-mc
rs
rs-mc
-20
0
(c)
20
0.2
40
60
80
dxy [cm]
0
-150
-100
-50
0
50
100
150
dz [cm]
(d)
Figure 5.7: ǫ(B|T ) vs azimuthal angle φ(a), pseudorapidity η(b), transverse impact parameter dxy(c) and longitudinal impact parameter dz(d).
59
∈(T|B) vs φ
∈(T|B) vs η
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0
-3
ckf
ckf-mc
ckf
ckf-mc
cosmic
cosmic-mc
cosmic
cosmic-mc
rs
rs-mc
rs
rs-mc
-2.5
-2
-1.5
0.2
-1
-0.5
0
φ [rad]
0
-1.5
-1
-0.5
(a)
0.5
1
1.5
η
(b)
∈(T|B) vs dxy
∈(T|B) vs dz
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0
-80
0
-60
-40
ckf
ckf-mc
ckf
ckf-mc
cosmic
cosmic-mc
cosmic
cosmic-mc
rs
rs-mc
rs
rs-mc
-20
0
(c)
20
0.2
40
60
80
dxy [cm]
0
-150
-100
-50
0
50
100
150
dz [cm]
(d)
Figure 5.8: ǫ(T |B) vs azimuthal angle φ(a), pseudorapidity η(b), transverse impact parameter dxy(c) and longitudinal impact parameter dz(d).
60
∈(T|B) vs N
∈(T|B) vs N
hits
lay
1
1
0.8
0.8
0.6
0.6
0.4
0.4
ckf
ckf
cosmic
0.2
0
cosmic
0.2
rs
6
8
10
12
14
16
18
20
22
24
26
number of hits
rs
0
4
6
8
(a)
12
14
number of layers
(b)
∈(T|B) vs run
∈(T|B) vs χ2
1
1
0.8
0.8
0.6
0.6
0.4
0.4
ckf
ckf
cosmic
0.2
0
0
10
cosmic
0.2
rs
2
4
6
(c)
8
10
track χ2/n.d.o.f.
0
57400
rs
57600
57800
58000
58200
58400
58600
58800
run number
(d)
Figure 5.9: Dependence of ǫ(T |B) on the applied cut for the reference Bottom track selection (number of track hits(a), number of Top layers crossed by the track projection(b), track
χ2 (c)) and dependence on the run number(d).
61
∈(B|T) vs dxy
∈(B|T) vs dxy
1
1
0.8
0.8
0.6
0.6
0.4
0.4
cosmicTop ckfBot
ckf
cosmicTop cosmicBot
cosmic
0.2
0
-80
0.2
rs
-60
-40
-20
0
20
40
60
80
dxy[cm]
0
-80
cosmicTop rsBot
-60
-40
-20
(a)
20
40
60
80
dxy[cm]
(b)
∈(B|T) vs dxy
∈(B|T) vs dxy
1
1
0.8
0.8
0.6
0.6
0.4
0.4
ckfTop ckfBot
ckfTop cosmicBot
ckfTop rsBot
0.2
0
-80
0
-60
-40
-20
0
(c)
20
40
rsTop ckfBot
rsTop cosmicBot
rsTop rsBot
0.2
60
80
dxy[cm]
0
-80
-60
-40
-20
0
20
40
60
80
dxy[cm]
(d)
Figure 5.10: ǫ(B|T ) vs dxy using the same algorithm for Bottom and Top tracks (a) and
reconstructing Top tracks with: CosmicTF (b), CKF (c) and RS (d).
62
∈(T|B) vs dxy
∈(T|B) vs dxy
1
1
0.8
0.8
0.6
0.6
0.4
0.4
ckfTop cosmicBot
ckf
cosmicTop cosmicBot
cosmic
0.2
0
-80
0.2
rs
-60
-40
-20
0
20
40
60
80
dxy[cm]
0
-80
rsTop cosmicBot
-60
-40
-20
(a)
20
40
60
80
dxy[cm]
(b)
∈(T|B) vs dxy
∈(T|B) vs dxy
1
1
0.8
0.8
0.6
0.6
0.4
0.4
ckfTop ckfBot
cosmicTop ckfBot
rsTop ckfBot
0.2
0
-80
0
-60
-40
-20
0
(c)
20
40
ckfTop rsBot
cosmicTop rsBot
rsTop rsBot
0.2
60
80
dxy[cm]
0
-80
-60
-40
-20
0
20
40
60
80
dxy[cm]
(d)
Figure 5.11: ǫ(T |B) vs dxy using the same algorithm for Bottom and Top tracks(a) and
reconstructing Bottom tracks with: CosmicTF(b), CKF(c) and RS(d).
63
Chapter 6
Summary on Tracking
In the first part of this thesis, the track reconstruction issues in CMS have been addressed.
Tracking is one of the fundamental elements of the event reconstruction, being the base for
most higher level algorithms.
The porting of the final fit code from the old software framework to the new one has been
completed and new features have been implemented.
Then, starting from some tools developed to check the results of the final fit algorithm,
the CMS Track Validation Tool has been developed. This fully configurable analysis program
evaluates the tracking performance for any tracking algorithm and software release.
The Validation Tool showed that the quality of some tracks is not optimal. Thus, the
Outlier Rejection algorithm, which improves the tracking performance by removing the large
χ2 hits during the track final fit, has been developed.
The first cosmic ray data, taken during the tracker commissioning at CMS site, have
been analyzed. In particular, the tracking efficiency using tracker information only has been
evaluated. The efficiency results of the order of 90% for all the tracking algorithms and
matches Monte Carlo prediction. Such results are remarkable, especially considering that the
tracker is still in the commissioning phase and that both the detector and the algorithms are
not designed for cosmic ray track reconstruction.
In conclusion, the CMS detector is now taking data in a cosmic global run. These data
are used for detector commissioning and to evaluate the reconstruction performance. They
prove that the experiment, and in particular the tracker detector, is ready for the upcoming
beam collisions and for the physics challenges of the Large Hadron Collider.
One of the most appealing challenges, the search for the MSSM Higgs boson, is addressed
in the second part of the thesis.
65
Chapter 7
Motivations for the Minimal
Supersymmetric Standard Model
The goal of this chapter is to give a short review of the theoretical background for the
search of the Heavy Neutral CP-odd MSSM Higgs Boson A. First, the open problems of the
Standard Model and the need for a Higgs boson will be recalled. Then, the motivations for
the Supersymmetry and in particular for the MSSM, will be briefly presented. Finally, the
Higgs particle spectrum in the MSSM will be described.
7.1
Open Problems of the Standard Model
The Standard Model (SM)[24, 25, 26, 27, 28] is a quantum theory that describes how all the
known fundamental particles interact via the strong, weak and electromagnetic forces. In its
present formulation, SM is a gauge theory with a SU (3)C × SU (2)L × SU (1)Y symmetry.
The SM particle masses and interactions have been tested at many collider experiments,
proving that the SM provides and incredibly successful description of Nature up to the order
of 100 GeV scale with no hints of additional structures. Certainly, a new framework will
be required at the Planck scale MP = (8πGNewton )−1/2 = 2.4 × 1018 GeV, where quantum
gravitational effects become important, but, because of some open issues, it seems reasonable
that New Physics can be discovered at the T eV scale.
The main open problem of the Standard Model is the origin of the fundamental particle
masses. In fact, the gauge symmetry forbids writing a mass term for the gauge bosons.
Fermionic masses are also not possible, because they would mix the left- and right-handed
fields, which have different transformation properties, and therefore would produce an explicit
breaking of the gauge symmetry. Thus, the SM Lagrangian only contains mass-less fields.
Nevertheless, experimental observations show that both the elementary fermions and the
weak force bosons (W and Z) are massive. Also, they show that the electromagnetic and
weak forces have similar behaviors at high energies, while, for energies below the T eV scale,
their symmetry is broken. As the Electro-Weak Symmetry Breaking (EWSB) occurs at the
scale of ∼ 100 GeV , new phenomena are expected in the TeV range or below.
Other open problems of the SM are the dark matter explanation, the unification of the
forces at high energies, the quantistic description of the gravity force and the origin of the
predominance of matter over anti-matter.
67
7.1.1
The Higgs Mechanism
The Higgs Theory[29, 30] predicts the presence of a new field which breaks the electroweak
symmetry, gives masses to fermions and does not disturb gravity nor electromagnetism. The
simplest version of the Higgs field has been included in the SM and consists of a SU (2)
doublet of complex scalar fields:
r 1 φ1 + iφ2
φα
(7.1)
φ=
=
φβ
2 φ3 + iφ4
(where φj are four scalar fields) that contributes to the Lagrangian with the following potential
term:
λ
V (φ) = µ2 φ† φ + (φ† φ)2
(7.2)
2
with µ2 < 0 and λ > 0. When a particular minimum of the potential is chosen, the gauge
symmetry is spontaneously broken (Fig. 7.1). In fact, V (φ) is gauge invariant, but it has a
Figure 7.1: Schematic view of the Higgs potential V shape. It is symmetric with respect to
zero, but, in order to minimize it, a non-zero value has to be assumed and thus the symmetry
is spontaneously broken.
nonzero vacuum expectation value (v.e.v.):
µ2
.
(7.3)
λ
Expanding the field about this minimum, it turns out that a particular gauge can be chosen
so that, out of the four scalar fields, only one massive physical degree of freedom remains,
the Higgs boson H. The other three mass-less degrees of freedom are Goldstone bosons,
which can be regarded as the longitudinal polarizations of the weak force bosons W ± , Z,
thus providing them with mass. A Yukawa interaction between the fermions and the Higgs
field φ is allowed in the Lagrangian: this interaction term, after the EWSB, results in a
fermionic mass term. With this mechanism, both the bosons and the fermions acquire a
mass value that is proportional to their coupling to the Higgs field.
Summarizing, adding the Higgs potential to the SM Lagrangian, it is possible to preserve
the gauge invariance of the Lagrangian itself (SU (3)C × SU (2)L × SU (1)Y ). When the Higgs
field assumes a minimum of the potential, this symmetry is spontaneously broken: the gauge
invariance reduces to SU (3)C × SU (1)em , fermions and bosons acquire a mass proportional
to their coupling to the Higgs:
v
MV2 = gφV V
mf = hf v
(7.4)
2
hφ† φi = v 2 = −
68
and there is only an additional particle in the SM spectrum, the Higgs boson H, whose mass
depends on λ and v:
m2HSM = 2λv 2 .
(7.5)
The Z and W masses are experimentally well known:
MZ = 91.1875 ± 0.0021 GeV,
MW = 80.398 ± 0.025 GeV .
(7.6)
From these values, the electroweak mixing angle θW and the Higgs v.e.v. can be obtained:
sin2 θW = 1 −
2
MW
= 0.223,
MZ2
v = 246 GeV .
(7.7)
The value of v is commonly referred to as the electroweak scale.
From a theoretical point of view, this mechanism solves in a simple way the problem of
the elementary particle masses and of the Electro-Weak symmetry breaking. Still, the Higgs
boson has not been observed experimentally and also it entails some theoretical troubles.
The most important is the Hierarchy Problem.
7.1.2
The Hierarchy Problem
SM can be regarded as an effective theory, valid in a certain range of energies, from ∼ M eV
up to an unknown scale Λ. Its low energy quantities (masses, couplings) are expected to be
functions of the parameters of a more fundamental theory valid at a scale Q > Λ.
The Higgs boson mass is subjected to one-loop quantum corrections (Fig. 7.2), depending
on the Higgs coupling to bosons and fermions, their masses and the cutoff scale Λ:
∆m2 =
Λ
Λ
λS
2
2
2
2
log
−2Λ
+
m
Λ
−
m
log
+
S
f
16π 2
mf
16π 2
mS
|λ2f |
fR
h
(7.8)
SL+SR
h
fL
(a)
h
h
(b)
Figure 7.2: Fermionic (a) and bosonic (b) contributions to the Higgs mass one-loop quantum correction.
In Fig. 7.3 the latest fit of the Higgs mass in the SM is shown. The χ2 has a minimum
at around 100 GeV, although the direct search bound is mH > 114 GeV . The indirect limit
implies that mH ≤ 246 GeV at 95% C.L. [34]. Thus, the SM Higgs boson is expected to have
a mass value well below the T eV scale.
69
Figure 7.3: The Higgs mass constraints in the SM.
For this reason, the quantum correction to the Higgs mass cannot be too large. From
eq. (7.8) it is clear that this correction is quadratically divergent with respect to Λ. Therefore,
to keep the correction small, Λ should be ≤ 1 T eV or an extremely fine tuning of the
parameters should occur.
7.2
A brief introduction to Supersymmetry and MSSM
The main idea leading to Supersymmetry [32, 33] (SUSY) is to find a solution for the Hierarchy Problem. Referring to eq. (7.8), if there were two scalars for each fermion, then it would
read:
λS − |λ2f | 2
Λ
2
∆m =
Λ + O log
+ ...
(7.9)
8π 2
m
In addition, if their couplings were λS = |λf |2 , then the quadratic divergence would
exactly cancel:
Λ
+ ...
(7.10)
∆m2 = O log
m
Therefore, if a symmetry between fermions and bosons existed that, for each fermion
implied the presence of a boson with the same coupling to the Higgs (and vice versa), then the
Hierarchy Problem would be solved. Such hypothetical symmetry is called Supersymmetry.
It can be shown that the generators Q of such symmetry must have the following properties:
• Q|Bosoni = |Fermioni and Q|Fermioni = |Bosoni.
• they are spinors, thus carrying spin 1/2.
• they satisfy the following commutation rules: {Q, Q† } = P µ , {Q, Q} = {Q† , Q† } = 0
and [P µ , Q] = [P µ , Q† ] = 0, where P µ is the four-momentum generator of space-time
translations.
70
The effect of Q is to transform SM particles into their Supersymmetric partners, called
Superpartners. The pair of a particle and its Superpartner is called Supermultiplet. From the
properties above, it turns out that, for each Supermultiplet, the following rules hold:
• Superpartners have the same couplings.
• Superpartners have the same mass.
• Supermultiplets are made of one state of helicity λmax and a state with helicity λmin =
λmax − 1/2.
Two kinds of Supermultiplets can be defined: Chiral and Vector Supermultiplets. Chiral
(or Matter) Supermultiplets are composed of a state with λmax = 1/2 and the other one with
λmin = 0. The simplest example is a Weyl fermion and two real (one complex) scalar called
sfermion. Vector (or Gauge) Supermultiplets, instead, have λmax = 1 and λmin = 1/2 like,
for example, a gauge vector boson and a fermion called gaugino.
Using these rules, the simplest Supersymmetric extension of the SM does not add any
particle to the SM spectrum, except the Superpartners of the SM particles. This model is
called Minimal Supersymmetric Standard Model (MSSM). The Chiral Supermultiplets are
reported in Table 7.1, while the Vector ones in Table 7.2.
Table 7.1: Chiral Supermultiplets in the Minimal Supersymmetric Standard Model. The
spin-0 fields are complex scalars, and the spin-1/2 fields are left-handed two-component Weyl
fermions.
Names
squarks, quarks
(×3 families)
sleptons, leptons
(×3 families)
Higgs, higgsinos
Q
u
d
L
e
Hu
Hd
spin 0
(e
uL deL )
u
e∗R
de∗
R
(e
ν eeL )
ee∗R
(Hu+ Hu0 )
(Hd0 Hd− )
spin 1/2
SU (3)C , SU (2)L , U (1)Y
(uL dL )
u†R
d†R
(ν eL )
e†R
e u+ H
e u0 )
(H
0
e
e
(Hd Hd− )
( 3, 2 , 61 )
( 3, 1, − 23 )
( 3, 1, 13 )
( 1, 2 , − 12 )
( 1, 1, 1)
( 1, 2 , + 12 )
( 1, 2 , − 12 )
Table 7.2: Gauge Supermultiplets in the Minimal Supersymmetric Standard Model.
Names
gluino, gluon
winos, W bosons
bino, B boson
spin 1/2
ge
±
f
f0
W W
e0
B
spin 1
g
±
W W0
B0
SU (3)C , SU (2)L , U (1)Y
( 8, 1 , 0)
( 1, 3 , 0)
( 1, 1 , 0)
The only difference with respect to the SM is the presence of a Higgs doublet instead of a
singlet. In fact, in the SM Lagrangian, H gives mass to up-type quarks, while its conjugate
H c to down-type fermions. In a Supersymmetric model, the complex conjugate would make
71
the Lagrangian not invariant under the Supersymmetric transformation; therefore, two different scalar fields are needed to give mass to up- and down-fermions.
It is beyond the purposes of this introduction to give a detailed description of a generic
Supersymmetric Lagrangian, so only the details needed to understand the properties of the
MSSM Higgs bosons will be addressed.
The most general Supersymmetric Lagrangian (eq. (7.11)) is composed of three terms: one
for the Chiral Supermultiplets (Lchiral ), one for the Gauge Supermultiplets and an additional
term with other gauge invariant interaction terms formed out of the fields in Chiral and
Gauge Supermultiplets not taken into account in covariant derivatives (Ladd ).
L = Lchiral + Lgauge + Ladd
(7.11)
In particular, defining the scalar fields as φ and the Weyl spinors as ψ, the Chiral term
can be written in terms of a function of the scalar fields called Superpotential W as:
Lchiral = −∂ µ φ∗i ∂µ φi − iψ †i σ̄ µ ∂µ ψi −
where W , W i and W ij are defined as:
1 ij
W ψi ψj + Wij∗ ψ †i ψ †j − W i Wi∗ .
2
1
1
W = M ij φi φj + y ijk φi φj φk
2
6
Wi =
δW
1
= M ij φj + y ijk φj φk
δφi
2
W ij =
δ2
W = M ij + y ijk φk
δφi δφj
(7.12)
(7.13)
(7.14)
The matrices M ij and y ijk are totally symmetric in their indices and correspond to the
fermion mass matrix and the Yukawa couplings respectively.
In the MSSM case, the Superpotential is:
WMSSM = uyu QHu − dyd QHd − eye LHd + µHu Hd .
(7.15)
The objects Hu , Hd , Q, L, u, d, e appearing here are chiral scalar Superfields corresponding
to the chiral Supermultiplets in Table 7.1. The dimensionless Yukawa coupling parameters
yu , yd , ye are 3 × 3 matrices in family space. The µ term in eq. (7.15) is the Supersymmetric
version of the Higgs boson mass in the Standard Model. As already stated, no other Higgs
mass terms are allowed, because terms like Hu∗ Hu or Hd∗ Hd in the Superpotential would lead
to a not Supersymmetric invariant Lagrangian and thus are forbidden. Direct fermion mass
terms are also forbidden in the Lagrangian, so they acquire mass from the Yukawa couplings
in the term:
∂W 2
ūu = ūyu uHu0
(7.16)
∂e
u∗R ∂e
uL
In general, the couplings due to the Superpotential have the form reported in Fig. 7.4, where
dashed lines correspond to scalars and full lines to fermions.
The Supersymmetric solution of the Hierarchy Problem implies that fermions and scalars
∗
= |yijk |2 . Also,
in the same Supermultiplet have the same couplings: λS = |λf |2 or y ijm yklm
j
∗ M kj and thus they have
from the symmetry of the matrix M it turns out that M 2 i = Mik
the same masses.
72
k
i
j
k
l
j
i
y ijk
∗
y ijm yklm
(a)
(b)
i
j
i
j
j
i
k
∗ y jkm
Mim
M ij
∗ M kj
Mik
(c)
(d)
(e)
Figure 7.4: The Superpotential interaction vertices in a Supersymmetric theory: (a)
∗
scalar-fermion-fermion Yukawa interaction y ijk , (b) quartic scalar interaction y ijm yklm
. (c)
3
∗ jkm
ij
(scalar) interaction vertex Mim y
(d) fermion mass term M (e) scalar squared-mass
∗
term Mik
M kj .
The µ term in eq. (7.15) provides for higgsino fermion mass contribution in the Lagrangian:
e +H
e− − H
e 0H
e0
Lhiggsino mass = −µ(H
u
u d ) + c.c.,
d
(7.17)
as well as Higgs squared-mass terms:
Lsupersymmetric Higgs mass = −|µ|2 |Hu0 |2 + |Hu+ |2 + |Hd0 |2 + |Hd− |2 .
(7.18)
The Supersymmetric Higgs mass term cannot induce a spontaneous Electro-Weak Symmetry
Breaking because Hu0 = Hd0 = 0 is a minimum for the potential of eq. (7.18). Of course,
EWSB is a necessary feature of a consistent theoretical description and, in order to be an
acceptable theory, Supersymmetry has to account for it. Moreover, an exact Supersymmetry
would imply that the Supersymmetric particles have the same mass of their SM partners and,
for example, no experimental hint of the Supersymmetric electron has been seen at a mass
of 0.5 M eV . These facts suggest that, if Supersymmetry is a valid theory, it must be spontaneously broken at the energies below the T eV scale. Therefore, unless a specific mechanism
of Supersymmetry breaking is known, no information on the spectrum can be obtained. The
cancellation of quadratic divergences in eq. (7.8) relies on equality of couplings and not on
equality of the masses of particles and Superpartners. Soft Supersymmetry Breaking terms
that give different masses to SM particles and their Superpartners, but preserve the structure of couplings of the theory, can be included in the Lagrangian. In the MSSM the Soft
73
Supersymmetry Breaking contribution to the Lagrangian is:
1
fW
f + M1 B
eB
e + c.c.
M3 gege + M2 W
2
e d −e
e u −e
e d + c.c.
e au QH
d ad QH
e ae LH
− u
LMSSM
= −
soft
†
e † m2Q Q
e−L
e † m2L L
e−u
e mu2 e
u −e
d m2d e
d −e
e m2e e
e
−Q
†
− m2Hu Hu∗ Hu − m2Hd Hd∗ Hd − (bHu Hd + c.c.)
†
(7.19)
In eq. (7.19), M3 , M2 , and M1 are the gluino, wino, and bino mass terms (adjoint representation gauge indices and gauge indices are suppressed). The second line in eq. (7.19) contains
the (scalar)3 couplings. Each of au , ad , ae is a complex 3 × 3 matrix in family space, with
dimensions of [mass]. They are in one-to-one correspondence with the Yukawa couplings of
the Superpotential. The third line consists of squark and slepton mass terms of type (m2 )ji .
Finally, in the last line of eq. (7.19) we have Supersymmetry-breaking contributions to the
Higgs potential. The soft Supersymmetry breaking terms add to the theory a huge number
of parameters (105) which are all expected to be of the order of 100 GeV − 1 T eV . These
parameters are actually constrained by several experimental results, like individual leptonic
number conservation, CP violation and K0 mixing and by some theoretical arguments, like
the assumption that the sector that generates the soft-braking terms is flavor-blind.
The Higgs sector of the MSSM, after including the Soft Supersymmetry Breaking terms,
will be described in the following section. Before going into it, it is worth recalling why
Supersymmetry is an interesting extension of the Standard Model: it provides a brilliant
solution to the Higgs Hierarchy problem and also predicts the presence of a weakly interacting, stable and massive particle, the neutralino (Superpartner of the neutrino) which turns
out to be a good Dark Matter candidate. Finally, Supersymmetry is compatible with the
Grand Unification Theories: SM couplings tend to converge at high energies but unification
is quantitatively ruled out, while, in the MSSM, it can be reached at αGU T ≃ 0.04 and
MGU T ≃ 1016 GeV (Fig. 7.5). For these reasons the search for Supersymmetric particles has
been a hot topic at LEP and TEVATRON experiments, and will hopefully have a definitive
answer at the LHC.
7.3
Higgs particles in the MSSM
In the MSSM, the description of electroweak symmetry breaking is slightly complicated by
the fact that there are two complex Higgs doublets Hu = (Hu+ , Hu0 ) and Hd = (Hd0 , Hd− ).
The scalar potential for the Higgs scalar fields in the MSSM is given by
V = (|µ|2 + m2Hu )(|Hu0 |2 + |Hu+ |2 ) + (|µ|2 + m2Hd )(|Hd0 |2 + |Hd− |2 )
(7.20)
+ [b (Hu+ Hd− − Hu0 Hd0 ) + c.c.]
1
1
+ (g2 + g′2 )(|Hu0 |2 + |Hu+ |2 − |Hd0 |2 − |Hd− |2 )2 + g2 |Hu+ Hd0∗ + Hu0 Hd−∗ |2
8
2
The minimum of this potential should break electroweak symmetry down to electromagnetism
SU (2)L ×U (1)Y → U (1)EM , in agreement with experiment. Using the freedom to make gauge
transformations to take Hu+ = Hd− = 0, Hu0 and Hd0 real and positive at the minimum, the
74
Figure 7.5: Gauge coupling running as a function of energy. The solid line is the SM, the
dotted (dashed) line is for MSSM with 1 T eV (10 T eV ) SUSY mass scale.
scalar potential becomes:
V = (|µ|2 + m2Hu )|Hu0 |2 + (|µ|2 + m2Hd )|Hd0 |2 − (b Hu0 Hd0 + c.c.)
1
+ (g2 + g′2 )(|Hu0 |2 − |Hd0 |2 )2 .
8
(7.21)
The vacuum expectation values of Hu0 and Hd0 , vu = hHu0 i and vd = hHd0 i, are related to the
mass of the Z 0 boson and the electroweak gauge couplings:
m2Z =
1 2 ′2 2 2 g g
vu vd ⇒ v 2 ≡ vu2 + vd2 ≃ (174 GeV )2
2
The ratio between the vacuum expectation values is defined as tan β:
vu
tan β ≡
vd
(7.22)
(7.23)
After applying the minimization conditions and diagonalizing the mass matrices, the
following Higgs mass eigenstates are found:
1. Two CP-odd neutral scalars
0 √
sin β − cos β
ImHu
G
= 2
A
cos β sin β
ImHd
2. Two charged scalars
G+
H+
=
sin β − cos β
cos β sin β
Hu+
Hd+
3. Two CP-even neutral scalars
0 √
h
cos α − sin α
ReHu − vu
= 2
H
sin α cos α
ReHd − vd
(7.24)
(7.25)
(7.26)
75
G± and G0 are the Goldstone bosons that give mass to the W ± and Z bosons, while H ± ,
h0 , H and A are the physical degrees of freedom.
At tree level, the masses and the other parameters of the theory are commonly expressed
as a function of tan β and mA . The Higgs masses are:
m2A = 2b/ sin(2β) = 2|µ|2 + m2Hu + m2Hd
q
1 2
mA + m2Z ∓ (m2A − m2Z )2 + 4m2Z m2A sin2 (2β)
m2h0 ,H =
2
m2H ± = m2A + m2W
(7.27)
(7.28)
(7.29)
while, the mixing angle α is determined by
sin 2α
= −
sin 2β
m2H + m2h0
m2H − m2h0
tan 2α
=
tan 2β
,
m2A + m2Z
m2A − m2Z
(7.30)
The couplings of h, H and A to standard particles are the same as in the Standard Model,
rescaled by α- and β-dependent factors (Table 7.3). It’s worth noting that down type fermion
couplings to A are enhanced by a factor tan β.
Table 7.3: α- and β-dependent scale factors for Higgs couplings to SM particles in the
Minimal Supersymmetric Standard Model.
¯
dd,ss̄,b
b̄
uū,cc̄,tt̄
W + W − ,ZZ
cos α/ sin β
sin α/ sin β
−iγ5 cot β
sin(β − α)
cos(β − α)
0
e+ e− ,µ+ µ− ,τ + τ −
h
H
A
−sin α/ cos β
cos α/ cos β
−iγ5 tan β
The following relations hold between the Higgs masses:
m2H ± ≥ m2A
mh ≤ mA ≤ mH
mh < | cos 2β|mZ
(7.31)
The last relation is actually bounded by LEP results. After adding radiative corrections the
exclusion value is weakened to mh <
∼ 130 GeV , compatible with LEP results and within the
LHC reach.
The value of the Higgs masses as a function of mA and tan β is shown in Fig. 7.6 Some
limit cases are interesting to be discussed:
• mA ≫ mZ , the decoupling limit. As it can be seen from eq. (7.28-7.30), in such limit
α ≈ β − π2 and sin2 (β − α) ≈ 1. Then h0 has a low mass value and the same coupling
of a SM Higgs for the same mass. A, H and H ± are much heavier, forming an isospin
doublet almost degenerate both in mass and couplings.
• Low mA and large tan β. In this scenario cos2 (β − α) ≈ 1, H has the same couplings
as a SM Higgs boson and A is degenerate with h.
Therefore, for large tan β values, A is always degenerated with one of the two CP -even neutral
Higgs bosons h or H.
76
Figure 7.6: Higgs masses as a function of mA for tan β = 3, 30.
Considering radiative corrections, some additional parameter have to be taken into account: MSU SY , M2 , µ, A and mg̃ . MSU SY is a soft SUSY-breaking mass parameter and
represents a common mass for all scalar fermions (sfermions) at the electroweak scale. Similarly, M2 represents a SU(2) gaugino mass at the electroweak scale. The “Higgs mass parameter” µ is the strength of the Supersymmetric Higgs mixing; A = At = Ab is a common
trilinear Higgs-squark coupling at the electroweak scale and mg̃ the gluino mass. Three of
these parameters define the stop and sbottom mixing parameters Xt = A − µ cot β and
Xb = A − µ tan β. In addition to all these MSSM parameters, the top quark mass also has a
strong impact on the predictions through radiative corrections. The parameters for several
benchmark scenarios [35] are reported in Table 7.4.
The present analysis is performed in the mh -max scenario, where the stop mixing parameter is set to a large value, Xt = 2MSU SY . This model is designed to maximize the theoretical
upper bound on mh for a given tan β. This model thus provides the largest parameter space
in the mh direction and conservative exclusion limits for tan β.
Table 7.4: Parameters defining the main MSSM benchmark scenarios.
MSU SY (GeV )
M2 (GeV )
µ (GeV )
mg̃ (GeV )
Xt (GeV )
mh -max
1000
200
-200
800
2MSU SY
no-mixing
1000
200
-200
800
0
large-µ
400
400
1000
200
-300
gluophobic
350
300
300
500
-750
small-αef f
800
500
2000
500
-1100
77
Chapter 8
Search for the Heavy Neutral
CP-odd Higgs Boson A
In this chapter the experimental search for the MSSM Higgs bosons is introduced. The
exclusion limits, in terms of the MSSM parameters, obtained so far at LEP and TEVATRON
are first presented. The expected signal production processes and decays at the LHC are
then discussed.
8.1
Exclusion limits from LEP and CDF
The Large Electron Positron Collider (LEP) started its operations in 1989 with a center
of mass energy of 91 GeV , at the Z peak. Later it was upgraded to a maximum energy
of 209 GeV , allowing for the production of a W pair and continued working until the end
of the year 2000. Combining the results of the four LEP experiments, the search for the
MSSM Higgs bosons has been finalized, leading to 95% CL exclusion limits in the tan β vs
mA plane [34]. Several MSSM scenarios have been investigated, both CP -conserving and
CP -violating. Only the results in the CP -conserving mh -max scenario are here presented for
consistency.
In the e+ e− collisions at the LEP energies, the main production process of h, H, and A are
the Higgs-strahlung processes e+ e− → hZ (or HZ when allowed in the parameter space) and
the pair production processes e+ e− → hA (or HA). The Higgs-strahlung and pair production
cross-sections are complementary: at the LEP energies, the process e+ e− → hZ is typically
more abundant for small tan β values, while e+ e− → hA dominates at large tan β.
The h boson decays mainly to fermion pairs, with only a small fraction of W W ∗ and ZZ ∗
decays, since its mass is below the corresponding on-shell processes. The A boson also decays
predominantly to fermion pairs, independently of its mass, since its coupling to vector bosons
is zero at leading order. For tan β > 1, decays of h and A to bb̄ and τ + τ − pairs are preferred
while the decays to cc̄ become important for tan β < 1.
In each of the four LEP experiments, the data analysis is performed in several steps. A
preselection is applied to reduce some of the large backgrounds, in particular from two-photon
processes. The remaining background, mainly from production of fermion pairs and W W
or ZZ, is further reduced by more selective cuts and applying multivariate techniques. For
the two production processes, searches have been carried out considering several final state
topologies. For the Higgs-strahlung process the topologies taken into account are the same
79
used in the search for the SM Higgs boson:
• the four-jet topology, (h → bb̄)(Z → q q̄), in which the invariant mass of two jets is close
to the Z mass while the other two jets are tagged as b.
• the missing energy topology, (h → bb̄, τ + τ − )(Z → ν ν̄), in which the event consists of
two b- or τ -jets and a large amount of missing energy compatible with mZ .
• the leptonic final state, (h → bb̄)(Z → e+ e− , µ+ µ− ), in which the invariant mass of
the two leptons is close to mZ .
• the final states with τ leptons, (h → τ + τ − )(Z → q q̄) and (h → bb̄, τ + τ − )(Z → τ + τ − ),
in which the other the τ + τ − or the q q̄ pair has invariant mass close to mZ .
In the case of the pair production process, e+ e− → hA, the principal signal topologies at
LEP are:
• the four-b final state (A → bb̄)(h → bb̄).
• the mixed final states (A → τ + τ − )(h → bb̄) and (A → bb̄)(h → τ + τ − ).
• the four-τ final state (A → τ + τ − )(h → τ + τ − ).
• the Higgs cascade decay, e+ e− → hA → (hh)h, gives rise to event topologies ranging
from six b=jets to six τ leptons.
After selection, the combined data are compared to a large number of simulated configurations, generated separately for the hypothesis of background only and signal-plus-background
hypothesis. The ratio Q = Ls+b /Lb of the corresponding likelihoods is used as hypothesis
test. For an assumed top quark mass of mt = 174.3 GeV , the exclusion limits found for a
95% confidence level are interpreted in the considered MSSM scenarios. The exclusions for
the mh -max scenario are shown in Fig. 8.1. In the region with tan β <
∼ 5, the exclusion is
provided mainly by the Higgs-strahlung process, providing a lower bound of about 114 GeV
for mh . At high tan β, the pair production process gives the main contribution, providing
limits of 92.8 and 93.4 GeV for mh and mA respectively.
The data also exclude some domains of tan β (Fig. 8.2). For mt = 174.3 GeV , the range
0.7 < tan β < 2 is excluded.
80
(a)
(b)
(c)
(d)
Figure 8.1: Exclusions, at 95% CL (light-green) and the 99.7% CL (dark-green), in the case
of the CP-conserving mh -max benchmark scenario, for mt = 174.3GeV . The figure shows the
theoretically inaccessible domains (yellow) and the regions excluded by this search, in four
projections of the MSSM parameters: (a): (mh , mA ); (b): (mh , tan β); (c): (mA , tan β); (d):
(mH ± , tan β). The dashed lines indicate the boundaries of the regions which are expected
to be excluded, at 95% CL, on the basis of Monte Carlo simulations with no signal. In the
(mh , tan β) projection (plot (b)), the upper boundary of the parameter space is indicated
for four values of the top quark mass; from left to right: mt = 169.3, 174.3, 179.3 and
183.0 GeV .
81
Figure 8.2: Domains of tan β which are excluded at the 95% CL (light-gray or lightgreen) and the 99.7% CL (dark-green), in the case of the CP-conserving mh -max benchmark
scenario, as a function of the assumed top quark mass.
82
The TEVATRON pp̄ collider at 1.96 T eV has been operating since year 1987 and will
take data at least until the end of 2009. Two experiments were built at this collider, CDF
and D0. As they are currently taking data, no definitive combined results for the search of
the MSSM Higgs particles have been published by the two experiments. Therefore, in the
following, only the preliminary results in the search for the CP -odd MSSM Higgs boson A
(and the corresponding mass-degenerate CP -even h or H) decaying into a τ pair obtained
by CDF with an integrated luminosity of 1.8 f b−1 will be presented [36, 37].
At hadron colliders (see. §8.2) there are two dominant production mechanism for neutral
MSSM Higgs bosons: gluon fusion gg → φ and associate production gg → bbφ, where φ can
denote any of h, A, H. The leading decay modes are bb̄ (∼ 90%) and τ + τ − (∼ 10%). Despite
the smaller branching fractions, Higgs searches in the di-τ channel have the advantage that
they do not suffer from the large multi-jet backgrounds as φ → bb̄ does. The di-τ channel
has been inclusively analyzed in three final states: τe τh , τµ τh and τµ τe , where τe , τµ and τh
are short-hand notations for the decay modes τ → eνe ντ , τ → µνµ ντ , τ → (hadrons ντ )
respectively.
The dominant, irreducible background in the final sample of selected events is Z/γ ∗
with subsequent decays to τ pairs. The second largest contribution comes from multi-jet
events with gluon of quark jets mis-identified as τh . Additional considered backgrounds are
Z → ee, µµ, W W , W Z, ZZ, W γ, Zγ and tt̄ production.
The number of expected SM background events and the number of observed events in
the data after applying all selection criteria are summarized in Table 8.1. To probe for
Table 8.1: Predicted backgrounds andR observed events after all selection cuts in the τe τh ,
τµ τh and τµ τe channels at CDF with L = 1.8 f b−1 . The quoted errors are statistical
only. For the jet fakes source, in the channel including τh the uncertainty is included in the
systematics.
source
Z → ττ
Z → ee, µµ
di-boson events
tt̄
jet fakes
Sum BG
DATA
τe τh
137639 ± 8.3
69.7 ± 2.0
4.3 ± 0.1
3.7 ± 0.1
466.5
1921.1
1979
τµ τh
1353.7 ± 8.1
107.3 ± 2.3
3.3 ± 0.05
3.0 ± 0.07
283.6
1750.8
1666
τe τµ
604.8 ± 5.5
19.2 ± 0.9
11.4 ± 0.1
9.1 ± 0.1
57.3 ± 3.3
701.9
726
possible Higgs signal, a binned likelihood fit of the partially reconstructed mass of the di-tau
/ T ) has been
system (mvis defined as the invariant mass of the visible τ -decay products and E
performed. An example fit for mA = 140 GeV is reported in Fig. 8.3. No signal evidence has
been observed in the range 90 GeV < mA < 250 GeV and the exclusion limits at 95% CL on
the production cross-section times the branching ratio are set as in Fig. 8.4. Considering four
benchmarks scenarios (standard version - µ = −200 GeV - and the variant with positive sign
µ of mh -max and no-mixing scenarios), these results are converted into exclusion regions in
the tan β vs mA plane, as shown in Fig. 8.5 for standard mh -max.
83
Figure 8.3: Partially reconstructed di-τ mass. The normalization of the backgrounds and
signal (mA = 140 GeV ) correspond to the fit results for signal exclusion at 95% CL.
Figure 8.4: Observed and expected limits at 95% CL for Higgs production cross-section
times branching fraction to τ pairs at CDF.
Figure 8.5: Excluded region in tan β vs mA plane for the mh -max scenario with µ < 0.
84
g
g
b̄
b
φ
g
b̄
g
(a)
φ
b
(b)
q
q̄
q
φ
W, Z
W, Z
φ
W, Z
q
q
(c)
q
W, Z
(d)
Figure 8.6: Production processes for the MSSM Higgs bosons at LHC: gluon fusion(a),
bottom quark associated production(b), vector boson fusion(c), Higgs-strahlung(d). The
last two processes are forbidden for A, which does not couple to W and Z.
8.2
Production at LHC
Before addressing the experimental search for the A boson at CMS, it is worth summarizing
the expected phenomenology of the MSSM Higgs at LHC.
The predicted cross section for the production of the MSSM Higgs bosons at LHC varies
of several order of magnitude as a function of the tree-level parameters mA and tan β. The
main production processes are the gluon fusion production process gg → φ and the b-quark
associated production process gg → bbφ (with φ = h/H/A) (Fig. 8.6). A contribution to the
bbφ final state comes also from the process qq → bbφ, but it is highly suppressed with respect
to gg → bbφ and therefore won’t be considered for the rest of this work.
At low tan β values, the dominant production for the CP -odd Higgs boson is gg → A,
while at large tan β values, is gg → bbA. Nevertheless, for tan β = 30, the gluon fusion cross
section is not completely suppressed, being just about one order of magnitude smaller than
the associated process cross section for A masses in the range 100 GeV ≤ mA ≤ 200 GeV
(Fig. 8.7). The CP -even Higgs bosons h and H are mainly produced through a direct
production process for small values of tan β, while for high values the dominant production
process for H is gg → bbH (Fig. 8.8).
MSSM Higgs bosons couplings are reported in
Table 7.3. From these couplings, it is clear that, for large tan β values, the branching ratios
for the decays into down-type fermions are preferred. On the other hand, for low values of
tan β other channels may contribute, and in particular, if the Higgs boson is heavy, the tt̄
decay may become dominant. The resulting branching ratios in the mh -max scenario for
tanβ = 3 and 30 as a function of the Higgs masses are presented in Fig. (8.9-8.11).
Therefore, in the mh -max scenario, the exclusion regions from LEP and CDF results
85
(a)
(b)
Figure 8.7: Neutral CP -odd MSSM Higgs production cross sections at LHC for gluon
fusion gg → A and the associated production gg, q q̄ → bb̄A/tt̄A, including all known QCD
corrections for tan β = 3 (a) and tan β = 30 (b).
(a)
(b)
Figure 8.8: Neutral CP -even MSSM Higgs production cross sections at LHC for gluon
fusion gg → h/H, vector-boson fusion qq → qqV V → qqh/qqH, Higgs-strahlung q q̄ → V ∗ →
hV /HV and the associated production gg, q q̄ → bb̄h/bb̄H/tt̄h/tt̄H/, including all known
QCD corrections for tan β = 3 (a) and tan β = 30 (b).
86
Figure 8.9: Branching ratios of the MSSM Higgs boson A for non-SUSY decay modes as a
function of its mass for tanβ = 3, 30 and maximal mixing.
Figure 8.10: Branching ratios of the MSSM Higgs boson h for non-SUSY decay modes as
a function of its mass for tanβ = 3, 30 and maximal mixing.
Figure 8.11: Branching ratios of the MSSM Higgs boson H for non-SUSY decay modes as
a function of its mass for tanβ = 3, 30 and maximal mixing.
87
constrain the values of tan β and mA in the range 5 < tan β <
∼ 50 and mA >
∼ 92 GeV .
For such ranges, the expected main A production processes at LHC are the gluon fusion and
the b quark associated production. For most regions in the tan β vs mA plane, the dominant
decay channels are the A → bb̄ and A → τ τ . The latter is the most promising channel for the
discovery of the MSSM Higgs both from a theoretical point of view, because it is less sensitive
to Supersymmetric radiative corrections [35], and from an experimental point of view, as will
be discussed at the beginning of the next section.
88
Chapter 9
Sensitivity for the MSSM
/ T decay in CMS
A → τ τ → eµE
9.1
Introduction
The A → τ τ decay is the favorite channel for the discovery of MSSM Higgs at LHC because
the A coupling to τ s is enhanced by a factor tanβ and, even if the A → bb̄ branching
ratio is almost ten times higher, the b decay channel is overwhelmed by the QCD multi-jet
background[38]. In the present analysis, in order to have a clean final state, the two τ s are
required to decay into different flavor leptons, thus ending up with one electron, one opposite
charged muon and missing transverse energy due to four neutrinos. In particular, this final
state does not contain τ jets, thus avoiding the difficult task of distinguishing them from b
and QCD jets.
The A → τ τ channel has already been extensively studied at CMS [39, R40, 41, 42, 43],
leading to 5σ discovery regions below tan β = 20 for mA < 300 GeV and L = 30 f b−1
/ T has already
(Fig. 9.1). In particular, an analysis in the decay channel A → τ τ → eµE
been performed in 2006, suggesting the discovery region shown in Fig. 9.2. Since then,
new reconstruction and analysis techniques have become available in the new CMS software
framework [19]. Moreover, this previous analysis, as the other searches for the Heavy Neutral MSSM Higgs bosons A in CMS, has been performed considering only the main signal
contribution coming from the associate production process, thus neglecting the contribution
from gluon fusion.
The goal of the present work, therefore, is to investigate new strategies for the A boson
search, test the new reconstruction algorithms and take into account the contribution from
the gg → A process.
In this chapter, after a brief review of the algorithms exploited to reconstruct the physics
objects and an overview of the signal and background samples used in this analysis, the key
issues of this analysis are investigated. In fact, the results of the analysis depends on how
the problems of the poor measurement of the Missing Transverse Energy, the low number of
b-tags in the gg → bbA sample and the mis-identification of τ -jets as leptons are addressed.
Then, the cuts and strategies for rejection of the background and the selection of the signal
contributions are described, and, finally, the obtained results are reported.
89
Figure 9.1: The 5σ discovery regions for the neutral Higgs bosons φ (φ=h,H,A) produced
in the association with b quarks pp → bbφ with the φ → µµ and φ → µµ decay modes in the
mh -max scenario.
Figure 9.2: Final results of the 2006 analysis: the 5σ discovery reach for heavy neutral
Higgs bosons H and A decaying via τ τ to e + µ final state. The dots give the 5σ limit for
the studied values of Higgs mass. The fast simulation result is also shown.
90
9.2
Event reconstruction
A clean and accurate reconstruction of the final state is the key for the outcome of any
analysis. For this reason, to avoid backgrounds containing more than two leptons, the event
is required to have exactly one muon and one electron with opposite charge values.
9.2.1
Trigger
The trigger table for the CMSSW releases used to produce the samples is developed for an
instantaneous luminosity L = 1032 cm−2 s−1 . Among the available trigger bits, the most
convenient and conservative choice is to make a minimal request of at least one lepton in the
event. The isolated paths have lower pT thresholds but require isolation already at trigger
level, while relaxed paths do not check isolation but have stronger pT thresholds. For this
analysis, the lepton pT and isolation cuts are studied and applied off-line and therefore, at
the trigger level, an inclusive choice has been made: the trigger selection is performed with a
logic OR between the isolated and relaxed single muon and single electron trigger bits. The
non-isolated single muon trigger bit has a pT threshold of 16 GeV , while the isolated 11 GeV
. The non-isolated single electron has a threshold of 17 GeV , the isolated 15 GeV . A mixed
electron-muon trigger is also available, but it is not expected to be necessary for the present
analysis because it has lower pT with respect to the single lepton paths, and the latter have
pT thresholds already well below the the offline pT cuts.
9.2.2
Leptons
Muons [44] are reconstructed with the globalMuon sequence, which matches tracks reconstructed in the muon chambers with a tracker track. The hits in the two track segments
are refitted together, providing the best estimate of the muon parameters. This procedure
assures a very strong signature, and therefore no other muon identification algorithms are
used. Muons are required to be isolated both in the tracker (no other tracks with pT > 1 GeV
in a cone with ∆R = 0.4) and in the calorimeter (the sum of the HCAL and ECAL deposits
within a cone with ∆R = 0.4 has to be less than 4 GeV ).
The sequence used to reconstruct electrons [45] is called pixelMatchGsfElectrons. Starting
from an ECAL super cluster, a pixel track seed matching the super cluster is searched for.
If the seed is found, the pattern recognition is performed with the Combinatorial Kalman
Filter algorithm in a loose cut configuration, while the final fit with the Gaussian Sum Filter
(GSF) [46]. GSF is a fitting algorithm dedicated to electrons that accounts for the electron
bremsstrahlung energy loss. As reconstructed pions are often mis-identified as electrons,
electrons are required to pass the tight version of the category based electron-id algorithm [47].
Electron isolation is also required: no tracks with pT > 1.5 GeV have to lie in a cone with
0.02 < ∆R < 0.2 around the electron; the ECAL deposit within a cone with ∆R = 0.3 is
required to be < 0.05×ESuperCluster , while the HCAL deposit in a cone with 0.15 < ∆R < 0.3
has to be < 0.2 × ESuperCluster .
For a more detailed discussion about the need for strong lepton isolation and identification
requests, see §9.4.1.
The request for one muon and one electron in the event, which are identified and isolated
according to the above criteria, can be considered as a sort of preselection cuts for this
analysis. Unless differently stated, plots in §9.3.1 are obtained for the events satisfying this
request.
91
9.2.3
Missing Transverse Energy
Besides leptons, the other reconstruction object used in the invariant mass calculation is the
/ T ) [48]. As the vectorial sum of the transverse momentum
Missing Transverse Energy (E
of the particles before and after the collision is zero, the unbalance in the total pT of the
reconstructed objects is a measurement of the transverse momenta of the neutrinos (and
of any other undetectable particle). The precision of this measurement is crucial for this
analysis: the mass peak mean value and width determination are highly dependent on the
/ T measurement accuracy.
E
/ T is provided by the sum of the calorimeter tower energies. This
A first estimate of E
measurement is very raw and needs some corrections. A first correction is the sum of the
/ T because muons nearly lose no energy
muon energy, which is not accounted for in the raw E
/ T . Another improvement applied
in the calorimeters. This measurement is called Type-0 E
/
to the E T determination is the correction for jet energies. As discussed in §9.4.3, the jet
/ T is Zero Suppression followed by the Jet Plus
correction that gives the highest benefit to E
Track algorithm [49][50]. This correction is applied to the uncorrected Iterative Cone 5
jets[51] and accounts for the calorimeter cells where some energy is deposited, but is not
sufficient to exceed the threshold set for the tower making (Zero Suppression) and replaces
the calorimeter energy deposit with the more precise measurement of the momentum of the
/ T measurement after the jet correction
tracks pointing to that deposit (Jet Plus Track ). The E
/T
is applied, is called Type-1 E
9.2.4
Jets
Jets [51, 52] are not directly used to compute the invariant mass of the Higgs, but they
are useful because, as the jet activity of the signal events is different from that of many
backgrounds, it is worth vetoing on the total number of jets in the event. Furthermore they
/ T , in this
are input to the b-tagging algorithms. To be consistent with the used Type-1 E
analysis, jets are corrected with the Zero Suppression and Jet Plus Track algorithms. A pT
threshold of 30 GeV is applied to corrected jets and they are required to be central (|η| < 2.5).
Jets within a cone with ∆R < 0.3 centered on the lepton direction are not considered.
9.2.5
b-tagging
A key element for this analysis is b-tagging [53]. It is primarily needed to reject the background and secondarily it may be useful to select the gg → bbA production processes. Several
b-tagging algorithms are available: after some studies, described in §9.4.2, the algorithm with
the best performance for this analysis is TrackCountingHighEfficiency [54]. The discriminator
value provided by the TrackCountingHighEfficiency algorithm is the three dimension impact
parameter significance of the track in the jet with the second highest impact parameter
significance. The discriminator threshold value optimizing efficiency and fake rate is 2.
9.2.6
Collinear Approximation
Because of the presence of four neutrinos in the final state, it is not possible to compute the
Higgs invariant mass with an exact formula. The Missing Transverse Energy, in fact, is a
measurement of the sum of the transverse momenta of all the invisible particles, but it does
not measure the z component. Some experiments, like for example CDF, compute the visible
92
mass of the Higgs by calculating the invariant mass between all the measured quantities
/ T ). This approach does not provide a direct measurement of
(lepton three-momenta and E
the Higgs mass which has to be inferred from MC studies.
The method used in the present analysis, called Collinear Approximation, can be used to
directly estimate the reconstructed Higgs mass. It is based on the fact that the τ s produced
by the Higgs decay are highly boosted and thus the directions of all the final state leptons are
close to the τ direction. Therefore, as shown in Fig. 9.3, this approximation safely assumes
that the τ s have the same direction of the measured leptons.
Figure 9.3: Schematic view of the transverse momenta of Higgs and of its decay products
in the collinear approximation.
The visible fractions of the τ transverse momenta, xτ →l , are defined as the fractions of
the two τ momenta which are carried by the reconstructed charged leptons:
pTl
pl
=
, l = e, µ
(9.1)
xτ →l =
pτ →l
pT τ →l
The transverse momentum of the Higgs is the vectorial sum of the charged lepton and
neutrino transverse momenta:
/ Tj , j = x, y
pHiggsj = pej + pµj + E
(9.2)
It can be shown that, under this approximation, xτ →l can be expressed in terms of the
transverse momentum of the Higgs boson and the transverse momenta of the charged leptons:
xτ →e =
xτ →µ =
pex pµy − pey pµx
pHiggsx pµy − pHiggsy pµx
(9.3)
pex pµy − pey pµx
pHiggsy pex − pHiggsx pey
This reconstruction method works only if the τ s are not emitted back-to-back in the
transverse plane. For τ decays the reconstruction must yield 0 < xτ →l < 1.
Once the visible fractions of the τ momenta are known, the invariant mass of the τ pair
can be evaluated by
meµ
mHiggs = mτ τ = √
(9.4)
xτ →e xτ →µ
where meµ is the invariant mass of the two charged leptons in the final state.
93
9.3
Signal and Background samples
As a preparation for the first data taking, the CMS collaboration has performed a computing
and analysis exercise, called CSA07, to test the data flow foreseen for the first years of LHC
operations. Even if the final goal of this analysis differs from the purpose of the CSA07
exercise, most of the samples used have been produced during the massive Monte Carlo data
production for the CSA07.
The signal samples have been produced in the two main production processes gg → bbA
and gg → A, forcing A to decay into two taus. Even though only the leptonic final state
is considered, the τ decay is not constrained to the exclusive channel in order to be able
to estimate the mis-identification of τ jets as leptons. Consistently with the expectations
for the MSSM Higgs bosons production described in §8, the signal has been generated with
tanβ = 30 for various masses, ranging from 100 GeV up to 800 GeV for gg → bbA and from
100 GeV up to 200 GeV for gg → A. The used signal samples are summarized in Table 9.1.
As the final state under investigation contains one electron, one muon and missing transverse energy, the backgrounds that can yield at least two leptons of different flavor have
been considered. In order to have samples corresponding to luminosities of the same order of
magnitude, for two backgrounds a private production with the fast simulation has been used
instead of the CSA07 samples. The used background samples are listed in Table 9.2.
Signal and background samples mainly correspond to luminosities of the same order of
magnitude.
To avoid large scale correction factors, a natural choice for this analysis is to
R
assume L = 10 f b−1 .
Other potential sources of background can be cross-checked running on the CSA07 datasoups1 . No major contaminations arise: events surviving the selection cuts are already considered in the separate samples, except for a tiny contribution from W +jets.
9.3.1
Event variables and cuts
The signal final state is characterized by the presence of one muon, one electron, missing
transverse energy and, in case of gg → bbA, of b-tagged jets. Therefore it is interesting to
/ T and of the jets is the signal and in the main
look at the properties of the leptons, of the E
background samples.
As far as the leptons are concerned, the most interesting distributions are the pT , the
difference of the φ angles of the muon and the electron (∆φ) and the combined impact
parameter significance, defined as:
σ=
s
d0e
δd0e
2
+
d0µ
δd0µ
2
(9.5)
where d0l and δd0l are the value and the error of the lepton impact parameter. The τ
leptons has a mean lifetime of ∼ 290 × 10−15 s (cτ = 87.1 µm) and, coming from the Higgs
decay, they are highly boosted. Therefore, they are expected to travel a few millimeters
before decaying and thus their daughters are significantly detached from the primary vertex.
The distributions of the main leptonic variables are shown in Fig. 9.4. From these plots, it
1
There are three CSA07 data soups: Chowder, containing the ALPGEN W+jet, Z+jet and tt+jet samples, Stew, containing lepton enriched QCD, bottomonia, charmonia, Gumbo, containing QCD, Photon+jets,
MinBias.
94
Table 9.1: Signal samples. Cross sections and branching ratios have been computed with
FeynHiggs [55]. Generator used: Pythia [56]; Data-set: CMSSW 167-CSA07.
Process
gg → A → τ τ
MA = 100 GeV
gg → A → τ τ
MA = 120 GeV
gg → A → τ τ
MA = 140 GeV
gg → A → τ τ
MA = 160 GeV
gg → A → τ τ
MA = 180 GeV
gg → A → τ τ
MA = 200 GeV
gg → bbA → τ τ
MA = 100 GeV
gg → bbA → τ τ
MA = 120 GeV
gg → bbA → τ τ
MA = 140 GeV
gg → bbA → τ τ
MA = 160 GeV
gg → bbA → τ τ
MA = 180 GeV
gg → bbA → τ τ
MA = 200 GeV
gg → bbA → τ τ
MA = 300 GeV
gg → bbA → τ τ
MA = 500 GeV
gg → bbA → τ τ
MA = 800 GeV
R
L [f b−1 ]
σ × BR [pb]
Events
224.1 × 10.9%
163398
95.3 × 11.2%
188994
17.71
45.0 × 11.5%
169994
32.85
23.1 × 11.8%
177796
65.23
12.6 × 11.9%
159593
106.44
7.3 × 12.1%
181996
206.04
868.4 × 10.9%
180196
1.90
506.6 × 11.2%
201994
3.56
313.8 × 11.5%
203994
5.65
203.6 × 11.8%
194994
8.12
137.3 × 11.9%
194794
11.92
95.4 × 12.1%
167196
14.48
21.5 × 11.8%
190596
75.13
2.7 × 9.7%
198997
759.82
0.3 × 7.9%
152396
6430.21
6.69
is already clear that a pT minimum cut would reduce the Drell-Yan background, while ∆φ
and σ cuts would reduce the other backgrounds.
In Fig. 9.5 the missing transverse energy distributions are shown. The Drell-Yan back/ T distribution softer than the signal, while the other backgrounds harder.
ground has a E
It is also interesting to look at the number of reconstructed jets per event, their pT , the
discriminator distribution and the number of b-tags per event. The corresponding plots are
shown in Fig. 9.6. W t and tt̄ have the largest jet and b-tagging activity, while the signal has
a jet activity more similar to the Drell-Yan and W W backgrounds. It is worth noting that,
even if for the b-tagging discriminator distribution the gg → bbA sample behaves like W t
95
event fraction
event fraction
gg->bbA
gg->A
ttbar
DY
Wt
WW
10-1
10-2
gg->bbA
gg->A
ttbar
DY
Wt
WW
10-1
10-2
10-3 0
20
40
60
80
100
10-3 0
120
pT,µ[GeV]
20
40
60
0.05
120
p [GeV]
(b)
event fraction
event fraction
0.06
100
T,e
(a)
0.07
80
gg->bbA
gg->A
ttbar
DY
Wt
WW
0.8
gg->bbA
gg->A
ttbar
DY
Wt
WW
0.7
0.6
0.5
0.04
0.4
0.03
0.3
0.02
0.2
0.01
0
0.1
20
40
60
80
100
120
140
0
0
160
180
∆ φ [o]
1
2
3
4
(c)
5
6
7
8
9
10
σ
(d)
Figure 9.4: Characterization of leptons: (a) muon pT , (b) electron pT , (c) ∆φ between e
and µ, (d) combined impact parameter significance.
event fraction
0.22
gg->bbA
gg->A
ttbar
DY
Wt
WW
0.2
0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
0
20
40
60
80
100
120
140
160
180 200
ET [GeV]
/ T distribution for the signal and for the main backgrounds.
Figure 9.5: E
96
Table 9.2: Background samples and cross sections: tt̄ [4], Z/γ ∗ → τ τ [56], tW [57],
W W [58], W Z [59], ZZ [60] and bbll [61].
Process
bbll
tW inclusive
W W inclusive
W Z inclusive
ZZ inclusive
Z/γ ∗ → τ τ
Mτ τ > 10 GeV
Generator
Data-set
CompHEP [61]
CMSSW 167-CSA07
TopRex [62]
CMSSW 167-CSA07
Pythia
CMSSW 167-CSA07
Pythia
CMSSW 167-CSA07
Pythia
CMSSW 167-CSA07
R
L [f b−1 ]
13.22
7.16
7.40
7.28
8.45
σ [pb]
830
62
114.3
49.9
16.1
Events
1931449
443790
845260
363290
136112
7559
9948432
1.32
840
5899999
7.02
CMSSW 1612
Pythia
Fast Sim
CMSSW 1612
tt̄
Pythia
Fast Sim
0.9
0.35
event fraction
event fraction
and tt̄ (Fig. 9.6(c)), it has much lower number of b-tags per event (Fig. 9.6(d)), just slightly
more than the other samples. This behavior is not obvious and will be addressed in §9.4.2.
gg->bbA
gg->A
ttbar
DY
Wt
WW
0.8
0.7
0.6
gg->bbA
gg->A
ttbar
DY
Wt
WW
0.3
0.25
0.5
0.2
0.4
0.15
0.3
0.1
0.2
0.05
0.1
0
0
1
2
3
4
5
0
0
6
7
number of jets
50
100
200
250
300
pT,jets [GeV]
(b)
0.4
gg->bbA
gg->A
ttbar
DY
Wt
WW
0.35
0.3
0.25
event fraction
event fraction
(a)
150
1
gg->bbA
gg->A
ttbar
DY
Wt
WW
0.9
0.8
0.7
0.6
0.5
0.2
0.4
0.15
0.3
0.1
0.2
0.05
0
-10
0.1
-5
0
5
10
(c)
15
20
25
30
discriminator
0
0
0.5
1
1.5
2
2.5
3
3.5
4
number of b-tags
(d)
Figure 9.6: Characterization of jets: (a) number of reconstructed jets per event, (b) jet pT ,
(c) discriminator for the TrackCountingHighEfficiency algorithm and (d) number of b-tags
per event.
97
Finally, the distributions of the reconstructed τ momentum fractions xτ →e and xτ →µ are
shown in Fig. 9.7. As expected from their topology, the signal and the Drell-Yan samples
have more often physical values (0 < xτ →l < 1) with respect to the other backgrounds.
gg->bbA
gg->A
ttbar
DY
Wt
WW
0.2
0.25
event fraction
event fraction
0.25
0.2
0.15
0.15
0.1
0.1
0.05
0.05
0
-1
-0.5
0
0.5
1
1.5
2
xτ → e
(a)
gg->bbA
gg->A
ttbar
DY
Wt
WW
0
-1
-0.5
0
0.5
1
1.5
2
xτ → µ
(b)
Figure 9.7: Distribution of the reconstructed τ momentum fractions xτ →e ((a)) and xτ →µ
((b)).
9.3.2
Fast Sim - Full Sim comparison
In order to save computing time and be able to quickly simulate and reconstruct events, the
Fast Simulation makes use of some approximations and parametrization, thus avoiding many
simulation and reconstruction steps performed in the Full Simulation. Therefore, the Fast
Simulation is suitable to produce high statistics samples, but its results are less accurate
than Full Simulation’s. Before blindly trusting the Fast Simulation data for this analysis, a
detailed comparison with a small sample of Full Simulation data has been performed. Fast
and Full Simulation data have been produced with the same generator and the same CMSSW
release cycle, so that the comparison is straightforward.
The first important difference is that, in the CMSSW 1 6 X releases, the trigger is not
implemented in the Fast Simulation. Having estimated that only a few percent of the events
can pass all the selection cuts without the required trigger bits, it was decided to skip the
trigger request for the fast simulation. This fact can lead to an overestimation of the tt̄ and
Drell-Yan backgrounds at the percent level.
Looking at the distribution plots of the most important variables for this analysis, the Fast
Simulation and the Full Simulation show a very good agreement both for the characteristics
of the leptons (Fig. 9.8) and for the properties of the jets (Fig. 9.9). A small difference can
be noticed for the pT of the electron (Fig. 9.8(b)), but it happens for values well below the
trigger and the selection cuts, so it can be neglected.
Significant differences between Fast and Full simulation are observed in the combined
impact parameter significance distribution (Fig. 9.10). σ (eq. 9.5) is computed starting from
the muon and electron impact parameter value and their errors. The impact parameter values
obtained with Full and Fast Simulation are compatible both for the electron and the muon,
while the errors are not (Fig. 9.11). A compelling explanation for the different behavior of the
impact parameter errors is that the track reconstruction for the fast simulation is performed
starting from a Gaussian smearing of the true simulated hits, without accounting for the
98
0.09
0.08
DY full sim
Entries
370
Mean
15.17
RMS
9.979
DY fast sim
Entries
19399
Mean
15.89
RMS
11.05
event fraction
event fraction
TTbar full sim
Entries
550
Mean
46.8
RMS
33.16
TTbar fast sim
Entries
36464
Mean
48.26
RMS
34.47
0.1
0.07
TTbar full sim
Entries
550
Mean
50.7
RMS
35.41
TTbar fast sim
Entries
36464
Mean
51.27
RMS
34.62
0.08
0.07
0.06
DY full sim
Entries
370
Mean
20.06
RMS
11.26
DY fast sim
Entries
19399
Mean
18.27
RMS
10.94
0.05
0.06
0.05
0.04
0.04
0.03
0.03
0.02
0.02
0.01
0.01
0
0
20
40
60
80
100
120
140
160
0
0
180
200
p [GeV]
20
40
60
80
100
T,µ
140
160
180
200
p [GeV]
T,e
(a)
event fraction
120
(b)
TTbar full sim
Entries
550
Mean
105.4
RMS
50.87
TTbar fast sim
Entries
36464
Mean
105.9
RMS
50.04
0.08
0.07
0.06
DY full sim
Entries
370
Mean
152.5
RMS
34.06
DY fast sim
Entries
19399
Mean
152.3
RMS
33.05
0.05
0.04
0.03
0.02
0.01
0
0
20
40
60
80
100
120
140
160
180
∆ φ [ °]
(c)
Figure 9.8: Fast Simulation - Full Simulation comparison: muon(a) and electron(b) pT and
∆φeµ (c)
99
0.9
0.8
DY full sim
Entries
370
Mean
0.2189
RMS
0.5232
DY fast sim
Entries
19399
Mean
0.1838
RMS
0.4433
event fraction
event fraction
TTbar full sim
Entries
550
Mean
1.709
RMS
1.032
TTbar fast sim
Entries
36464
Mean
1.751
RMS
1.043
1
0.18
0.16
DY full sim
Entries
81
Mean
56.67
RMS
32.69
DY fast sim
Entries
3566
Mean
55.11
RMS
32.72
0.14
0.7
0.12
0.6
0.5
0.1
0.4
0.08
0.3
0.06
0.2
0.04
0.1
0
0
TTbar full sim
Entries
940
Mean
76.85
RMS
48.4
TTbar fast sim
Entries
63865
Mean
76.35
RMS
50.04
0.2
0.02
2
4
6
8
10
12
14
0
0
16
18
20
number of jets
50
100
150
event fraction
(a)
200
250
300
350
400
pT,jets [GeV]
(b)
TTbar full sim
Entries
550
Mean
0.9891
RMS
0.7385
TTbar fast sim
Entries
36464
Mean
1.017
RMS
0.7724
1
0.9
0.8
DY full sim
Entries
370
Mean
0.03243
RMS
0.1771
DY fast sim
Entries
19399
Mean
0.01943
RMS
0.1421
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
2
4
6
8
10
12
14
16
18
20
number of b−tags
(c)
Figure 9.9: Fast Simulation - Full Simulation comparison: number of jets per event(a), jet
pT distribution(b), number of b-tags per event(c).
100
event fraction
long non Gaussian tails of the hit position residue distributions and without considering
the presence of fake hits or hits wrongly associated to the track. The impact parameter
measurement is driven by the hits in the innermost layers, which are the most problematic
because they have the highest occupancy. Neglecting the contribution of such hits in the Fast
Simulation results in an underestimation of the impact parameter error.
The effect of the error underestimate is to overestimate the combined impact parameter
significance (Fig. 9.10) and, in the end, if a minimum cut on this variable is used, it would
imply a significant overestimation of the background produced with the Fast Simulation. In
order to correct this bias, the most natural solution is to correct the Fast Simulation data
by scaling the impact parameter error, thus pushing the mean value of the Fast Simulation
distribution up to approximately the mean value of the Full Simulation distribution. The
chosen scale factors are 1.5 for the electron and 1.7 for the muon. After the scaling, the
resulting impact parameter significance distribution has a behavior compatible with the Full
Simulation (Fig. 9.12 and Table 9.3).
Provided this correction, the Fast Simulation can be considered as “validated” for the
purposes of this analysis, and will be trustfully used throughout it.
TTbar full sim
Entries
550
Mean
1.771
RMS
1.233
TTbar fast sim
Entries
36464
Mean
2.441
RMS
1.71
0.6
0.5
DY full sim
Entries
370
Mean
2.548
RMS
1.846
DY fast sim
Entries
19399
Mean
3.23
RMS
2.208
0.4
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
8
9
10
σ
Figure 9.10: Fast Simulation - Full Simulation comparison: combined impact parameter
distribution.
Table 9.3: Mean and RMS values of the combined impact parameter significance distribution for the Full Simulation and the Fast Simulation before and after the scaling of the
impact parameter errors.
Sample
DY Full Sim
DY Fast Sim
DY Fast Sim scaled
tt̄ Full Sim
tt̄ Fast Sim
tt̄ Fast Sim scaled
mean
2.5
3.2
2.3
1.8
2.4
1.6
RMS
1.8
2.2
1.8
1.2
1.7
1.3
101
0.9
0.8
DY full sim
Entries
370
Mean
0.006522
RMS
0.007003
DY fast sim
Entries
19399
Mean
0.006063
RMS
0.007973
event fraction
event fraction
TTbar full sim
Entries
550
Mean
0.002813
RMS
0.003934
TTbar fast sim
Entries
36464
Mean
0.002835
RMS
0.005556
1
0.7
TTbar full sim
Entries
550
Mean
0.004253
RMS
0.005237
TTbar fast sim
Entries
36464
Mean
0.003473
RMS
0.005564
0.9
0.8
0.7
DY full sim
Entries
370
Mean
0.007068
RMS
0.008545
DY fast sim
Entries
19399
Mean
0.006329
RMS
0.007404
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
0
0.01
0.02
0.03
0.04
0
0
0.05
d0µ [cm]
0.01
0.02
0.03
0.05
0.06
0.07
0.08
0.09
0.1
d0e [cm]
(b)
TTbar full sim
Entries
550
Mean
0.002286
RMS
0.001606
TTbar fast sim
Entries
36464
Mean
0.00133
RMS
0.001289
1
0.9
0.8
DY full sim
Entries
370
Mean
0.003099
RMS
0.001547
DY fast sim
Entries
19399
Mean
0.002135
RMS
0.002031
event fraction
event fraction
(a)
0.04
0.7
TTbar full sim
Entries
550
Mean
0.004007
RMS
0.001736
TTbar fast sim
Entries
36464
Mean
0.002656
RMS
0.001834
0.8
0.7
0.6
DY full sim
Entries
370
Mean
0.005264
RMS
0.002354
DY fast sim
Entries
19399
Mean
0.00403
RMS
0.002535
0.5
0.6
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
0
0.002
0.004
0.006
0.008
0
0
0.01
δd0µ [cm]
0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02
δd0e [cm]
(c)
(d)
event fraction
Figure 9.11: Fast Simulation - Full Simulation comparison: impact parameter value for
muon(a) and electron(b) and impact parameter error for muon(c) and electron(d).
TTbar full sim
DY full sim
Entries
550 Entries
370
Mean
2.548
1.771 Mean
RMS
1.233 RMS
1.846
0.6
TTbar fast sim scaled
Entries
Mean
RMS
0.5
DY fast sim scaled
36464 Entries
1.627 Mean
1.349 RMS
19399
2.299
1.837
0.4
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
8
9
10
σ
Figure 9.12: Fast Simulation - Full Simulation comparison: combined impact parameter
distribution after the scaling of the impact parameter error.
102
9.4
Crucial issues
This analysis is very delicate in some aspects that, if not properly addressed, can lead to a
low signal to noise ratio, a poor measurement of the Higgs mass or an incorrect or biased
estimate of the production cross section. In particular, a feed-through of τ jet events in
the final selection, if not properly taken into account, would imply an overestimate of the
signal. Also, the b-tagging is a very challenging task for the signal events, and, if not properly
studied, would make the background suppression and weighting the two signal contributions
/ T measurement is fundamental to isolate a Higgs mass peak
difficult. Finally, a precise E
from the background.
9.4.1
Lepton mis-identification
event fraction
Simulated samples contain fully leptonic, fully hadronic and semileptonic di-τ decay final
states. Thus, the rate of the mis-identification of τ jets as leptons can be studied.
In order to check if loose selection requests on the lepton identification and isolation are
sufficient to exclude hadronic and semileptonic τ decay events the final selection, the following
test has been performed using the gg → bbA → τ τ sample with MA = 160 GeV . Leptons are
required to be isolated from other tracks (muons: no tracks with pT > 1 GeV in a cone with
∆R = 0.4; electrons: no tracks with pT > 1.5 GeV in a 0.02 < ∆R < 0.2 cone), electrons are
identified with the loose fixed threshold electron-id and a preliminary set of cuts is applied
(pTe,µ > 20 GeV , σ > 2, 100 < ∆φ < 170, #jets = [0, 1], #b-tags = [0, 1]). With these
selection criteria, the final mass plot contains about 15% of events with a feed-through of τ
jets (Fig. 9.13).
mcoll
Entries
157
Mean
153.9
RMS
52.62
mcoll_emuN
Entries
23
Mean
166.4
RMS
57.43
0.24
0.22
0.2
0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
0
100
200
300
400
500
600
700
800
900 1000
mτ τ [GeV]
Figure 9.13: Feed-through of τ jets using tracker isolation only and loose fixed threshold
electron-id. The white area are the total entries in the invariant mass plot, while the red
area are the entries with mis-identified leptons.
Clearly such high rate of feed-through is not acceptable for a precise estimate of the signal
contribution in the e-µ final state.
The largest fake contribution comes from the mis-identification of τ jet pions as electrons.
To reduce it, a stronger electron-id can been exploited. The highest purity is obtained with
the tight category based electron-id. Using it with the same set of cuts, the feed-through
drops at 5% level.
103
An additional request of a calo-based lepton isolation leads to a further reduction of the
feed-through. Requiring that the sum of the HCAL and ECAL deposits within a cone with
∆R = 0.4 around the muons is less than 4 GeV and that the energy deposit in ECAL and
HCAL is less than 0.05 and 0.2 times the electron super cluster energy respectively, the
feed-through rate lowers to 3%.
9.4.2
b-tagging
The capability to tag b jets is crucial for the background suppression and for the signal
process selection (gg → A and gg → bbA). Both bbA and tt̄ have two generated b quarks per
event. However, as can be seen in Fig. 9.6(d) the number of b tags per event is very different:
in almost 75% of tt̄ events there is at least one b-tag, while more than 85% of bbA events
have no b-tags.
This difference can be understood looking at the properties of the b quarks in the two
samples (Fig. 9.14).
0.06
Entries 1.236937e+07
Mean
RMS
0.05
56.44
37.31
bbA160
Entries
393994
Mean -0.001395
RMS
2.703
TTbar
event fraction
bbA160
Entries
393994
Mean
16.45
RMS
19.27
TTbar
event fraction
0.07
0.14
Entries 1.236937e+07
Mean
RMS
0.12
0.0006112
1.547
0.1
0.04
0.08
0.03
0.06
0.02
0.04
0.01
0.02
0
20
40
60
80
100
120
140
160
180 200
p [GeV]
-10
-8
-6
-4
-2
0
(a)
2
4
6
8
10
η
b
T,b
(b)
Figure 9.14: (a) pT distribution of the b partons in bbA (black) and tt̄ (red) samples. (b)
η distribution of b quarks in the same samples.
The b quarks in the tt̄ sample have a hard pT spectrum, peaking at ∼ 40 GeV , and a
narrow η distribution, while those in the signal sample peak at pT = 5 GeV and have a
broad η distribution. These topological characteristics imply that in bbA events, just a few
b quarks end up in a taggable reconstructed jet. The CMS b-tagging group has developed
a validation tool that evaluates the performance of b-tagging algorithms. The input to this
tool are the reconstructed jets with pT > 30 GeV and |η| < 2.4, which can be considered as
a sort of definition of taggable jets. The validation tool also makes use of an associator that
matches reconstructed jets to the parton that originated that jet2 . Using this associator, the
number of reconstructed jets matching a b quark per event has been studied and the result
is reported in Fig. 9.15.
The difference between the two samples is remarkable, showing that in 80% of the events
the b quarks in the bbA do not generate any reconstructed jet (this happens just in 10% of tt̄
events). Clearly it shows that the small number of b-tags in the associated production signal
events is not due to a low b-tagging efficiency but to the topological characteristics of the
2
Basically, this associator, called JetFlavourIdentifier looks if among the generated particles there is a b
quark in the jet cone extrapolated at the primary vertex.
104
event fraction
bbA160
Entries
2619
Mean
0.1409
RMS
0.3692
TTbar
Entries
36464
Mean
1.18
RMS
0.6985
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
2
4
6
8
10
12
14
16
18
20
number of b-quark jets
Figure 9.15: Number of reconstructed jets with pT > 30 GeV and |η| < 2.4 associated to
a b parton per event in bbA (black) and tt̄ (red) samples.
b partons. In fact, even with an ideal and full efficient b-tagging algorithm, the number of
b-tags per event could not exceed 0.2.
Actually, as b-tagging is a tough task, the performance of the various algorithms provided
by the b-tagging group3 have been privately evaluated (and cross-checked with the official
b-tagging validation tool) in order to find the most suitable for this analysis. It turns out that
the best performance are provided by the TrackCountingHighEfficiency algorithm (Table 9.4).
Table 9.4: b-tagging performance for the TrackCountingHighEfficiency algorithm on the tt̄
background and on the two signal production processes with MA = 160 GeV before (first
three rows) and after the preselection request of one e and one µ in the event (last three
rows).
sample
tt̄
gg → bbA
gg → A
tt̄ (e+µ)
gg→bbA (e+µ)
gg→A(e+µ)
# jets
b assoc
1.5
0.3
0.02
1.3
0.2
0.01
# jets
non-b assoc
2.8
1.7
2.1
0.8
0.4
0.8
# b-tags
1.5
0.3
0.14
1
0.2
0.05
b
effic.
74%
65%
70%
72%
68%
66%
ucsd
effic.
15%
9%
6%
13%
15%
6%
fake
rate
27%
45%
92%
10%
28%
86%
It is worth noting that the fake rate is higher in the signal samples than in the tt̄ and
that, after requiring a muon and an electron in the event, the fake rate is reduced, suggesting
that many fakes come from the mis-tagging of τ jets. Of course, in the gg → A sample, as no
b quarks are expected, the b-tags are almost all fakes. Nevertheless, before the preselection,
the total number of b-tags in the gg → A is half the one in the gg → bbA sample. After the
preselection request, this fraction is still high, being around 25%.
3
The algorithm tested were: TrackCountingHighEfficiency, TrackCountingHighPurity, JetProbablity and
ImpactParameterMVA.
105
These results show that the use of the b-tagging in this analysis is not trivial and that
it has to be accurately considered. In particular, a request of one btag in the event highly
reduces the gg → bbA sample, while it suppresses, even if not completely, the gg → A.
Actually, in both the production processes, most of the signal has no b-tags and, in order to
reduce the tt̄ a b-tagging veto can be exploited.
9.4.3
Missing Transverse Energy measurement
metres_JPT−RG
Entries
2619
Mean
0.612
RMS
13.49
0.08
metres_I5−RG
Entries
2619
Mean
5.984
RMS
17.24
0.07
0.06
mcoll_JPT
event fraction
event fraction
/ T resolution is a key issue for this analysis because it is
As already said in §9.2.3, the E
the most delicate term in the collinear approximation invariant mass formula. Since Type/ T is too rough for this analysis, several jet correction algorithms4 have been tested in
0 E
/ T resolution. The best results are obtained with the combination of
order to improve the E
the Zero Suppression and the Jet Plus Track correction (JetPlusTrackZSPCorJetIcone5 ). A
comparison between the JetPlusTrackZSPCorJetIcone5 and the Monte Carlo correction for
Iterative Cone 5 jets (MCJetCorJetIcone5 ) is reported in Fig. 9.16.
Entries
Mean
RMS
χ2 / ndf
Constant
Mean
Sigma
0.24
0.22
0.2
0.18
mcoll_I5
Entries
Mean
RMS
χ2 / ndf
Constant
Mean
Sigma
0.16
0.05
0.14
0.12
0.04
67
156.5
49.11
0.01964 / 5
0.2373 ± 0.3126
152.2 ± 54.0
44.75 ± 52.60
67
189.1
82.12
0.1273 / 10
0.1387 ± 0.2182
179.3 ± 104.3
66.34 ± 93.89
0.1
0.03
0.08
0.06
0.02
0.04
0.01
0
−100
0.02
−80
−60
−40
−20
0
(a)
20
40
60
80
100
∆ ET [GeV]
0
0
100
200
300
400
500
600
700
800
900 1000
mτ τ [GeV]
(b)
/ T corrected with JetPlusTrackZSPCorJetIcone5 (blue)
Figure 9.16: Comparison between E
/ T with respect to the
and with MCJetCorJetIcone5 (red). (a) Residue of the reconstructed E
/ T calculated at generator level. (b) Invariant mass plot using the two correction algorithms
E
(sample: gg → bbA, with MA = 160 GeV , cuts used will be described in §9.5.2 - soft strategy).
/ T calculated at generator level (Fig. 9.16(a)) has shorter
The residue with respect to the E
tails for the JetPlusTrackZSPCorJetIcone5 correction. Also, it is less biased, having a mean
value close to zero (0.6 for JetPlusTrackZSPCorJetIcone5, 6.0 for MCJetCorJetIcone5 ).
Consequently, the invariant mass distribution (Fig. 9.16(b)) obtained with the JetPlusTrackZSPCorJetIcone5 is narrower with respect to MCJetCorJetIcone5 (Gaussian Fit σ
equal to 44.8 and 66.3). Such improvement is fundamental to be able to distinguish the
signal peak on top of the background contributions.
Only drawback of the JetPlusTrackZSPCorJetIcone5 correction seems to be a tendency
to underestimate the mean Higgs mass value (equal to 152.2 GeV for a generated 160 GeV
Higgs in the example above). Possible improvements for this correction algorithm are being
investigated.
4
The tested jet corrections are: MCJetCorJetIcone5, MCJetCorJetMcone5, MCJetCorJetFastjet6 and JetPlusTrackZSPCorJetIcone5
106
9.5
9.5.1
Event selection
Summary of Selection Cuts
A review of the variables that can be used to apply cuts is the following:
• Trigger: the trigger request of single isolated or relaxed electron or muon has been
described in §9.2.1
• µ,e (qµ · qe < 0): in order to suppress the backgrounds with more than two leptons in
the final state, only the events with exactly one electron and one muon with opposite
charges are considered.
• Iso + Id: strong identification and isolation requests are fundamental to reduce the
feed-through of τ -jets, as discussed in §9.4.1.
• pT,e, pT,µ: a lower cut on the lepton pT is needed to suppress the contribution from
the Z/γ ∗ → τ τ background (Fig. 9.4(a) and 9.4(b)). This cut has a small effect on the
invariant mass distribution: the harder the cut, the higher values it pushes the mass.
• σ: both the signal and the backgrounds peak at combined impact parameter significance
values of ∼ 2 (Fig. 9.4(d)). Nevertheless, the signal shows longer tails and a minimum
cut on σ is useful to reject many background events (mostly tt̄). Cutting on high values
of σ is not advisable since it would reject too many signal events and since it would
degrade the invariant mass distribution because the requirement of highly displaced
leptons is in contrast with the collinearity assumption used to reconstruct the mass.
• #jets: The jet activity of the signal samples is much lower (∼ 74% of events with no
jets for gg → bbA and ∼ 62% for gg → A) with respect to the tt̄ and W t backrounds
(∼ 10% and ∼ 13%) while it is slightly higher than in the W W and Z/γ ∗ → τ τ (∼ 80%
and ∼ 84%). Therefore, a veto on the number of jets is useful to reduce tt̄ and W t
without rejecting many signal events.
• #b-tags: As discussed in §9.4.2, the request on the number of b-tags is the key cut
for this analysis. Several strategies based on this selection criterion can be developed
in order to suppress a particular background or to select the signal from the associated
production process. These strategies will be discussed in the next section.
• ∆φmin: As shown in Fig. 9.4(c), when the τ s decay from the same neutral boson
(signal and Drell-Yan samples) the directions of the final state leptons tend to be backto-back. In the other cases, the directions are not correlated, and the ∆φ distribution
is almost flat. A minimum cut on ∆φ is thus useful to reduce the contribution from all
the backgrounds except Z/γ ∗ .
• ∆φmax: On the other hand, as discussed in §9.2.6, if the two leptons are exactly backto-back, the collinear approximation is not valid. Therefore, a cut on the maximum
value of ∆φ is needed. Of course, if this cut value is very high, many signal events are
not rejected but their mass is not accurately reconstructed; conversely, if the cut is too
low, the reconstructed mass has a better resolution, but most of the signal events are
lost.
107
• 0 < x < 1: Another consistency check of the collinear approximation is the reconstructed τ momentum fractions: x < 0 and x > 1 are unphysical values. This request
is also useful to reduce some backgrounds (see Fig. 9.7).
9.5.2
Analysis Strategies
The application of the b-tagging selection cut is not obvious as it can lead to different signal
and background contributions. Therefore, three different strategies have been developed:
• soft strategy: #b-tags = [0, 1]. Inclusive approach: keeps high statistics for the signal
and applies no severe reduction of the background. A gluon fusion signal contribution
survives also in this case (∼ 19%).
• b-one strategy: #b-tags = [1]. This strategy has an exclusive approach, as it suppresses the Drell-Yan background and the gg → A signal, and is dominated by the tt̄
and gg → bbA contributions.
• b-zero strategy: #b-tags = [0]. A selective approach is accomplished by highly
reducing the tt̄ background. The signal has a significant contribution from both the
production processes (∼ 17% of the total).
The list of cuts used for each strategy is summarized in Table 9.5.
Table 9.5: Selection cuts for the three strategies.
cut
trigger
eId
Iso
pT,e > [GeV ]
pT,µ > [GeV ]
σ>
#jets
#b-tags
∆φmin [◦ ]
∆φmax [◦ ]
xe,µ
b-one
b-zero
soft
single e OR µ, iso OR relaxed
tight category based
track and calo based
28
32
30
23
27
25
2
2
2
[0,1]
[0,1]
[0,1]
[1]
[0]
[0,1]
0
120
100
175
175
170
(0,1)
(0,1)
(0,1)
The samples can be grouped into three categories according to the shape of their invariant
mass plot:
• z-shape: all the backgrounds with a Z boson: Z/γ ∗ , bbll, W Z, ZZ. It is dominated
by the Drell-Yan contribution.
• tt̄-shape: all the backgrounds with two W in the final state: tt̄, tW , W W . Main
contribution is tt̄.
• signal: gg→bbA and gg→A samples
For each category, the invariant mass distribution after the selection cuts are reported in
Fig. 9.17-9.19, while the cut efficiencies are in Table 9.6-9.8.
108
tt-shape background
entries/25 GeV
entries/25 GeV
z-shape background
sum
DY
60
bbll
WZ
50
ZZ
sum
45
ttbar
40
Wt
35
WW
30
40
25
30
20
15
20
10
10
0
0
5
100
200
300
400
500
600
700
800
0
0
900 1000
mτ τ [GeV]
100
200
300
400
(a)
600
700
800
900 1000
mτ τ [GeV]
(b)
signal+background
A - mA =160 GeV
gg->bbA
gg->A
25
20
entries/25 GeV
signal
entries/25 GeV
500
all
100
bck sum
bckz
80
bckt
15
60
10
40
5
20
0
0
100
200
300
400
500
600
700
800
0
0
900 1000
mτ τ [GeV]
100
200
300
400
(c)
500
600
700
800
900 1000
mτ τ [GeV]
(d)
Figure 9.17: Invariant mass plot after the selection cuts for the soft strategy: z-shape(a)
and tt̄-shape(b) backgrounds, signal contribution(c) and sum of signal and background(d).
tt-shape background
entries/25 GeV
entries/25 GeV
z-shape background
sum
5
DY
bbll
WZ
4
ZZ
sum
30
ttbar
Wt
25
WW
20
3
15
2
10
1
0
0
5
100
200
300
400
500
600
700
800
0
0
900 1000
mτ τ [GeV]
100
200
300
400
(a)
600
700
800
900 1000
mτ τ [GeV]
(b)
signal+background
A - mA =160 GeV
gg->bbA
gg->A
12
10
8
entries/25 GeV
signal
entries/25 GeV
500
all
35
bck sum
30
bckz
25
bckt
20
6
15
4
10
2
0
0
5
100
200
300
400
500
(c)
600
700
800
900 1000
mτ τ [GeV]
0
0
100
200
300
400
500
600
700
800
900 1000
mτ τ [GeV]
(d)
Figure 9.18: Invariant mass plot after the selection cuts for the b-one strategy: z-shape(a)
and tt̄-shape(b) backgrounds, signal contribution(c) and sum of signal and background(d).
109
tt-shape background
entries/25 GeV
entries/25 GeV
z-shape background
sum
60
DY
bbll
50
WZ
ZZ
sum
25
ttbar
Wt
20
WW
40
15
30
10
20
5
10
0
0
100
200
300
400
500
600
700
800
0
0
900 1000
mτ τ [GeV]
100
200
300
400
(a)
600
700
800
900 1000
mτ τ [GeV]
(b)
signal+background
A - mA =160 GeV
gg->bbA
gg->A
20
18
16
14
12
entries/25 GeV
signal
entries/25 GeV
500
all
80
bck sum
70
bckz
60
bckt
50
10
40
8
30
6
20
4
10
2
0
0
100
200
300
400
500
(c)
600
700
800
900 1000
mτ τ [GeV]
0
0
100
200
300
400
500
600
700
800
900 1000
mτ τ [GeV]
(d)
Figure 9.19: Invariant mass plot after the selection cuts for the b-zero strategy: z-shape(a)
and tt̄-shape(b) backgrounds, signal contribution(c) and sum of signal and background(d).
110
Table 9.6: Total andR relative selection cut efficiencies for the soft strategy. Nevents is the
number of events for L = 10 f b−1 .
sample
Nevents
ǫ(trigger)[%]
ǫ(e± ,µ∓ ,eId)[%]
ǫ(Iso)[%]
ǫ(pT,e )[%]
ǫ(pT,µ )[%]
ǫ(σ)[%]
ǫ(#jets)[%]
ǫ(#b-tags)[%]
ǫ(∆φmin )[%]
ǫ(∆φmax )[%]
ǫ(xe,µ )[%]
Nevents
sample
Nevents
ǫ(trigger)[%]
ǫ(e± ,µ∓ ,eId)[%]
ǫ(Iso)[%]
ǫ(pT,e )[%]
ǫ(pT,µ )[%]
ǫ(σ)[%]
ǫ(#jets)[%]
ǫ(#b-tags)[%]
ǫ(∆φmin )[%]
ǫ(∆φmax )[%]
ǫ(xe,µ )[%]
Nevents
Z/γ ∗
75590000
100 (100)
0.59 (0.6)
0.20 (32.9)
0.03 (13.1)
5 · 10−3 (20.7)
2 · 10−3 (45.9)
2 · 10−3 (93.4)
2 · 10−3 (100)
2 · 10−3 (85.0)
1 · 10−3 (45.8)
5 · 10−4 (35.2)
235.6
sample
Nevents
ǫ(trigger)[%]
ǫ(e± ,µ∓ ,eId)[%]
ǫ(Iso)[%]
ǫ(pT,e )[%]
ǫ(pT,µ )[%]
ǫ(σ)[%]
ǫ(#jets)[%]
ǫ(#b-tags)[%]
ǫ(∆φmin )[%]
ǫ(∆φmax )[%]
ǫ(xe,µ )[%]
Nevents
gg→bbA
259080
29.24 (29.2)
4.00 (13.6)
1.34 (33.6)
0.66 (49.1)
0.30 (44.7)
0.18 (60.5)
0.17 (95.1)
0.17 (100)
0.17 (98.5)
0.08 (46.6)
0.03 (44.1)
89.1
bbll
1460800
68.94 (17.0)
1.48 (5.5)
0.34 (10.4)
0.10 (57.8)
0.01 (57.6)
7 · 10−3 (32.5)
5 · 10−3 (84.2)
5 · 10−3 (100)
4 · 10−3 (75.0)
3 · 10−3 (87.5)
1 · 10−3 (14.3)
10.6
tt̄
8400000
100 (100)
6.50 (6.4)
0.62 (9.5)
0.42 (68.4
0.31 (72.1)
0.08 (25.5)
0.03 (43.7)
0.03 (100)
0.03 (74.1)
0.02 (81.9)
5 · 10−3 (22.2)
379.1
gg→A
40640
28.43 (28.4)
4.07 (14.3)
1.40 (34.5)
0.70 (50.0)
0.35 (50.0)
0.22 (62.2)
0.19 (88.7)
0.19 (100)
0.18 (93.6)
0.10 (55.9)
0.05 (51.7)
21.4
WZ
499000
16.98 (68.9)
0.93 (2.2)
0.10 (23.1)
0.06 (28.2)
0.03 (11.6)
0.01 (60.2)
9 · 10−3 (81.5)
9 · 10−3 (100)
7 · 10−3 (68.9)
6 · 10−3 (71.2)
1 · 10−3 (26.9)
4.1
tW
620000
30.81 (22.3)
3.63 (11.3)
0.75 (30.2)
0.58 (67.8)
0.45 (74.0)
0.15 (31.8)
0.12 (96.3)
0.12 (100)
0.10 (80.6)
0.08 (79.2)
0.01 (4.7)
81.2
ZZ
499000
12.45 (12.4)
0.40 (3.2)
0.05 (12.6)
0.02 (44.1)
8 · 10−3 (36.7)
4 · 10−3 (45.4)
3 · 10−3 (80.0)
3 · 10−3 (100)
1 · 10−3 (50.0)
1 · 10−3 (100)
0 (0)
0
WW
1143000
22.32 (22.3)
2.52 (11.3)
0.76 (30.2)
0.52 (67.8)
0.38 (74.0)
0.12 (31.8)
0.12 (96.3)
0.12 (100)
0.09 (80.6)
0.08 (79.2)
4 · 10−3 (4.7)
40.5
111
Table 9.7: Total andR relative selection cut efficiencies for the b-one strategy. Nevents is the
number of events for L = 10 f b−1 .
sample
Nevents
ǫ(trigger)[%]
ǫ(e± ,µ∓ ,eId)[%]
ǫ(Iso)[%]
ǫ(pT,e )[%]
ǫ(pT,µ )[%]
ǫ(σ)[%]
ǫ(#jets)[%]
ǫ(#b-tags)[%]
ǫ(∆φmin )[%]
ǫ(∆φmax )[%]
ǫ(xe,µ )[%]
Nevents
sample
Nevents
ǫ(trigger)[%]
ǫ(e± ,µ∓ ,eId)[%]
ǫ(Iso)[%]
ǫ(pT,e )[%]
ǫ(pT,µ )[%]
ǫ(σ)[%]
ǫ(#jets)[%]
ǫ(#b-tags)[%]
ǫ(∆φmin )[%]
ǫ(∆φmax )[%]
ǫ(xe,µ )[%]
Nevents
112
Z/γ ∗
75590000
100 (100)
0.59 (0.6)
0.19 (32.9)
0.03 (16.3)
7 · 10−3 (24.4)
3 · 10−3 (43.2)
3 · 10−3 (94.0)
1 · 10−5 (0.3)
1 · 10−5 (100)
1 · 10−5 (100)
0 (0)
0
sample
Nevents
ǫ(trigger)[%]
ǫ(e± ,µ∓ ,eId)[%]
ǫ(Iso)[%]
ǫ(pT,e )[%]
ǫ(pT,µ )[%]
ǫ(σ)[%]
ǫ(#jets)[%]
ǫ(#b-tags)[%]
ǫ(∆φmin )[%]
ǫ(∆φmax )[%]
ǫ(xe,µ )[%]
Nevents
gg→bbA
259080
29.24 (29.2)
4.00 (13.7)
1.34 (33.6)
0.73 (54.5)
0.36 (49.1)
0.22 (61.2)
0.21 (95.6)
0.02 (09.5)
0.02 (100 )
0.02 (92.3)
0.01 (69.4)
33.3
bbll
1460800
68.94 (68.9)
1.48 (2.2)
0.34 (23.1)
0.11 (33.2)
0.02 (15.5)
0.01 (60.3)
9 · 10−3 (85.9)
2 · 10−3 (18.8)
2 · 10−3 (100)
2 · 10−3 (100)
7 · 10−4 (42.4)
10.6
tt̄
8400000
100 (100)
6.50 (6.5)
0.62 (9.5)
0.44 (71.7)
0.33 (75.1)
0.08 (25.2)
0.04 (43.8)
0.02 (51.4)
0.02 (100)
0.02 (93.8)
4 · 10e−03 (20.3)
286.8
gg→A
40640
28.43 (28.4)
4.07 (14.3)
1.40 (34.5)
0.78 (55.4)
0.42 (53.6)
0.26 (61.9)
0.23 (88.0)
5 · 10−3 (2.2)
5 · 10−3 (100)
5 · 10−3 (100)
3 · 10−3 (66.7)
1.4
WZ
499000
17.00 (17.0)
0.93 (5.5)
0.10 (10.4)
0.06 (63.2)
0.04 (58.1)
0.01 (33.3)
0.01 (83.7)
0 (0)
0 (0)
0 (0)
0 (0)
0
tW
620000
30.81 (30.8)
3.63 (11.8)
0.75 (20.7)
0.60 (80.4)
0.48 (79.4)
0.16 (32.7)
0.13 (79.9)
0.06 (46.3)
0.06 (100)
0.05 (92.2)
0.01 (21.5)
64.4
ZZ
499000
12.45 (12.5)
0.40 (3.2)
0.05 (12.6)
0.02 (47.1)
0.01 (40.6)
4 · 10−3 (46.2)
3 · 10−3 (66.7)
0 (0)
0 (0)
0 (0)
0 (0)
0
WW
1143000
22.32 (22.3)
2.52 (11.3)
0.76 (30.2)
0.55 (72.4)
0.43 (77.2)
0.14 (31.8)
0.13 (96.5)
2 · 10e−03 (1.8)
2 · 10e−03 (100)
2 · 10e−03 (90.0)
2 · 10e−04 (11.1)
2.7
Table 9.8: Total andR relative selection cut efficiencies for the b-zero strategy. Nevents is the
number of events for L = 10 f b−1 .
sample
Nevents
ǫ(trigger)[%]
ǫ(e± ,µ∓ ,eId)[%]
ǫ(Iso)[%]
ǫ(pT,e )[%]
ǫ(pT,µ )[%]
ǫ(σ)[%]
ǫ(#jets)[%]
ǫ(#b-tags)[%]
ǫ(∆φmin )[%]
ǫ(∆φmax )[%]
ǫ(xe,µ )[%]
Nevents
sample
Nevents
ǫ(trigger)[%]
ǫ(e± ,µ∓ ,eId)[%]
ǫ(Iso)[%]
ǫ(pT,e )[%]
ǫ(pT,µ )[%]
ǫ(σ)[%]
ǫ(#jets)[%]
ǫ(#b-tags)[%]
ǫ(∆φmin )[%]
ǫ(∆φmax )[%]
ǫ(xe,µ )[%]
Nevents
Z/γ ∗
75590000
100 (100)
0.59 (0.6)
0.19 (32.9)
0.02 (10.3)
3 · 10−3 (16.4)
2 · 10−3 (49.4)
2 · 10−3 (90.7)
2 · 10−3 (99.3)
1 · 10−3 (75.2)
7 · 10−4 (63.3)
2 · 10−4 (34.8)
182.4
sample
Nevents
ǫ(trigger)[%]
ǫ(e± ,µ∓ ,eId)[%]
ǫ(Iso)[%]
ǫ(pT,e )[%]
ǫ(pT,µ )[%]
ǫ(σ)[%]
ǫ(#jets)[%]
ǫ(#b-tags)[%]
ǫ(∆φmin )[%]
ǫ(∆φmax )[%]
ǫ(xe,µ )[%]
Nevents
gg→bbA
259080
29.24 (29.2)
4.00 (13.7)
1.34 (33.6)
0.60 (44.5)
0.25 (41.2)
0.15 (59.0)
0.14 (94.4)
0.13 (91.8)
0.12 (98.4)
0.08 (66.8)
0.03 (39.1)
83.8
bbll
1460800
68.9 (68.9)
1.48 (2.2)
0.34 (23.1)
0.08 (24.1)
7 · 10−3 (9.0)
4 · 10−3 (55.9)
3 · 10−3 (76.3)
1 · 10−3 (70.5)
2 · 10−3 (72.1)
1 · 10−3 (90.3)
4 · 10−4 (25.0)
5.3
tt̄
8400000
100 (100)
6.50 (6.5)
0.62 (9.5)
0.40 (65.5)
0.28 (69.2)
0.07 (25.8)
0.03 (43.9)
0.02 (49.2)
0.01 (65.0)
9 · 10−3 (89.3)
2 · 10−3 (23.0)
167.6
gg→A
40640
28.42 (28.4)
4.07 (14.3)
1.40 (34.5)
0.64 (45.4)
0.30 (46.6)
0.18 (61.2)
0.16 (86.7)
0.15 (97.5)
0.14 (89.4)
0.10 (70.1)
0.04 (43.3)
17.0
WZ
499000
17.0 (17.0)
0.93 (5.5)
0.10 (10.4)
0.05 (53.0)
0.03 (55.4)
9 · 10−3 (31.1)
7 · 10−3 (84.4)
7 · 10−3 (100)
5 · 10−3 (63.0)
4 · 10−3 (94.1)
8 · 10−4 (18.8)
4.1
tW
620000
30.8 (30.8)
3.63 (11.8)
0.75 (20.7)
0.56 (75.0)
0.42 (74.9)
0.14 (32.7)
0.11 (79.9)
0.06 (53.8)
0.05 (78.0)
0.04 (86.8)
0.01 (14.0)
30.8
ZZ
499000
12.5 (12.5)
0.40 (3.2)
0.05 (12.6)
0.02 (41.2)
6 · 10−3 (28.6)
3 · 10−3 (50.0)
2 · 10−3 (75.0)
2 · 10−3 (100)
7 · 10−4 (33.3)
7 · 10−4 (100)
0 (0)
0
WW
1143000
22.3 (22.3)
2.52 (11.3)
0.76 (30.2)
0.48 (63.2)
0.34 (71.6)
0.11 (31.9)
0.11 (96.3)
0.10 (98.1)
0.08 (73.2)
0.07 (88.0)
5 · 10−3 (6.9)
52.7
113
9.6
9.6.1
Results
Fitting with known background shapes
For all the strategies, after the selection cuts are applied, a significant signal contribution
survives. The significance of the observed Higgs events can be estimated either through a
simple counting of background and signal events or through a fit to discriminate the signal
contribution from the background contaminations.
In order to disentangle the signal contribution from the background, a first fitting strategy [64], which assumes a complete knowledge of the background shapes, has been developed.
The two background contributions (z-shape and tt̄-shape) are first fitted separately with
a Landau function5 . The resulting fit functions have well distinct parameters: the z-shape
Landau peaking at values close the Z mass and being quite sharp, while the tt̄-shape Landau
peaking at higher values (about 200 GeV ) and having a large width. The signal contribution
is parametrized as a Gaussian.
The three contributions (z-shape, tt̄-shape, signal) are then summed and a global fit on
the resulting histogram is performed. In this fit, for each selection strategy, the values of the
most probable value (MPV) and the width of the background Landau functions are assumed
known and thus are used as fixed parameters. The free parameters are the background
weights (Wz , Wtt̄ ) and the signal mean (mA ), width (σA ) and weight (WA ). Results are
reported in Fig. 9.20-9.21.
In all cases, the weights of the three contributions are consistent with one within the
errors, the mass is compatible with the expected value of mA = 160 GeV , while the signal
width is slightly underestimated. The resulting significances [65] are summarized in Table 9.9.
Table 9.9: Significances for the three strategies as estimated from event counting
or from
R
the fit, with and without statistical errors (mA = 160 GeV , tan β = 30 and L = 10 f b−1 ).
strategy
σcount
σcount+stat
σf it
σf it+stat
9.6.2
b-one
1.7
1.2
1.8
1.1
b-zero
4.6
3.3
5.3
2.7
soft
4.6
3.3
5.3
3.2
Toy Monte Carlo
The uncertainties arising from the fitting procedure are evaluated by performing a set of toy
experiments (Monte Carlo trials). For simplicity, they have been carried out for the soft
strategy only. The toy experiments are implemented with the RooFit package [63].
The sum of the z-shape, tt̄-shape and signal fit functions in Fig. 9.20 is taken as the
probability density function (pdf) for the toy Monte Carlo.
At each trial, a Monte Carlo data sample isRrandomly built from the pdf. The sample yield
is equal to the number of events expected at L = 10 f b−1 . A global fit is then performed
5
in the b-one strategy case, the z-shape background is suppressed and therefore its content is also added
to the tt̄-shape contribution.
114
mcoll
Mean
125.3
RMS
51.1
χ2 / ndf 77.34 / 37
385.4 ± 38.1
A:
MPV: 87.84 ± 2.18
w:
16.16 ± 1.25
70
60
50
tt -shape background fit
entries/25 GeV
entries/25 GeV
z-shape background fit
40
50
40
mcoll
Mean
317
RMS
181
χ2 / ndf
56.3 / 37
244.3 ± 16.4
A:
200.7 ± 5.4
MPV:
w:
53.67 ± 2.94
30
30
20
20
10
10
entries/25 GeV
signal fit
30
25
00
100 200 300 400 500 600 700 800 900 1000
mτ τ [GeV]
mcoll
Mean
158.7
RMS
56.1
2
χ / ndf
28.11 / 37
24.03 ± 2.87
A:
m:
154.2 ± 4.3
σ:
44 ± 3.0
20
mcoll
Mean
120
100
80
15
100 200 300 400 500 600 700 800 900 1000
mτ τ [GeV]
combined fit
entries/25 GeV
0
0
RMS
χ 2 / ndf
W z:
Wtt:
WA:
mA
σA
241
168.3
53.26 / 35
0.9731 ± 0.1314
0.9677 ± 0.0670
1.294 ± 0.307
153.3 ± 9.4
35.94 ± 5.79
60
10
40
5
20
0
0
100 200 300 400 500 600 700 800 900 1000
mτ τ [GeV]
00
100 200 300 400 500 600 700 800 900 1000
mτ τ [GeV]
Figure 9.20: Fit with known background shapes for the soft strategy.
115
(a)
(b)
Figure 9.21: Global fit with known background shapes for the b-one(a) and b-zero(b)
strategies.
on the sample: the Landau parameters are fixed, while weights and signal mass and width
are let free.
The results for 5000 toy experiments are reported in Fig. 9.22-9.23. The signal parameters
(yield, mean and sigma) do not show worrisome biases with respect to the nominal values.
The background yields are reasonably consistent with the expectations.
9.6.3
Mass Scan
The same analysis hasR been performed for different values of mA , from 140 GeV to 800 GeV
with tan β = 30 and L = 10 f b−1 . The results in terms of significance are summarized in
Table 9.10.
Table 9.10: Significance for the 140 ≤ mA ≤ 300 GeV
from event counting or from the fit,
R
with and without statistical error (tan β = 30 and L = 10 f b−1 ).
mA [GeV ]
σcount
σcount+stat
σf it
σf it+stat
140
2.4
1.7
2.4
1.5
160
4.6
3.3
5.3
3.2
200
3.7
2.7
4.1
2.1
300
2.2
1.6
-
The highest sensitivity is reached in the range 160 ≤ mA ≤ 200 GeV with a significance
(with statistical errors) of the order of 2-3σ. For mA > 200 GeV the production cross section
decreases fast, and, even if the background is suppressed, the signal contribution is small.
A significance estimate based on event counting is still possible up to mA = 300 GeV . At
lower mass values, instead, even if the production cross section is higher, a large Drell-Yan
116
Last Model Fit
events/25 GeV
events/25 GeV
PDF models
80
PDF
Signal − Nevs=105.9
Bckg1 − Nevs=244.2
Bckg2 − Nevs=484.2
Model − Nevs=834.2
70
60
100
80
60
50
40
40
30
20
20
10
0
0
100
200
300
400
500
600
700
800
0
0
900 1000
mττ [GeV]
100
200
300
400
(a)
500
600
700
800
900 1000
mττ [GeV]
(b)
HPullYieldBckg1
Entries
5000
Mean
−0.2781
RMS
1.063
2
χ / ndf
65.86 / 17
Constant
943.1 ± 17.0
Mean
−0.2925± 0.0153
Sigma
1.018 ± 0.011
Pull Yield Bckg1
900
800
700
HPullYieldBckg2
Pull Yield Bckg2
Entries
Mean
RMS
χ2 / ndf
Constant
Mean
Sigma
1000
800
5000
−0.02084
0.9273
23.75 / 16
1059 ± 18.9
−0.03004± 0.01313
0.9143 ± 0.0098
600
600
500
400
400
300
200
200
100
0
−10
−8
−6
−4
−2
0
(c)
2
4
6
8
10
0
−10
−8
−6
−4
−2
0
2
4
6
8
10
(d)
Figure 9.22: Toy Monte Carlo assuming the background shapes as known. (a): pdf shape
for the toy Monte Carlo trials. (b): fit for the last toy sample. (c): pull distribution for the
z-shape background yield. (d): pull distribution for the tt̄-shape background yield.
117
HPullMeanSignal
Entries
5000
Mean
−0.2568
RMS
1.386
2
χ / ndf
133.2 / 29
Constant
744.5 ± 15.0
Mean
−0.2161± 0.0181
Sigma
1.217 ± 0.017
Pull Mean Signal
800
700
600
HPullSigmaSignal
Entries
5000
Mean
0.02435
RMS
1.301
2
χ / ndf
231.4 / 24
Constant
896.3 ± 17.9
Mean
0.1804 ± 0.0160
Sigma
1.013 ± 0.014
Pull Sigma Signal
1000
800
600
500
400
400
300
200
200
100
0
−10
−8
−6
−4
−2
0
2
4
6
8
0
−10
10
−8
−6
−4
−2
(a)
0
2
4
6
8
10
(b)
HPullYieldSignal
Entries
5000
Mean
0.2907
RMS
1.089
2
χ / ndf
80.25 / 18
Constant
944.4 ± 17.5
Mean
0.339 ± 0.015
Sigma
1.011 ± 0.012
Pull Yield Signal
1000
800
600
400
200
0
−10
−8
−6
−4
−2
0
2
4
6
8
10
(c)
Figure 9.23: Pull distributions for the signal parameters obtained with the fit with known
background shapes: mean(a), sigma(b) and yield(c).
background contamination leads to a lower sensitivity.
9.6.4
Fit constraining the ratio of the background yields
The previous results rely on a very good knowledge of the background shapes. Such scenario
is probably too optimistic, since the background shapes with real data may differ from those
extracted from Monte Carlo. In addition, the background shapes are affected by the choice of
the selection cuts, and cannot be immediately inferred from an analysis with loose selection
criteria.
Within the CMS collaboration, data-driven methods to estimate the background shapes
have already been developed and could be applied to the present analysis[66]. Yet, they
would not provide a perfect, ideal knowledge of the background shapes. Therefore, it has to
be proven that the signal can be extracted from a fit where the background shapes are also
free parameters.
A possible strategy is the following. The samples are selected with a set of loose cuts (loose
strategy, see Table 9.11), leading to the results in Fig. 9.24. The background fit parameters
differ from the soft strategy by less then 20%. These values are used as starting point for
a fit where the background shapes are free parameters. The fit reaches a convergence when
a Gaussian constraint on the ratio between the number of z-shape and tt̄-shape events is
provided. This ratio can be obtained comparing the number of events with the loose strategy
for Monte Carlo and real data, and assuming that the cut efficiencies for the soft strategy
scale consistently for the simulated and measured data.
The result is reported in Fig. 9.25 and Table 9.12. All the parameters are consistent
118
tt-shape background
2000
sum
1800
DY
1600
bbll
entries/25 GeV
entries/25 GeV
z-shape background
WZ
1400
ZZ
sum
350
ttbar
300
Wt
WW
250
1200
1000
200
800
150
600
100
400
50
200
0
0
100
200
300
400
500
600
700
800
0
0
900 1000
mτ τ [GeV]
(a)
2000
1800
1600
200
300
400
500
600
700
800
900 1000
mτ τ [GeV]
(b)
mcoll
tt-shape background fit
Mean
112
RMS
68.82
χ 2 / ndf
1547 / 37
9219 ± 170.3
A:
76.46 ± 0.44
MPV:
w:
13.79 ± 0.18
entries/25 GeV
entries/25 GeV
z-shape background fit
100
1400
350
300
mcoll
Mean
RMS
χ2 / ndf
A:
MPV:
w:
324.1
206.3
106.4 / 37
1927 ± 42.5
195.2 ± 2.2
65.27 ± 1.21
250
1200
1000
200
800
150
600
100
400
50
200
0
0
0
0
100 200 300 400 500 600 700 800 900 1000
mτ τ [GeV]
100 200 300 400 500 600 700 800 900 1000
mτ τ [GeV]
(c)
Figure 9.24: Background shapes obtained with loose selection cuts.
119
Table 9.11: Summary of loose strategy selection cuts.
cut
trigger
eId
Iso
pT,e > [GeV ]
pT,µ > [GeV ]
σ>
#jets
#b-tags
∆φmin [◦ ]
∆φmax [◦ ]
xe,µ
loose
single e OR µ, iso OR relaxed
tight category based
track and calo based
20
20
0
[0,2]
[0,1]
0
176
(0,1)
with the expected values within the errors, which, not surprisingly, are quite large on the
yield estimates. Therefore, this fit strategy is reliable if the background parameters can be
estimated within ∼ 20% of the true values for data after the final selection cuts.
events/25 GeV
combined fit
Data
Fit
Signal:
Yield=186.6± 88.0
mA=152.1± 9.2
σ= 36.4± 5.9
z−shape:
Yield=221.8± 38.5
MPV= 84.2± 4.8
w= 14.5± 2.5
tt−shape:
Yield=452.6± 73.6
MPV=217.6± 29.2
w= 57.2± 7.8
120
100
80
60
40
20
0
0
100
200
300
400
500
600
700
800
900 1000
mτ τ [GeV]
Figure 9.25: Fit with constraint on the background yield ratio for the soft strategy.
This fitting procedure has been also tested with toy Monte Carlo experiments: some biases on the fit parameters are caused by the bigger freedom on input parameters and by the
yield ratio constraint pushing the two backgrounds in the same direction. In particular, the
signal yield tends to be overestimated.
In conclusion, a possible strategy with free background shapes has also been identified.
120
Table 9.12: Parameters obtained from the fit with constraint on the background yield ratio
and corresponding expected values.
signal (exp)
signal (fit)
z-shape (exp)
z-shape (fit)
tt̄-shape (exp)
tt̄-shape (fit)
Yield
105.9±10.3
186.6±88.0
244.2±15.6
221.8±38.5
484.2±22.0
452.6±73.6
mA /MPV
154.2±4.3
152.1±9.2
87.8±2.2
84.2±4.8
200.7±5.4
217.6±29.2
σA /width
44.0±3.0
36.4±5.9
16.2±1.3
14.5±2.5
53.7±2.9
57.2±7.8
It seems to be sensitive to a signal excess already with 10 f b−1 luminosity; the fit converges
to the expected values if an input reasonable knowledge of the background shapes and an
additional constraint to the fit are provided.
121
Conclusions
The A → τ τ decay is a powerful channel for the MSSM Higgs discovery. Significances of 2-3σ
/ T ) in the mass range
have been estimated for the exclusive leptonic channel (A → τ τ → eµE
−1
140-300 GeV and for tan β = 30 already at 10 f b integrated luminosity (Fig. 9.26).
σ for L=10fb-1, tanβ=30
Significance
6
significance from counting
5
significance from fit
4
3
2
1
0
140
160
180
200
220
240
260
280
300
mA [GeV]
Figure 9.26: Significance as a function of mA (tan β = 30 and
errors are included.
R
L = 10 f b−1 ). Statistical
The efficiency of each reconstruction and selection step has been evaluated. Key points
of the selection strategies have been identified: b-tagging, missing transverse energy, lepton
identification and isolation. They are potential sources of systematic effects which will need
/ T measurement,
to be properly estimated. The dominant uncertainty is expected from the E
which will depend on the actual calorimeter response and the applied missing energy algorithm. Such issues, first addressed in the TDR, are still under study within the collaboration.
Global fits of the final selected samples have been performed to extract possible signal
events from background. Various fit strategies have been proposed according to more severe
or relaxed assumptions on the background shapes and systematic biases in the the fit have
been investigated via toy Monte Carlo analysis.
/ T is a promising channel for MSSM Higgs
This work suggests that the A → τ τ → eµE
search. It has to be recalled that the final analysis will include the CP -even H boson, which,
for the mA and tan β values considered in this analysis, is expected to be degenerate with A
in terms of mass, coupling values and production cross section.
123
124
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Acknowledgments
First, I would like to thank the whole CMS Milano-Bicocca group for the opportunity to
undertake this thesis work.
In particular, I would like to acknowledge the pixel group: our boss Luigi Moroni and my
tutor Sandra Malvezzi for sharing their knowledge with me, the passion for researching they
communicate and the patience towards me; Daniele Pedrini, Dario Menasce, Silvano Sala,
Marco Rovere for the competent advices and their helpfulness.
Many thanks also to all ECAL Milano-Bicocca people, computing administrators Paolo
Dini, Luca Carbone, my Ph.D. fellows Roberto Salerno, Martina Malberti, Valentina Tancini,
Leonardo Sala, Silvia Taroni and the ex-Milano people Lorenzo Uplegger, Mauro Dinardo,
for their kind support.
Also, I would like to thank Wolfgang Adam, Boris Mangano, Kevin Burkett, Chiara
Genta for the profitable discussions on tracking issues and Sasha Nikitenko, Chiara Mariotti,
Guillermo Gomez-Ceballos for the precious help on the Higgs analysis.
Special thanks to Stefano Magni for teaching me the art of programming and, most
importantly, a smart approach to the research work.
129