Final Report: pdf

Transcription

Final Report: pdf

An Investigation of QCD Radiation from Top Quarks
Caroline Robson
University College London
Supervised by Dr. Mark Lancaster
April 7, 2004
Abstract
Presented here is a study of QCD radiation distributions in events involving tt̄ pair production. The HERWIG Monte Carlo simulation package is used to make a theoretical comparison
of the momentum and spatial distribution of gluons radiated from the incoming partons, the tt̄
pair and the decay b and b̄ quarks in the channel pp̄ −→ tt̄ −→ W ± bb̄ and a calculation of the
size of the top quark dead cone is made.
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[4]
CONTENTS
Contents
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4
1
2
BACKGROUND
Introduction
The nature of QCD radiation from heavy quarks is currently a phenomenon that is not well understood. In the case of the heaviest of the six quark flavours, the top quark, it is known that gluon
radiation carries away momentum from the quarks although the effect has not been quantified.
This may be causing errors in the reconstructed top mass and the aim of this investigation was to
use Monte Carlo simulations in order to elucidate the nature of the radiation pattern, which may
contribute towards a reduction the top mass uncertainty.
Pressing questions in the field include the nature of an extra hadronic jet observed in several
top quark candidate events and the total energy, and therefore mass, which is lost from the top
quarks through gluon radiation. There is also an uncertainty in the nature of the quark-gluon
radiation vertex, which may be resolved by a direct calculation of the angles at which gluons are
radiated from these heavy quarks. This investigation is based upon the CDF detector at Fermilab’s
Tevatron pp̄ collider, where the top quark was discovered in 1995. The measurement made of the
top mass is subject to statistical and systematic errors of approximately five per cent, although it
is hoped that this will be greatly improved with data from Run II.
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2.1
Background
The Tevatron
The Tevatron pp̄ synchrotron is currently the world’s most powerful particle accelerator. It is
situated at the Fermi National Accelerator Laboratory near Chicago, Illinois, and originally began
operations in 1983. The Tevatron itself consists of a four-mile long underground ring in which
bunches of protons and antiprotons are accelerated to energies of 1 TeV, giving a centre of mass
collision energy of 2 TeV.
Figure 1: Aerial view of the Tevatron (top ring) and the Main Injector (bottom ring)
The first stage of the process involves producing protons. This is done in the Cockroft-Walton
pre-acelerator, in which hydrogen gas is negatively ionised so that each atom has two electrons.
The ions are then accelerated by a linear accelerator to 400 MeV and then passed through a carbon
foil which removes the electrons to leave only protons. A circular accelerator bends the beam of
protons into a circular path and then boosts the energy to 8 GeV. The next stage is the Main
2.2
CDF
5
Injector (the bottom ring on Figure 1), which has several functions. The first is that it accelerates
protons to 150 GeV. Secondly, it produces 120 GeV protons to be sent to the antiproton source,
which collides them with a nickel target and stores resulting antiprotons. When there are enough
antiprotons they are sent back to the main injector, which boosts their energy to 150 GeV. Finally,
the protons and antiprotons are fed into the Tevatron. An antiproton recycler stores the antiprotons that return from the Tevatron so that they can be used again.
The Tevatron (top ring on Figure 1) receives the 150 GeV protons and antiprotons and accelerates them to 1 TeV in opposite directions. The bunches travel at 99.9999%c and are kept in line
by 1,000 helium-cooled superconducting magnets. The beams are brought together in the CDF
and D0 detectors positioned on the Tevatron ring.
2.2
CDF
The Collider Detector at Fermilab (CDF) Collaboration was the first to measure the mass of the
top quark and is officially credited with its discovery in 1995, although data from the D0 experiment
was used alongside the CDF data in further calculations. CDF is a general-purpose particle detector
and between Run I (1992-1996) and Run II (2001-present) underwent a substantial upgrade. Figure
2 shows the installation of the silicon vertex detector. This is the centremost tracking detector,
which determines the trajectories of charged particles via the electron-hole pairs they create as
they pass through the solid state silicon ionisation chambers. After the silicon vertex detector is
the Central Outer Tracker, a gas drift chamber which operates via the detection of charged ions.
A solenoid coil sits between the tracking detectors and calorimiters to bend the tracks of charged
particles so that their momentum and energy can be determined.
Figure 2: The CDF detector in its assembly hall during installation of the new silicon vertex
detector. One of the plug calorimeters has been removed to allow access
The calorimeters (electromagnetic and hadronic) are constructed from alternating layers of absorbers and scintillation detectors, which cause particles to shower and enable a calculation of
the energy lost at each stage. The inelastic production of secondary particles causes energy to
be deposited in each absorbing layer until all or most of the primary particle’s energy is lost. In
the electromagnetic calorimeters, high energy electrons and positrons lose most of their energy by
bremsstrahlung and photons lose energy via the production of electron-positron pairs. The depth
of penetration of an electromagnetic shower is related to the radiation length and increases logarithmically with primary energy. This means that the physical size of elecromagnetic calorimeters
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3
THE TOP QUARK
increases slowly with the energy of the particles it is designed to detect. The penetration of hadronic
showers is determined by the nuclear absorption length, which is generally longer than radiation
length and so the hadronic calorimeters are thicker than the electromagnetic ones. The calorimeter
modules at CDF are divided up into smaller cells, enabling the determination of position as well as
energy. The outermost detectors are the muon chambers, which detect highly penetrating muons
via scintillation detectors. The presence of quarks, heavy bosons and gluons is detected via the
products of their decay chains and neutrinos are inferred from missing energy which is required to
comply with the laws of conservation of energy and momentum. The entire CDF detector is 27
metres long, ten metres high and weighs around 500 tons.
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The Top Quark
3.1
Discovery of the Top Quark
The top quark is the heaviest of the set of six quarks predicted by the Standard Model of Particle
Physics and is the heaviest known fundamental particle. Formulated in the 1960s, the predictions
of the Standard Model have so far proven accurate and in 2001 the final predicted particle, the
tau neutrino, was discovered at the Tevatron. The top quark was the final quark to be discovered
because due to its mass it requires large collision energies to be produced.
3.2
Importance of the Top Mass
“The top mass represents one of the crucial parameters for testing the standard model
while the production properties, should they display anomalies, could point to the existence of exotic phenomena”[?]
The mass of the top quark was established from data produced during CDF Run I as 175.9 GeV
± 4.8 GeV (statistical) ± 4.9 GeV (systematic). The main background factors in top events are
discussed in Section 6.1. The top mass is of particular interest because it is much heavier than the
other quarks; the bottom quark, as the next heaviest, has a mass of only 5 GeV. The top mass also
lies in the energy range of 150 - 200 GeV, which is currently of interest in particle physics. The
hypothesised Higgs boson is predicted to lie within this region and its mass is constrained by the
mass of the top quark, along with that of the W boson. The Higgs particle or set of particles is
thought to be responsible for the breaking of electroweak symmetry in the early universe and will
hopefully explain why the mediators of the weak interaction, the W and Z bosons, are very heavy
while the photon, mediator of the electromagnetic force, is massless. It is important to know the
top mass as accurately as possible as a difference of 5% in the top mass corresponds to a difference
of around 100% in the mass of the Higgs.
3.3
3.3.1
Production of the Top Quark at the Tevatron
The Parton Model
The top quark is produced at the Tevatron via the annihilation of two incoming valence quarks
from the colliding proton and antiproton. In the parton model, a high energy proton is considered
to be a composite object made up of quasi-free quarks and gluons. Each of these particles carries
a fraction xi of the proton’s momentum. The ‘partons’ are confined within the proton as the net
colour charge of all macroscopically observable particles must be zero. At short distances or very
high energies the αs coupling constant is small and the quarks within the proton can move almost
freely as the coupling to surrounding quarks and gluons can be neglected. However αs increases
with the interquark distance and the result is that the quarks are confined within a particle of
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radius ∼ 10−15 m - the approximate size of a proton. When protons are collided at high energies
the valence quarks can be knocked beyond this radius and annihilate to produce new particles. The
remaining ‘spectator’ quarks also hadronise.
Figure 3: The Parton Model: High energy protons and antiprotons are made up of quasi-free quarks
3.3.2
The tt̄ Decay Chain
Tops and antitops are most commonly produced in pairs from a gluon created by the annihilating
valence quarks (See Figure 4). It is also possible for the proton and antiproton to each radiate
gluons which then annihilate with each other to create a tt̄ pair but this is very rare and so has
been neglected in this study. Due to the large mass of the top quark its lifetime is too short to
allow it to hadronise so top hadrons are never observed. More than 99% of the time the top quarks
decay in the tt̄ −→ W + W − bb̄ channel [?]. W bosons most often decay to a q q̄ pair, resulting in
six hadronic jets being produced in the detector. However this channel has a large background
component from other processes. Instead, the ‘lepton plus four jets’ channel is more commonly
used in the study of top events because while the cross section is of the order of one third of that of
the six jet channel, there are much fewer background processes that produce similar results. The
data is therefore purer, increasing the likelihood of a candidate event involving top quarks.
Figure 4: Feynman diagram showing production and decay of the top quark at the Tevatron via
the lepton plus four jets channel
4
QCD Radiation
Quantum Chromodynamics is the study of the colour interactions between quarks. These interactions are mediated by the strong force and its exchange particle, the massless gluon. The
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5
DETECTOR PARAMETERS
mathematical theory behind QCD was produced in the 1970s and is has become increasingly important as colliders of higher and higher energies have been built. QCD is particularly important to
the study of heavy quark and hadronic jet production as gluons carry the colour charge and cause
quarks to be bound into hadronic states. All quarks can radiate gluons and it is known that these
gluons take with them some of the quark’s energy and momentum. In the case of the top quark,
this can cause a considerable uncertainty on the mass because the nature of this energy loss is
not well understood. Gluon emission occurs because as a quark becomes more isolated from other
quarks the coupling αs , and therefore the potential energy, of the binding colour force increases.
At a critical point the potential stored in the colour field manifests itself as spontaneously emitted
gluons, which then split into q q̄ pairs. These recombine into colourless hadronic states, creating a
highly collimated hadronic jet in the direction of the original quark.
In a large proportion of top events an extra isolated hadronic jet has been observed in the detector and it is thought that this may be the result of the hadronisation of high energy gluon
emissions from the top and antitop quarks. However gluons also radiate from the initial parton
quarks and the bottom quark decay products of the W bosons, as illustrated in Figure 5. Thus in
order to calculate the energy loss from the top quarks due to gluon radiation, the gluons of different
origins have to be distinguished from each other.
Figure 5: Gluon radiation from the initial parton quarks, top quarks and bottom quarks
The radiated gluons themselves are not directly observed but are instead detected via their
hadronic decay products. Gluons create quark-antiquark pairs which then hadronise into jets containing mostly pions. π + hadrons leave tracks in the tracking detectors because they are electrically
charged and also energy deposits in the hadron calorimeters. Neutral π 0 particles do not leave signals in the tracking detectors but they do deposit energy in the electromagnetic calorimeters.
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5.1
Detector Parameters
Transverse Momentum
At CDF the beamline is taken as the z -axis in conventional three-dimensional spatial coordinates.
The protons and antiprotons have equal momentum in opposite directions so when they collide
there is no z component of momentum in the centre of mass frame. Thus the energy given out in
the x and y directions can be taken as the total energy transferred to new particles. The transverse
momentum PT is defined as:
PT =
q
Px2 + Py2
(1)
5.2
Pseudorapidity
5.2
9
Pseudorapidity
The polar angle to the beamline, θ, is not a convenient quantity to use due to the fact that often
there are several particles travelling at angles very close to the beam direction. In order to describe
the differences in these angles it is more useful to use a logarithmic scale. Rapidity is a scale
which equals zero at 90◦ to the beamline and infinity along the beamline (see Figure 6. Forward
and backward topologies can then be described by positive and negative rapidities. Rapidity is
usually denoted as y but in the case of massless particles such as gluons, the quantity is redefined
as pseudorapidity, η.
Figure 6: Schematic of the detector, demonstrating θ and η
Pseudorapidity is calculated as follows from θ:
θ
η = − ln(tan )
2
(2)
Pseudorapidity also becomes very useful when considering Lorentz transformations into frames
other than the centre of mass frame as a change in pseudorapidity, ∆η, is Lorentz invariant.
5.3
Phi
Phi is the azimuthal angle in the transverse plane, as shown in Figure 7.
Figure 7: The transverse plane, showing the x,y axes and φ
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6
6
RECONSTRUCTING THE TOP MASS
Reconstructing the Top Mass
6.1
The Reconstruction Process at CDF
Top events decaying in the lepton plus jets channel are characterised by the appearance of a single
isolated high PT electron or muon, four leading hadronic jets arising from the b quarks from the
top decays and the hadronically decaying W boson and missing transverse energy indicating the
presence of a neutrino. Jets from the hadronisation of b quarks are tagged by reconstructing either
secondary vertices from the decays of the bottom’s hadronic products (SVX tagging) or extra leptons where the bottom quark has decayed semileptonically (SVT tagging). Restrictions are put on
the energies and distributions of the leptons and jets in order to help reduce background events.
The restrictions at CDF are set at ET >20 GeV and | η |<1 for the electron or muon, ET >20
GeV for the missing neutrino energy and for three of the four jets, ET >15 GeV and | η |<2.
The restriction on the fourth jet is lower at ET >8 GeV and | η |<2.4 in order to increase event
acceptance, as long as at least one of the jets is SVX or SLT-tagged. If none of the jets have been
tagged, the fourth jet must satisfy the same requirements as all of the others in order for the event
to be accepted.
Once the momenta and masses of the quarks and leptons have been calculated, the most basic
requirements are that the total PT of the tt̄ pair and its QCD products is zero and that the invariant masses of the l ν and q q̄ pairs must be equal to the W mass. The mass of the top must also be
equal to the mass of the antitop. A jet is defined as a cluster of calorimeter towers within cones of
radius ∆R = 0.4 in η − φ space:
∆R =
q
(∆η)2 + (∆φ)2
(3)
The jet energies have to undergo a series of corrections to account for losses in the cracks bewteen
the calorimeter cells, losses outside the defined jet radius and the uncertainty on the energy scale.
Corrections are also made for contributions from the ‘underlying event’. This includes the hadronisation products of the spectator partons from the proton and antiproton and the results of gluon
radiation from these quarks. Estimations are made using both simulated and real data.
There are many different configurations for assigning jets to particular quarks. Generally each
set of data is fitted to the hypothesis that pp̄ −→ tt̄ −→ W + W − bb̄ −→ l+ νbq q̄ b̄ or q q̄bl− ν̄ b̄ via a
χ2 fit and the lowest χ2 configuration used. The data is then fitted to simulated Monte Carlo
(discussed in Section 7.1) data in order to find the mass value with the optimum likelihood of being
correct.
The background in top events is calculated by accounting for factors including the reduced energy
and pseudorapidity requirement on the fourth jet, the likelihood function of the mass calculation,
the SVX and SLT-tagging efficiencies and the cross sections of possible background events. In
Reference [?] the background factors to the top mass result of 175.9 GeV in the sample used were
calculated as follows:
• 67%: Other events involving W + jets
• 20%: Multijet events where a jet is misidentified as a lepton and other bb̄ events where a b
hadron has decayed semileptonically.
• 13%: Z events where the Z decays leptonically; WW,WZ and ZZ diboson events and from
the production of single top quarks.
6.2
6.2
Isolated Track Asymmetry
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Isolated Track Asymmetry
The tt̄ is colour connected to the valence quarks of the incoming pp̄ pair unlike the the other quarks,
which usually come from gluon initial states [?]. The top is thus coupled to the proton and the
antitop to the antiproton. Reference [?] suggests that along with the fact that the probability of
gluon emission is dependant on the bending angle of the colour line associated with the radiating
quark, this should cause an asymmetry in the radiation patterns of the top and the antitop. The
study found that there was a difference in the track multiplicities but that this differed from
the values predicted by perturbative QCD theory. The authors suspected that the result was
due to inaccuracies in their interpretation of the underlying event and the hard (high energy) jet
hadronisation process.
6.3
The Effect of Gluon Radiation on the Top Mass
A study was made in 1995 of the effect of gluon radiation on the reconstructed top mass (Reference
[?]). The extra hadronic jets in a sample of top events were assigned to either ‘production’ gluons
radiating from the initial partons and the top quarks before their decay, or ‘decay’ gluons radiated
during and after the decay. They cannot be precisely separated from each other due to interference
but for the purposes of the study these definitions were used as working approximations. In pp̄
collisions there are other processes which can contribute to the production of the extra jet but
their influence was taken to be negligible due to their low cross sections. One of the results of the
study was that the production gluons were found to have slightly higher energies than the decay
gluons. This is in contrast to the results of this investigation, although the spatial distributions
were found to be of a similar shape. When the top mass is reconstructed from its W boson and
bottom quark decay products, the mass will be correct if the extra jet came from a production
gluon but Mtt̄ is underestimated if the gluon was a decay gluon. In calculating the invariant mass
of the top quark, a shoulder was observed on the lower side of the main Breit-Wigner resonance
peak when the momentum of the extra jet was omitted. In the case where it was included, an
even larger shoulder appeared on the upper side of the resonance peak, indicating an asymmetrical
background with a preference for mass values higher than the ’true’ value. Thus Mtt̄ cannot be
unambiguously reconstructed in either case. However, if the production and decay gluons were
found to have different characteristics then a strategy could be devised to decide whether or not
the extra jet should be included in reconstructed mass.
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7.1
Software
HERWIG Monte Carlo Event Generator
The simulated top event data in this investigation was created using the HERWIG (Hadron Emission Reactions With Interfering Gluons) Monte Carlo program. All of the particles and decays
have well-defined formulae describing their associated probabilities of occurrence. Monte Carlo
throws a random number into this bank of formulae and propagates an event. This is repeated
thousands or millions of times and the data can then be analysed to find trends and average values
for various parameters based upon probability. HERWIG is multipurpose Monte Carlo generator
which supports all combinations of hadron, lepton and photon beams. Hard scattering processes
are factorised into several components from the beginning. These include the hard subprocess (the
breaking up of the pp̄ pair in this case), the perturbative initial and final state beam showers,
non-perturbative hadronisation, resonance decays and the hadronisation of the spectator partons
in the remnants of the beam. The latter is not well understood and as such cannot be precisely
calculated so HERWIG uses relatively simple models to predict the outcomes of these processes.
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8
QUARK PT LOSSES
In Reference [?] a comparison of the kinematical distributions for top quark pairs when calculated via Next to Leading Order (NLO) QCD and by the HERWIG Monte Carlo simulation is
discussed. It was found that distributions which do not always agree at leading order, such as PT ,
η and Mtop , agree perfectly between HERWIG and NLO for values of PT and Mtop that are not
too large. At large PT and Mtop (>200 GeV) the distributions begin to diverge slightly because
the NLO calculations only take into account one gluon emission from each top. The Monte Carlo
simulation, however, picks up on the fact that there may be multiple gluon emissions from any one
quark.
7.2
ROOT
ROOT is an object oriented data analysis framework originally devised at CERN for the analysis of
LEP I data. Its functionality has increased such that it will be able to handle the large amounts of
data that will be produced at the LHC and is routinely used for the analysis of CDF data. Within
ROOT, data is stored as a set of objects and direct access to separate parts of the data can be
achieved without the need to analyse the bulk of it. The main function of ROOT utilised in this
investigation was its histogramming capability.
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8.1
Quark PT Losses
Generating the Event Sample
The first step in this investigation was to look at the transverse momentum losses of initial parton
quarks from the pp̄ pair, the top quarks themselves and the bottom quarks in their decay chain. As
the main three types of heavy/ high energy quarks in the process, these are the main QCD emitters
contributing to the radiation pattern in the detector. A sample of 10,000 events involving a tt̄ pair
was created with HERWIG. The top mass was calculated using a real data sample of only 76 events
and the number of events that will form the basis of CDF Run II top quark statistics is estimated
to be around 2,000. Therefore 10,000 events was judged to provide adequate statistics for the
theoretical study of top events. There were some corruptions during the generation process so the
final number of events analysed was 8,606. For each event HERWIG generates a log file containing
a list of particles in the event in the approximate order in which they occur. Each log contains
on average between 400 and 800 entries, which are indexed consecutively with an IHEP number.
Each different type of particle also has its own PDG number, which is a standardised identification
number used in all types of Monte Carlo. Antiparticles have negative numbers. The standard PDG
numbers for the quarks and antiquarks are shown in Table 1. Other parameters in the files include
the momentum components Px , Py and Pz , the energy, mass and velocity components and also the
IHEP number of the particle’s mother. For example, if a gluon is radiated from a top quark, the
top quark is listed as the gluon’s mother.
Table 1: Standard Monte Carlo Identification Numbers for Quarks and Antiquarks
Quark
d
u
s
c
b
t
PDG
1
2
3
4
5
6
Antiquark
d¯
ū
s̄
c̄
b̄
t̄
PDG
-1
-2
-3
-4
-5
-6
8.2
8.2
Coding Logic
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Coding Logic
The principal C++ logic involved looping over all of the particles in each event and selecting
the particles required for each calculation. Once a particular particle was selected, its transverse
momentum components could be extracted and manipulated. In HERWIG, particles are sometimes
entered more than once and this happens quite often for quarks. The variables are measured and
registered at various stages of the quark’s progress, for example before and after emission of a gluon
or when there has been a momentum change due to another factor. The first and final time each
quark appears, its IHEP is the standard Monte Carlo number. The various ‘intermediate’ states of
the quark are labelled internally by HERWIG with the number 94. In order to calculate the PT lost
by the quark over its lifetime, the transverse momentum components were extracted just after the
quark appeared (i.e. from its first appearance in each log) and just before it annihilated or decayed
(from its last appearance in each log). The transverse momentum at each point was calculated and
the final momentum subtracted from the initial momentum. Relevant sections of code can be seen
in Appendix A.3.
8.3
Results
Calculations of the PT lost from the initial parton quarks, top quarks and bottom quarks during
their lifetimes gave the results shown in Table 2.
Table 2: PT Changes During Quark Lifetimes
Quark
Initial q
Initial q̄
t
t̄
b
b̄
Mean PT Loss (GeV)
10.43
10.24
10.21
10.01
26.99
24.91
The calculations for the initial parton quarks (either up, down or in rare cases, strange) and
the top quarks were fairly straightforward but in the case of the b and b̄ quarks there were extra
hadronisation effects to be taken into account. The mean PT loss from an initial quark or antiquark
was calculated as 10.34 GeV; from a top or antitop the mean PT loss was 10.11 GeV but the mean
loss from a bottom or antibottom quark was well over double the value of the other two at 25.95
GeV.
8.4
Bottom Quark Hadronisation
Of the three types of quark, the bottom quarks have the longest lifetime and are the only ones
which go on to produce hadrons. During the process of jet formation there are extra uū and dd¯
pairs which are listed in the particle logs as coming from some of the intermediate state b and b̄
quarks. The total PT of these extra quarks was calculated by looking for particles with the same
mother particle as the final state b or b̄. An investigation of a sample of Monte Carlo log files
implied that the q q̄ pairs always list the second-to-last b or b̄ as their mother. This is most likely
a reflection of the order in which HERWIG calculates the event probabilities and made it easier to
locate the q q̄ pairs in the logs. An asymmetry was found in the mean value of the total PT of these
extra quarks, with the mean for those associated with the b at 31.90 GeV and those associated
with the b̄ much lower at 20.06 GeV. The two calculations were coded in the same fashion so either
14
8
QUARK PT LOSSES
there is a real asymmetry or the assumption based on the example logs that the quarks always
stem from the penultimate b or b̄ entry is wrong. If this was the case, however, the systematic error
would be expected to apply equally to both the b and b̄ due to the thousands of events included in
the statistics. The implication is therefore that there is a genuine asymmetry. The shapes of the
distributions are similar, as can be seen in Figures 8 and 9. For the b quarks the mean PT of the
extra q q̄ pairs is higher than the mean PT lost. The q q̄ pairs are therefore part of the hadronisation
process and not the decay chain. Perturbations in the colour field during the fragmentation process
can cause gluons and q q̄ pairs to appear in the vacuum and go on to create pions and B mesons
with the outgoing b and b̄ quarks, contributing to the final B jets.
h1_26
Entries
8608
Mean
31.9
RMS
29.52
# Events
HADRONISATION LOSSES FROM B QUARK SYSTEM
250
200
150
100
50
0
0
20
40
60
80
100
120
140
160
180 200
PT (GeV)
Figure 8: Hadronisation losses from the b quark system
8.5
Extrapolating Back From B Mesons
In order to clarify the amount of PT lost from b and b̄ quarks in the hadronisation process, measurements of the PT of the first B mesons were taken on the premise that due to the large mass
of the b compared to the d and u, there would be little change in momentum between the final
state b or b̄ quark and the first meson it creates when it combines with a lighter quark. The results
were inconsistent with this assumption as the mean PT of the B mesons was found to be higher.
For example in the case of the b quark the PT was found to increase by a factor of 1.64 from 29.2
GeV to 47.83 GeV. The mean PT of the b̄ quark was found to increase by a factor of 1.65 from
Extrapolating Back From B Mesons
15
h1_27
Entries
8608
Mean
20.06
RMS
18.09
HADRONISATION LOSSES FROM BBAR QUARK SYSTEM
# Events
8.5
350
300
250
200
150
100
50
0
0
20
40
60
80
100
120
140
160
180 200
PT (GeV)
Figure 9: Hadronisation losses from the b̄ quark system
16
9
DIRECT GLUON PT CALCULATIONS
28.94 GeV to 47.83 GeV. Upon taking a random sample from the log files and calculating the total
momentum P, the values for the quark and the meson were found to agree much better although
there was still an increase. The hadronisation process therefore gives a considerable energy boost
to the b and b̄ quarks and using the PT of the B mesons as an approximation to the PT of the b
and b̄ is not a useful method.
8.6
The Cone
Only the b and b̄ quarks undergo a large change in momentum due to direct hadronisation but
all three types of quark (initial, top and bottom) are affected by what HERWIG calls the ’cone’.
When the PT of the cone was plotted for each case, all of the entries in the histograms were binned
around the value of 1 GeV. Upon the inspection of five randomly chosen log files, the momentum
of the cone is within a few MeV of this value each time. This suggests that HERWIG is producing
an extra hadronisation ’fudge factor’ in order to describe the effects of the underlying event i.e.
the hadronisation of the spectator partons and any other perturbative effects due to multiple
interactions in the same beam crossing. At 1 GeV this is a small but still significant factor. The
fragmentation of the beam remnants is at the present time too complicated to calculate accurately
and so HERWIG’s estimation of its effects is based upon relatively simplistic models.
9
9.1
Direct Gluon PT Calculations
Logic
The next stage of the investigation was to select the gluon radiation events directly from the Monte
Carlo data and plot their PT distributions. The overall logic involved first selecting the gluons
from each event via their PDG number of 21. Gluons can radiate other gluons and in some events
a series of gluons appear to come from one quark. The code had to select those whose mother
particle was not another gluon so that only the quark-gluon vertex was being analysed. The next
problem was that although the initial and final states of each quark were generally labelled with
the standard Monte Carlo PDG numbering, the intermediate states were labelled with HERWIG’s
internal numbering of 94. This number is the same for all flavours so it was not simply enough to
select each type of quark based upon its standard PDG number; the logic also involved looking for
quarks with a PDG of 94, whose mother particle had a PDG corresponding to the standard quark
labelling, or whose mother’s mother had a standard PDG. Therefore the gluons from initial and
final states of each quark were extracted separately from the intermediate states and the results
¯ s and s̄ quarks a limit on the IHEP number was set at
combined. For the initial parton u, ū ,d, d,
28 in order to exclude any gluons potentially radiating from the decay q q̄ pairs of the W bosons.
This value was chosen from a study of 21 random logs in which it was determined that the IHEP
of the highest-IHEP gluon to be emitted from one of the initial quarks was 26 and the IHEP of the
lowest-IHEP appearance of u, d and s quarks from W ± decays was 31. The value of 28 was chosen
as it is in the middle of the two values and therefore minimises the likelihood of either missing gluon
emissions from the initial parton quarks or mistaking any hadronisation or decay quark radiation
for parton quark radiation. The value of PT was calculated for each gluon radiated and then the
values for each event were summed in order to give a calculation of the total momentum lost to each
quark through gluon radiation. The PT of the maximum PT gluon (i.e the one that would form the
basis for clustering in standard jet clustering algorithm see Section ??) was also calculated. See
Appendix A.4 for the relevant code.
9.2
Results
9.2
17
Results
The initial and final states of the initial parton q and q̄ were observed to produce no gluons. In the
sample of 8,606 events however, the intermediate states produced 43,263 gluons between the two.
Similarly for the initial and final states of the b there were two gluons radiated in the whole sample
and for the b̄ there were none. The intermediate states radiated 19,742 gluons. The intial and
final states of the t and t̄ produced larger statistics at 444 and 450 respectively, although these are
still very much short of the intermediate state numbers of 12,601 and 12,229. Checks were made
using 21 randomly selected logs and at that level the statistics were observed to approximately
correlate. It should be stressed at this point that the ‘initial and final’ and ‘intermediate’ states do
not necessarily represent real phenomena; instead they represent a method of breaking up the data
based upon the methods used by HERWIG to propagate events. These methods are based upon
the probabilities of processes occurring in a certain order and the numbering system reflects this.
The main PT results are shown in Table 3.
Table 3: PT of Radiated Gluons
Quark
Initial Parton q
Initial Parton q̄
t
t̄
b
b̄
Mean Gluon PT (GeV)
4.046
3.905
7.603
7.702
7.658
7.631
Mean Total PT (GeV)
13.54
9.405
14.42
13.43
13.78
12.43
PT of Max PT Gluon
5.178
4.582
9.340
8.962
9.200
8.284
Looking at the initial parton q and q̄, the mean PT of the gluons they radiate is of the order of
approximately half of the that of the other quarks. The gluons radiating from the top and bottom
pairs have very similar average PT , although a trend towards the antiquarks radiating gluons of
slightly lower momentum can be observed. This appears to occur for all of the different types of
quark studied although the effect is most pronounced in the mean total PT of the initial parton
antiquarks. Reference [?] describes an asymmetry in the track multipicity for jets radiated from
the t and t̄ due to differences in the bending angles of the colour lines. The results presented here
suggest that on a probabilistic level there is also an asymmetry in the amount of momentum given
to the radiated gluons between matter and antimatter. Table 2 in Section 8.3 shows a similar trend
in the overall PT lost from each quark. The shapes of the PT distributons are similar in each case,
with a peak at the lower end of the scale and a long tail leading into the higher PT region. For
example, the mean PT of the intitial q gluons and the t and b gluons are shown in Figures 10, 11
and 12. For plots of the mean PT of the q̄, t̄ and b̄ quarks, together with plots of the total PT and
the PT of the maximum PT gluon, see Appendix 2.
10
10.1
Spatial Gluon Distributions
Pseudorapidity, η
The gluons from the initial partons were found to be biassed in their distribution towards one side
of the detector or the other. Gluons from the initial q appeared mostly in the negative η side
(i.e. in the topology of the p̄) and the q̄ gluons appeared mostly in the positive side (towards the
direction of the p. This implies that a substantial amount of the outgoing parton’s momentum
comes from the opposite particle in the pp̄ collision. There is a very slight asymmetry in the mean
pseudorapidities, with the q gluons having a mean η of -2.204 and the q̄ gluons having a mean
18
10
SPATIAL GLUON DISTRIBUTIONS
h1_43
Entries
23180
Mean
4.046
RMS
5.664
# Events
PT OF GLUONS RADIATING FROM INITIAL Q
8000
7000
6000
5000
4000
3000
2000
1000
0
0
20
40
60
80
100
120
140
160
180 200
PT (GeV)
Figure 10: Mean PT of gluons radiating from initial parton quark
Pseudorapidity, η
19
h1_49
Entries
13045
Mean
7.603
RMS
9.682
PT OF GLUONS RADIATING FROM TOP
# Events
10.1
2000
1800
1600
1400
1200
1000
800
600
400
200
0
0
20
40
60
80
100
120
140
160
180 200
PT (GeV)
Figure 11: Mean PT of gluons radiating from t quark
20
10
h1_55
Entries
10017
Mean
7.658
RMS
8.648
# Events
PT OF GLUONS RADIATING FROM B
1200
1000
800
600
400
200
0
0
20
40
60
80
100
120
140
160
180 200
PT (GeV)
Figure 12: Mean PT of gluons radiating from b quark
10.1
Pseudorapidity, η
21
η of 2.297. This is a relatively small difference although it could be enough to cause noticeable
asymmetries in jet distribution. Figures 13 and 14 show the distribution in η of gluons from the
initial parton q and q̄, in which the bias can be clearly seen.
The distributions of the gluons from the top and bottom quarks are located in the central region of the detector, with no obvious bias to either side. Coupled with the fact that the mean PT
values for the gluons from each type of quark are very similar, a large amount of real data would
be needed in order to determine likelihoods of either type of gluon by statistical methods. Figures
15 and 16 show the η distributions of gluons from the t and b quarks. Note the mean values of
0.013 and 0.014, which are very close to each other even on the logarithmic η scale.
h1_97
Entries
23180
Mean
-2.204
RMS
1.495
# Gluons
PSEUDORAPIDITY OF GLUONS FROM INITIAL Q
1000
800
600
400
200
0
-8
-6
-4
-2
0
2
4
6
8
Pseudorapidity
Figure 13: Pseudorapidity distribution of gluons radiating from initial parton q
Plots of η distributions of the max PT gluon for each type of quark are displayed in Appendix ??
A summary of the mean η values are presented in Table 4. For the initial parton quarks and the t
quarks, the η of the max PT gluons are shifted towards positive η compared with the overall means.
The t̄, b and b̄ gluons show the opposite trend, both having started in positive η and reducing in
value slightly for the max PT gluons. The shift is most prominent for the initial parton quarks,
with ∆η being an order of magnitude bigger than for tops and bottoms.
22
10
h1_100
Entries
20083
Mean
2.297
RMS
1.513
PSEUDORAPIDITY OF GLUONS FROM INITIAL QBAR
# Gluons
900
800
700
600
500
400
300
200
100
0
-8
-6
-4
-2
0
2
4
6
8
Pseudorapidity
Figure 14: Pseudorapidity distribution of gluons radiating from initial parton q̄
Table 4: η of Radiated Gluons
Quark
Initial Parton q
Initial Parton q̄
t
t̄
b
b̄
Mean Gluon η
-2.204
2.297
0.013
0.018
0.014
0.026
Mean η of Max PT Gluon
-1.778
2.639
0.002
0.027
0.011
0.022
Pseudorapidity, η
23
h1_103
Entries
13045
Mean
0.01287
RMS
1.043
PSEUDORAPIDITY OF GLUONS FROM TOP
# Gluons
10.1
900
800
700
600
500
400
300
200
100
0
-8
-6
-4
-2
0
2
4
6
8
Pseudorapidity
24
10
h1_109
Entries
10017
Mean
0.01394
RMS
1.05
PSEUDORAPIDITY OF GLUONS FROM B
# Gluons
700
600
500
400
300
200
100
0
-8
-6
-4
-2
0
2
4
6
8
Pseudorapidity
10.2
10.2
Azimuthal Distribution in φ
25
Azimuthal Distribution in φ
The gluon distributions from all of the quarks studied were approximately even, with a mean of
∼ π. This implies that the distribution of quarks inside the proton and antiproton must be in a
constant state of flux i.e. in the HERWIG model, the alignment of quarks inside the p and p̄ is on
average unaffected by magnetic fields, or the influence of the electromagnetic force is suppressed
by the more dominant strong coupling. Figure 17 demonstrates a typical distribution.
h1_139
Entries
13045
Mean
3.122
RMS
1.815
# Gluons
PHI OF GLUONS FROM TOP
160
140
120
100
80
60
40
20
0
0
1
2
3
4
5
6
Phi (radians)
Figure 17: Typical distribution of the gluon radiation pattern in the transverse plane. The distribution in φ is approximately even, with a mean of ∼ π
10.3
Gluon Distributions in η − φ Space
It is useful to look at two-dimensional distributions in order to gain an idea of how much the gluon
distributions overlap. Plotted in η − φ space, the initial parton quark gluons distributions can be
seen to overlap slightly, although the peaks can still be made out. The distributions are spread
over a large range in the detector, from η of approximately -5 to 5 (See Figure 18).
The top and bottom quark gluons occupy a much narrower space in the central region of the
detector. As can be seen from Figures 19 and 20 the distributions overlap each other. The total
radiation pattern for initial parton quarks, top quarks and bottom quarks is shown in Figure 21.
Gluons from the initial q q̄ pair could be distinguished statistically due to the fact that their mean
26
10
h2_1001
Entries
86526
Mean x -0.1145
3.141
Mean y
RMS x
2.702
1.814
RMS y
GLUONS RADIATING FROM Q + QBAR
Phi (radians)
6
5
4
3
2
1
0
-6
-4
-2
0
2
4
6
Pseudorapidity
Figure 18: Distribution of gluons from the initial parton quarks in η − φ space. The peaks can be
clearly seen.
10.4
Ratios Between Gluon Types
27
PT is in the region of approximately half that of the gluons from the tops and bottoms. The tops
and bottoms, however, are much harder to tell apart due to their similar mean PT .
h2_1009
Entries
51588
Mean x 0.01563
3.131
Mean y
RMS x
1.031
1.812
RMS y
Phi (radians)
GLUONS RADIATING FROM T + TBAR
6
5
4
3
2
1
0
-6
-4
-2
0
2
4
6
Pseudorapidity
Figure 19: Distribubution of gluons from the tt̄ pair. Both are located centrally in the detector.
10.4
The top and bottom gluon distributions are however not identical. The gluons from the bb̄ pair
occupy a slightly narrower region in η than those from the tt̄ pair. Although this is not immediately
clear from the distributions in Figures 19 and 20, the difference becomes apparent when the ratio
of top and bottom gluons is plotted over the same parameters. Figure 22 is a lego plot showing the
ratio of the two gluon distributions. The towers are plotted with a difference of 0.1 in each of η and
φ, giving a separation ∆R of 0.14 (as calculated in Equation 3). These values correspond to the size
of the calorimeter cells in the CDF detector and hence give an indication of the population ratios
that could be expected for cells in different regions. As can be seen, there are regions at the edges
of the coupled distribution where the gluons are almost exclusively from top quarks. These regions
are located at approximately η = -2 to -3.5 and η = 2.5 to 4. In the central region of the detector
the ratio of top to bottom gluons is more even, although there are still slightly more top gluons
than bottom. The ratio at the centre is approximately 0.6 in favour of top gluons. Although due
to interference effects the origin of a gluon can never be determined with 100% accuracy, QCD jets
in the aforementioned η cuts are more likely to be from top quarks than initial or bottom quarks.
28
10
h2_1010
Entries
36802
Mean x 0.01547
3.134
Mean y
RMS x
0.9969
1.807
RMS y
GLUONS RADIATING FROM B + BBAR
Phi (radians)
6
5
4
3
2
1
0
-6
-4
-2
0
2
4
6
Pseudorapidity
Figure 20: Distribubution of gluons from the bb̄ pair. Again located centrally.
29
DISTRIBUTION OF GLUONS FROM INITIAL, TOP AND B QUARKS
Phi (radians)
10.4
6
5
h2_203
Entries 177598
Mean x -0.04678
3.136
Mean y
RMS x
2.028
1.814
RMS y
4
3
2
1
0
-6
-4
-2
0
2
4
6
Pseudorapidity
Figure 21: Total radiation pattern of gluons from all three quark types
30
11
THE TOP QUARK DEAD CONE
Gluons from initial parton quarks can be statistically ‘removed’ using their lower mean PT . Thus
these areas of the CDF detectors may be more useful than others for top quark QCD studies.
RATIO OF TOP QUARK GLUONS TO BOTTOM QUARK GLUONS
h2_206
Entries
51588
Mean x 0.04718
3.151
Mean y
RMS x
1.942
1.825
RMS y
1
0.8
0.6
0.4
0.2
0
6
Ph
i (r 5
ad
ian4
s) 3
2
1
0
-6
-4
-2
0
6 ity
4orapid
2Pseud
Figure 22: Lego plot showing the ratio of top gluons to bottom-radiated ones
Figure 23, overleaf, shows the overall numerical ratios in η − φ space of the gluons from initial,
top and bottom quarks over the 8,606 event sample. The off-centre peaks of the parton quark
distributions (in yellow) can be clearly seen, as can the disparity between the numbers of gluons
from the tt̄ and bb̄ pairs.
11
11.1
The Top Quark Dead Cone
Gluon Emission From Heavy Quarks
Due to the fact that quarks have mass, the phase space available for the emission of gluons is
reduced. Near the phase space boundary, corresponding to the radiation of gluons approximately
collinearly to the quark’s direction of motion, there is a suppression of the gluon emission cross
section. In the case of massless quarks there would be a collinear singularity along the propagation
direction causing gluons to radiate collinearly. For heavy quarks there are next-to-leading order
loop diagrams which cause the probability that gluons will be radiated collinearly to be cancelled
out. This suppression results in the phenomenon of the ‘dead cone’, within which gluons cannot be
radiated because angular momentum and helicity would not be conserved (see Figure 24). In theory
11.1
Gluon Emission From Heavy Quarks
31
PROPORTION OF GLUONS FROM INITIAL, TOP AND BOTTOM QUARKS
blue = bottom quarks
red = top quarks
# Gluons
250
yellow = initial quarks from p/pbar
200
150
100
50
0
6
Ph
i
(ra5
dia 4
ns
) 3
2
1
0
-6
-4
-2
0
6 ity
orapid
2 seu4
d
P
Figure 23: Stack histogram showing the numerical ratios of gluons from the three quark types in
the sample of 8,606 events
32
11
the quark (spin- 12 ) should only be able to emit gluons (spin-1) at 90◦ to the quark’s direction of
motion, otherwise a component of the gluon’s helicity along the direction of the quark’s momentum
would mean that helicity had not been conservedcause an increase in helicity. However helicity is
not a perfect quantum number, allowing energy smearing and interference effects to reduce this
angle. The higher the quark’s energy with respect to its mass, the smaller the dead cone angle is.
the light quarks (u, d, s) are often approximated as radiating gluons collinearly as their masses are
small in comparison to their energies. The heavier quarks, however, have more pronounced dead
cones.
Figure 24: The dead cone is the area around a quark’s direction of motion within which gluons
cannot be emitted due to energy and momentum conservation
11.2
Calculation from QCD and Parton Distributions
A working approximation based upon the quark and gluon cross sections [?] is:
2Mqq̄
θ∼ √
s
(4)
This assumes that the quarks are stable, but in practice the heavy quarks decay weakly after a
finite time.
The centre of mass energy is calculated from the two beam energies:
√
p
s = 2 E1 E2
(5)
The energy which actually goes into top production, however, is related to the momentum fractions
of the incoming partons:
√
0
s =
√
√
x1 x2 s
(6)
The proton is described in the most general sense as a bound state of two u quarks and a d. However
on a deeper level this model does not give a complete picture. Quarks have a finite probability of
emitting gluons and those inside the proton are no exception. The quarks continually interact with
each other via the exchange of virtual gluons and also emit gluons which can create q q̄ pairs before
annihilating again. The result is a quark-gluon sea wihtin the proton and depending on the point in
time at which the proton and antiproton collide, a quark other than the standard u or d can be the
one to get knocked out. Due to the creation of q q̄ pairs it may even be an antiquark. Similarly for
the antiproton, u, d, s, s̄, or in rare cases, c or c̄ quarks have a probability of appearance. The cross
sections for these processes are much smaller than those for the standard component quarks and as
such are rare but their probabilities are still finite. On a superficial level however, the momentum
fractions xi carried by the quarks which become detatched from the pp̄ pair can be taken to be
11.3
Calculation From Relativistic Kinematics
33
approximately one third of the total p or p̄ momentum. Therefore the centre of mass energy which
goes into the production of the tt̄ pair at the Tevatron centre of mass energy of 2 TeV is calculated
to an approximation as follows:
√
0
s =
√
0.33 · 0.33 · 2T eV = 660GeV
(7)
Inserting this into the dead cone angle approximation in Equation 4, taking Mtt̄ = 176 GeV:
2M
2 · 176
θ ∼ √ t0t̄ θ ∼
= 0.53rad ≈ 31◦
660
s
(8)
By comparison, for the initial parton quarks from the pp̄ pair, taking the mass of the most
common parton, the u quark as Mqq̄ = 5MeV:
θ∼
2 · 5 · 10−3
= 1.5 · 10−5 rad ≈ (8 · 10−4 )◦
660
(9)
Thus it can be seen that due to the lighter quarks’ much lower mass, they are usually assumed
to radiate collinearly.
11.3
Calculation From Relativistic Kinematics
By considering the conservation of relativistic energy and momentum, the minimum angle at which
gluons should radiate can be calculated in terms of the mass of the quark. Assume θ is the angle at
which the gluon is radiated with respect to the initial momentum and α is the angle through which
the quark is deflected, as shown in Figure 25). In practice, α is very small due to the mass of the
top quark and is usually neglected. For now it will be kept in the calculation for demonstration
purposes.
Figure 25: Schematic diagram of the angles through which quark and gluon are deflected during
emission
In this notation, P~ is a four-vector and P is a three-vector. The norm of a four-vector is
invariant i.e. the same in all frames. Therefore:
P~ = (mu, imc)
P~ 2 = −M 2 c2
(10)
(11)
34
11
Where M is the rest mass. The initial momentum P~i can therefore be calculated a follows. The
speed of light, c, is set to 1 in natural units and is neglected in this calculation.
P~i2 = (P~g + P~qq̄ )2 − Mq2q̄
= P~g2 + P~q2q̄ + 2P~g P~qq̄
(12)
(13)
Where P~g and P~qq̄ are the four-momenta of the gluon and the quark or antiquark respectively.
Now P~g2 = −Mg2 and the gluon is massless, so P~g2 = 0. Therefore:
P~i2 = P~q2q̄ + 2P~g P~qq̄
=
−Mq2q̄
(14)
+ Mg Mqq̄
(15)
= −Mq2q̄
(16)
But Eg2 6= 0 ⇒ Eg2 = Pg2 + Mg2 ⇒ Eg = Pg as Mg = 0. Multiplying the energies together:
~ qq̄ = Pg · Pqq̄ = Eg Pqq̄ cos(θ + α)
Eg E
~ qq̄ = Pqq̄ cos(θ + α)
⇒E
⇒
~ q2q̄
E
=
Pq2q̄ cos2 (θ
+ α)
(17)
(18)
(19)
~ q2q̄ is the norm of the energy momentum four-vector (P, i E ). Its result is P~q2q̄ − Mq2q̄ .
E
c
⇒ Pq2q̄ cos2 (θ + α) = P~q2q̄ − Mq2q̄
P~q2q̄ − Mq2q̄
2
cos (θ + α) =
P~q2q̄
cos2 (θ + α) = 1 −
Mq2q̄
P~q2q̄
(20)
(21)
(22)
Using the identity cos2x = 2cos2 − 1,
This gives the final result:
Mq2q̄
1
1
cos(θ + α) + = 1 −
2
2
P~q2q̄
(23)
1
1 Mq2q̄
cos(θ + α) = −
2
2
P~q2q̄
(24)
11.4
Monte Carlo Results
35
cos(θ + α) = 1 − 2
11.4
Mq2q̄
P~q2q̄
(25)
Monte Carlo Results
Each gluon in the code had been selected based on the fact that it came directly from a quark and
not another gluon. The quarks which had radiated gluons could be easily selected by looking for
the mother of each gluon. This had the added advantage of being able to extract the momentum
components of the quark just before it radiated each gluon in the case of multiple gluon emission.
The gluon-radiating t and t̄ quarks were studied and the intial parton quarks were included for
comparison. The three momentum components Px , Py and Pz of the gluons and their parent quarks
were used to calculate firstly the mean momentum of the quarks at the radiation vertices and
secondly the angle between the two momentum vectors, i.e. the radiation angle. The momentum
distribution of the t and t̄ quarks is shown in Figure 26.
h1_214
Entries
25794
Mean
105.9
RMS
73.06
# Top quarks
MOMENTUM OF TOP AND TBAR QUARKS
250
200
150
100
50
0
0
100
200
300
400
500
600
700
P (GeV)
Figure 26: Total momentum of the t and t̄ pair
The mean value of the top momentum is 105.9 GeV. This is the three momentum and in the
kinematical formulation in Equation 25 its square must be added to the square of the mass of top
36
11
to form the square of the relativstic four-momentum. At this point the trajectory of the quarks is
assumed not to deflect, α is assumed zero and the radiation angle θ is calculated.
cosθ = 1 −
2 · 175.92
⇒ θ = 1.03rad = 58.95◦
105.92 + 175.92
(26)
This is of the order of double the value predicted using the centre of mass energy of the hard
scattering system. Figure ?? displayes the distribution of the gluon radiation angle in the HERWIGgenerated events.
# Gluons
ANGLE OF GLUON RADIATION FROM T AND TBAR QUARKS
500
h1_210
Entries
25794
Mean
0.5365
RMS
0.4655
400
300
200
100
0
0
0.5
1
1.5
2
2.5
3
Angle of Radiation (radians)
Figure 27: Distribution of angles at which gluons radiated from t and t̄ quarks in the sample
As can be seen there is a region at low θ where there are very few gluon radiations. There is not
a perfect cut off due to energy smearing, although there is a clear peak at ∼ 0.1 rad. This is much
lower than the two values calculated via the QCD approximation and the kinematics. The mean
value of 0.54 rad is very similar to the minimum angle of 0.53 rad calculated in the QCD parton
momentum approximation. With a minimum angle of 0.1 rad, as is implied by the HERWIG data,
the mean momentum calculated via kinematics would be ∼ 1753 GeV. This is of the order of 17
times the value of the mean momentum calculated from the simulated data. For comparison, the
momentum and gluon radiation distributions of the initial parton quarks were plotted (see Figures
?? and ??).
Monte Carlo Results
37
h1_215
Entries
23180
Mean
243.4
RMS
116.3
MOMENTUM OF INITIAL QUARKS
# Top quarks
11.4
160
140
120
100
80
60
40
20
0
0
100
200
300
400
500
600
700
800
900
P (GeV)
Figure 28: Total momentum of the initial parton quarks
38
11
# Gluons
ANGLE OF GLUON RADIATION FROM INITIAL QUARKS
600
h1_211
Entries
23180
Mean
0.5123
RMS
0.5247
500
400
300
200
100
0
0
0.5
1
1.5
2
2.5
3
Angle of Radiation (radians)
Figure 29: Distribution of angles at which gluons radiated from the initial parton quarks in the
sample
39
The average momentum of the initial partons was found to be 243.4 GeV and the peak of the
gluon radiation distribution at approximately 0.05 rad. Using kinematics as before (Equation 25
the theoretical minimum angle was calculated. The rest mass of an average initial parton was again
taken as 5 MeV.
cosθ = 1 −
2 · 0.0052
⇒ θ = 4.11 · 10−5 rad = (2.35 · 103 )◦
243.42 + 0.0052
(27)
Thus the minumum angle suggested by the HERWIG distribution is not sufficiently small to
account for the larger momentum of the initial parton quarks. The minimum angle suggested by the
QCD parton approximation is however of the same order of magnitude, if slightly larger at 1.5·10−5
rad. There are several approximations that have gone into these calculations, most notably the
assumption that the initial partons each carry one third of the proton’s momentum. However,
within the scope of the defined kinematical formulae, the HERWIG results for momentum and
dead cone angle do not agree well. Because of the incomputable collinear singularity of a ‘massless’
quark, HERWIG generates a suppression region around light quarks so that gluons are only radiated
down to a small dead cone cut off angle. This can be seen in the radiation angle distribution (Figure
??) in the peak at 0.05 rad.
12
12.1
Future developments
Comparison with CDF Data
In order to gain a comprehensive understanding of the nature of QCD radiation in events at the
Tevatron, a comparison with the real CDF data needs to be made. The theoretical calculations
made in the previous section suggest that the gluon radiation angles should be much larger than
those simulated by HERWIG. The calculations in this study were made using data which was known
to contain top quarks and to decay via the most common channel. Working with the real data is
much more complicated due to its statistical nature. The study of the lab frame gluon distributions
for the different quarks may help to isolate those jets which are most likely to have originated from
top quark gluon emissions. The isolated jet observed in several top quark candidate events could
also be compared with the simulated momentum and η − φ distributions. The disparities between
the HERWIG distributions and the theoretical calculations could be investigated further, using real
data to verify one or the other, or neither.
12.2
A Jet Algorithm
A potential next step in this investigation would have been to use the simulated momentum and
spatial gluon distributions in order to improve upon the jet clustering algorithms currently in use
at CDF, potentially including the possibility of extra hadronic jets. A typical clustering algorithm
works by selecting the calorimeter tower with the highest energy deposit in a jet, then associating
with it all others within a fixed separation, usually ∆R = 0.4 at CDF. From the remaining towers
in the cluster, the one with the highest energy is selected and together with all of the others within
∆R, forms a second jet. The process is repeated until all of the calorimeter towers have been
accounted for. At the current time the hadronic products of the top quark’s gluon radiation may
be getting excluded completely or being mistaken as being from a different origin. Either way there
are potential errors on the reconstructed top mass and these need to be quantified.
40
13
15
ACKNOWLEDGEMENTS
Conclusion
The main success of this investigation has been to isolate the η region in the lab frame in which jets
produced by QCD radiation from top quarks may be the most easily identified. There have been a
few surprises in the apparent distribution asymmetries between gluons radiating from t and t̄ quarks
and in the wider scope of the investigation, quarks and antiquarks generally. The gluons radiating
from the top quark pair were found to have a very similar mean PT to those radiating from the
bottom quarks, although the initial parton quark gluons radiated away on average approximately
half this amount of PT per gluon. There was a disparity in the total PT radiated from each quark
with respect to its antiquark partner, the antiquarks losing less momentum in total compared to
the quarks. This effect was most pronounced in the case of the initial parton quarks. The PT of
the maximum PT gluons also showed a marked difference between quarks and antiquarks. The
top quarks were found to lose on average 14.42 GeV in PT through gluon radiation and the PT of
gluons from the antitops totalled on average 13.78 GeV. In Reference [?] shoulders on the lower and
upper sides of the Breit-Wigner peaks of the reconstructed top mass were found when the the extra
hadronic jets were included or omitted, respectively. Thus it was found that the mass of the top
cannot be unambiguously determined in either case. However, if the jet source can be determined
as most likely being the top quarks then the decision can be made to include the jet. The finding of
this investigation was that in the η regions of -2.0 to -3.5 and 2.5 to 4.0, gluon jets are more likely
to be from top quarks than bottom quarks. Jets arising from the initial parton quarks have a lower
mean PT and as such, over large statistics, can be eliminated. The asymmetries between gluon
PT for quarks and antiquarks may also be useful in determining whether a jet arose from the t or
t̄. A comparison with real CDF data needs to be made in order to establish whether this is possible.
The theoretical calculations of the top quark dead cone did not agree well with the results suggested by the HERWIG simulations. For the t and t̄ the angular distribution of gluon radiation
suggested a dead cone that is of the order of 10% of the size of that calculated using kinematics and
approximtely only 20% of that calculated by an approximation based on the centre of mass energy
of the system. The initial parton quarks are generally assumed to be almost massless in gluon radiation studies and HERWIG creates an artificial cut off region close to the direction of momentum.
However, this cut off region was found to be a much better approximation to the centre of mass
QCD calculation in this case, agreeing to within an order of magnitude. The understanding of this
process is still somewhat limited and again the results need to be compared to experimental data
in order to work out what is really happening. Once the findings of this investigation have been
compared to experimental data, progress can be made towards the improvement of jet clustering
algorithms and the reduction of the uncertainty on the top mass.
14
Website
A website dedicated to this project is located at:
http://www.hep.ucl.ac.uk/˜crobson/
15
Acknowledgements
I would like to thank Dr Mark Lancaster for his patience and dedication during the course of this
project and Dr David Waters for acting as a second supervisor. I would also like to thank Dr Stuart
Boogert and Dr Mark Sutton for their invaluable help and advice.
REFERENCES
41
References
[1] S. Frixione. Top Quark Distributions in Hadronic Collisions. 1995, [hep-ph/9503213].
[2] CDF Collaboration. Measurement of the Top Mass. Physical Review Letters, 80(13):2767–2772,
1995.
[3] CDF Collaboration. Measurements of Soft QCD Radiation in Top Events from pp̄ Collisions at
√
s = 1.8 TeV. 2002, CDF/PUB/TOP PUBLIC/6243.
[4] L.H. et al. Orr. Gluon Radiation in tt̄ Production at the Fermilab Tevatron pp̄ Collider. Physical
Review D., 52(1):124–132, 1995.
[5] W.J. Webber R.K. Ellis, W.J. Stirling. QCD and Collider Physics. Cambridge, 1996.
42
A
A.1
A
Code
Setting Up Histogram Objects in ROOT
CODE
A.1
43
// Set up histograms (ref.no, title, no.of bins, min, max, zero (must be there))
//Initial state quarks______________________________________________________
gH->Hbook1(1,"PT OF GLUONS RADIATING FROM INITIAL STATE QUARK",150,0.0,150.0
,0.);
gH->Hbook1(2,"PT OF GLUONS RADIATING FROM INITIAL STATE ANTIQUARK",150,0.0,1
50.0,0.);
gH->Hbook1(3,"TOTAL PT OF GLUONS RADIATING FROM INITIAL STATE Q+QBAR",200,0.
0,200.0,0.);
gH->Hbook1(4,"CONE LOSSES FROM QUARK SYSTEM",200,0.999,1.001,0.);
gH->Hbook1(5,"CONE LOSSES FROM ANTIQUARK SYSTEM",200,0.9,1.1,0.);
gH->Hbook1(6,"PT OF GLUONS RADIATING FROM INITIAL STATE QUARK CORRECTED FOR
CONE LOSSES",150,-2.0,150.0,0.);
gH->Hbook1(7,"PT OF GLUONS RADIATING FROM INITIAL STATE ANTIQUARK CORRECTED
FOR CONE LOSSES",150,-2.0,150.0,0.);
gH->Hbook1(8,"TOTAL PT OF GLUONS RADIATING FROM INITIAL STATE Q+QBAR CORRECT
ED FOR CONE LOSSES",200,0.0,200.0,0.);
gH->Hbook1(9,"Q CODING TEST",100,0.0,100.0,0.);
//Top quark_________________________________________________________________
gH->Hbook1(10,"PT OF GLUONS RADIATING FROM TOP",150,0.0,150.0,0.);
gH->Hbook1(11,"PT OF GLUONS RADIATING FROM ANTITOP",150,0.0,150.0,0.);
gH->Hbook1(12,"TOTAL PT OF GLUONS RADIATING FROM T+TBAR",200,0.0,200.0,0.);
gH->Hbook1(13,"CONE LOSSES FROM TOP SYSTEM",100,0.0,100.0,0.);
gH->Hbook1(14,"CONE LOSSES FROM ANTITOP SYSTEM",100,0.0,100.0,0.);
gH->Hbook1(15,"PT OF GLUONS RADIATING FROM INITIAL STATE TOP CORRECTED FOR C
ONE LOSSES",100,0.0,100.0,0.);
gH->Hbook1(16,"PT OF GLUONS RADIATING FROM INITIAL STATE ANTITOP CORRECTED F
OR CONE LOSSES ",100,0.0,100.0,0.);
gH->Hbook1(17,"TOTAL PT OF GLUONS RADIATING FROM T+TBAR CORRECTED FOR CONE L
OSSES",300,0.0,300.0,0.);
gH->Hbook1(18,"TQ CODING TEST",100,0.0,100.0,0.);
//Bottom quark______________________________________________________________
gH->Hbook1(19,"PT OF GLUONS RADIATING FROM B QUARK (NO CORRECTIONS)",250,0.0
,250.0,0.);
gH->Hbook1(20,"PT OF GLUONS RADIATING FROM BBAR QUARK (NO CORRECTIONS)",250,
0.0,250.0,0.);
gH->Hbook1(21,"TOTAL PT OF GLUONS RADIATING FROM B+BBAR (NO CORRECTIONS)",35
0,0.0,350.0,0.);
gH->Hbook1(22,"CONE LOSSES FROM B QUARK SYSTEM",100,0.0,100.0,0.);
gH->Hbook1(23,"CONE LOSSES FROM BBAR QUARK SYSTEM",100,0.0,100.0,0.);
gH->Hbook1(24,"PT OF GLUONS RADIATING FROM B QUARK CORRECTED FOR CONE LOSSES
",200,0.0,200.0,0.);
gH->Hbook1(25,"PT OF GLUONS RADIATING FROM BBAR QUARK CORRECTED FOR CONE LOS
44
A
CODE
SES",200,0.0,200.0,0.);
gH->Hbook1(26,"HADRONISATION LOSSES FROM B QUARK SYSTEM",200,0.0,200.0,0.);
gH->Hbook1(27,"HADRONISATION LOSSES FROM BBAR QUARK SYSTEM",200,0.0,200.0,0.
);
gH->Hbook1(28,"PT OF GLUONS RADIATING FROM B QUARK CORRECTED FOR HADRONISATI
ON LOSSES",250,-250,250.0,0.);
gH->Hbook1(29,"PT OF GLUONS RADIATING FROM BBAR QUARK CORRECTED FOR HADRONIS
ATION LOSSES",250,-250,250.0,0.);
gH->Hbook1(30,"TOTAL PT OF GLUONS RADIATING FROM B + BBAR CORRECTED FOR HADR
ONISATION LOSSES",350,-250,350.0,0.);
gH->Hbook1(31,"PT OF GLUONS RADIATING FROM B QUARK CORRECTED FOR CONE AND HA
DRONISATION LOSSES",200,0.0,200.0,0.);
gH->Hbook1(32,"PT OF GLUONS RADIATING FROM BBAR QUARK CORRECTED FOR CONE AND
HADRONISATION LOSSES",200,0.0,200.0,0.);
gH->Hbook1(33,"TOTAL PT OF GLUONS RADIATING FROM B + BBAR CORRECTED FOR CONE
AND HADRONISATION LOSSES",200,0.0,200.0,0.);
gH->Hbook1(34,"B CODING TEST",200,0.0,200.0,0.);
//Calculations directly from gluons__________________________________________
gH->Hbook1(35,"PT OF FIRST B MESON",300,0.0,300.0,0.);
gH->Hbook1(36,"PT OF FIRST BBAR MESON",300,0.0,300.0,0.);
gH->Hbook1(37,"PT DIFFERENCE BETWEEN B MESON AND THE INITIAL B QUARK",600,-3
00,300.0,0.);
gH->Hbook1(38,"PT DIFFERENCE BETWEEN BBAR MESON AND THE INITIAL BBAR QUARK",
400,-200,200.0,0.);
gH->Hbook1(39,"PT DIFFERENCE BETWEEN B AND B MESON MINUS HARONISATION LOSSES
",300,-150,150.0,0.);
gH->Hbook1(40,"PT DIFFERENCE BETWEEN BBAR AND BBAR MESON MINUS HARONISATION
LOSSES",400,-200,200.0,0.);
gH->Hbook1(41,"PT OF
,200,0.0,200.0,0.);
200,0.0,200.0,0.);
s)",200,0.0,200.0,0.);
)",200,0.0,200.0,0.);
.0,200.0,0.);
0,200.0,0.);
0.0,200.0,0.);
GLUONS RADIATING FROM INITIAL Q (initial/final states)"
GLUONS RADIATING FROM INITIAL Q (intermediate states)",
GLUONS RADIATING FROM INITIAL Q",200,0.0,200.0,0.);
GLUONS RADIATING FROM INITIAL QBAR (initial/final state
GLUONS RADIATING FROM INITIAL QBAR (intermediate states
GLUONS RADIATING FROM INITIAL QBAR",200,0.0,200.0,0.);
GLUONS RADIATING FROM TOP (initial/final states)",200,0
GLUONS RADIATING FROM TOP (intermediate states)",200,0.
GLUONS RADIATING FROM TOP",200,0.0,200.0,0.);
GLUONS RADIATING FROM TBAR (initial/final states)",200,
A.1
gH->Hbook1(51,"PT
.0,200.0,0.);
gH->Hbook1(52,"PT
gH->Hbook1(53,"PT
,200.0,0.);
gH->Hbook1(54,"PT
200.0,0.);
gH->Hbook1(55,"PT
gH->Hbook1(56,"PT
0.0,200.0,0.);
gH->Hbook1(57,"PT
.0,200.0,0.);
gH->Hbook1(58,"PT
45
OF GLUONS RADIATING FROM TBAR (intermediate states)",200,0
OF GLUONS RADIATING FROM TBAR",200,0.0,200.0,0.);
OF GLUONS RADIATING FROM B (initial/final states)",200,0.0
OF GLUONS RADIATING FROM B (intermediate states)",200,0.0,
OF GLUONS RADIATING FROM B",200,0.0,200.0,0.);
OF GLUONS RADIATING FROM BBAR (initial/final states)",200,
OF GLUONS RADIATING FROM BBAR (intermediate states)",200,0
OF GLUONS RADIATING FROM BBAR",200,0.0,200.0,0.);
gH->Hbook1(59,"TOTAL PT OF GLUONS
al states)",200,0.0,200.0,0.);
e states)",200,0.0,200.0,0.);
.0,0.);
final states)",200,0.0,200.0,0.);
iate states)",200,0.0,200.0,0.);
,200.0,0.);
tes)",200,0.0,200.0,0.);
es)",200,0.0,200.0,0.);
ates)",200,0.0,200.0,0.);
tes)",200,0.0,200.0,0.);
.);
s)",200,0.0,200.0,0.);
)",200,0.0,200.0,0.);
ates)",200,0.0,200.0,0.);
tes)",200,0.0,200.0,0.);
);
RADIATING FROM EACH INITIAL Q (initial/fin
RADIATING FROM EACH INITIAL Q (intermediat
RADIATING FROM EACH INITIAL Q",200,0.0,200
RADIATING FROM EACH INITIAL QBAR (initial/
RADIATING FROM EACH INITIAL QBAR (intermed
RADIATING FROM EACH INITIAL QBAR ",200,0.0
RADIATING FROM EACH TOP (initial/final sta
RADIATING FROM EACH TOP (intermediate stat
RADIATING FROM EACH TOP ",200,0.0,200.0,0.);
RADIATING FROM EACH TBAR (initial/final st
RADIATING FROM EACH TBAR (intermediate sta
RADIATING FROM EACH TBAR ",200,0.0,200.0,0
RADIATING FROM EACH B (initial/final state
RADIATING FROM EACH B (intermediate states
RADIATING FROM EACH B ",200,0.0,200.0,0.);
RADIATING FROM EACH BBAR (initial/final st
RADIATING FROM EACH BBAR (intermediate sta
RADIATING FROM EACH BBAR",200,0.0,200.0,0.
gH->Hbook1(77,"PT OF MAX PT GLUON FROM INITIAL Q (initial/final states)",200
46
,0.0,200.0,0.);
gH->Hbook1(78,"PT
0.0,200.0,0.);
gH->Hbook1(79,"PT
gH->Hbook1(80,"PT
200,0.0,200.0,0.);
gH->Hbook1(81,"PT
00,0.0,200.0,0.);
gH->Hbook1(82,"PT
gH->Hbook1(83,"PT
00.0,0.);
gH->Hbook1(84,"PT
0.0,0.);
gH->Hbook1(85,"PT
gH->Hbook1(86,"PT
,200.0,0.);
gH->Hbook1(87,"PT
200.0,0.);
gH->Hbook1(88,"PT
gH->Hbook1(89,"PT
.0,0.);
gH->Hbook1(90,"PT
0,0.);
gH->Hbook1(91,"PT
gH->Hbook1(92,"PT
200.0,0.);
gH->Hbook1(93,"PT
00.0,0.);
gH->Hbook1(94,"PT
A
CODE
OF MAX PT GLUON FROM INITIAL Q (intermediate states)",200,
OF MAX PT GLUON FROM INITIAL Q",200,0.0,200.0,0.);
OF MAX PT GLUON FROM INITIAL QBAR (initial/final states)",
OF MAX PT GLUON FROM INITIAL QBAR (intermediate states)",2
OF MAX PT GLUON FROM INITIAL QBAR",200,0.0,200.0,0.);
OF MAX PT GLUON FROM TOP (initial/final states)",200,0.0,2
OF MAX PT GLUON FROM TOP (intermediate states)",200,0.0,20
OF MAX PT GLUON FROM TOP",200,0.0,200.0,0.);
OF MAX PT GLUON FROM TQBAR (initial/final states)",200,0.0
OF MAX PT GLUON FROM TQBAR (intermediate states)",200,0.0,
OF MAX PT GLUON FROM TQBAR",200,0.0,200.0,0.);
OF MAX PT GLUON FROM B (initial/final states)",200,0.0,200
OF MAX PT GLUON FROM B (intermediate states)",200,0.0,200.
OF MAX PT GLUON FROM B",200,0.0,200.0,0.);
OF MAX PT GLUON FROM BBAR (initial/final states)",200,0.0,
OF MAX PT GLUON FROM BBAR (intermediate states)",200,0.0,2
OF MAX PT GLUON FROM BBAR",200,0.0,200.0,0.);
gH->Hbook1(95,"PSEUDORAPIDITY OF GLUONS FROM INITIAL Q (initial/final states
)",100,-8.0,8.0,0.);
gH->Hbook1(96,"PSEUDORAPIDITY OF GLUONS FROM INITIAL Q (intermediate states)
",100,-8.0,8.0,0.);
gH->Hbook1(97,"PSEUDORAPIDITY OF GLUONS FROM INITIAL Q",100,-8.0,8.0,0.);
gH->Hbook1(98,"PSEUDORAPIDITY OF GLUONS FROM INITIAL QBAR (initial/final sta
tes)",100,-8.0,8.0,0.);
gH->Hbook1(99,"PSEUDORAPIDITY OF GLUONS FROM INITIAL QBAR (intermediate stat
es)",100,-8.0,8.0,0.);
gH->Hbook1(100,"PSEUDORAPIDITY OF GLUONS FROM INITIAL QBAR",100,-8.0,8.0,0.)
;
gH->Hbook1(101,"PSEUDORAPIDITY OF GLUONS FROM TOP (initial/final states)",10
0,-8.0,8.0,0.);
gH->Hbook1(102,"PSEUDORAPIDITY OF GLUONS FROM TOP (intermediate states)",100
,-8.0,8.0,0.);
gH->Hbook1(103,"PSEUDORAPIDITY OF GLUONS FROM TOP",100,-8.0,8.0,0.);
gH->Hbook1(104,"PSEUDORAPIDITY OF GLUONS FROM TBAR (initial/final states)",1
00,-8.0,8.0,0.);
gH->Hbook1(105,"PSEUDORAPIDITY OF GLUONS FROM TBAR (intermediate states)",10
0,-8.0,8.0,0.);
A.1
47
gH->Hbook1(106,"PSEUDORAPIDITY
-8.0,8.0,0.);
8.0,8.0,0.);
00,-8.0,8.0,0.);
0,-8.0,8.0,0.);
OF GLUONS FROM TBAR",100,-8.0,8.0,0.);
OF GLUONS FROM B (initial/final states)",100,
states)",100,-8.0,8.0,0.);
states)",100,-8.0,8.0,0.);
0.);
nal states)",100,-8.0,8.0,0.);
te states)",100,-8.0,8.0,0.);
.0,0.);
s)",100,-8.0,8.0,0.);
)",100,-8.0,8.0,0.);
es)",100,-8.0,8.0,0.);
s)",100,-8.0,8.0,0.);
",100,-8.0,8.0,0.);
,100,-8.0,8.0,0.);
es)",100,-8.0,8.0,0.);
s)",100,-8.0,8.0,0.);
OF MAX PT GLUON FROM INITIAL Q (initial/final
OF GLUONS FROM B (intermediate states)",100,OF GLUONS FROM B",100,-8.0,8.0,0.);
OF GLUONS FROM BBAR (initial/final states)",1
OF GLUONS FROM BBAR (intermediate states)",10
OF GLUONS FROM BBAR",100,-8.0,8.0,0.);
OF MAX PT GLUON FROM INITIAL Q (intermediate
OF MAX PT GLUON FROM INITIAL Q",100,-8.0,8.0,
OF MAX PT GLUON FROM INITIAL QBAR (initial/fi
OF MAX PT GLUON FROM INITIAL QBAR (intermedia
OF MAX PT GLUON FROM INITIAL QBAR",100,-8.0,8
OF MAX PT GLUON FROM TOP (initial/final state
OF MAX PT GLUON FROM TOP (intermediate states
OF MAX PT GLUON FROM TOP",100,-8.0,8.0,0.);
OF MAX PT GLUON FROM TBAR (initial/final stat
OF MAX PT GLUON FROM TBAR (intermediate state
OF MAX PT GLUON FROM TBAR",100,-8.0,8.0,0.);
OF MAX PT GLUON FROM B (initial/final states)
OF MAX PT GLUON FROM B (intermediate states)"
OF MAX PT GLUON FROM B",100,-8.0,8.0,0.);
OF MAX PT GLUON FROM BBAR (initial/final stat
OF MAX PT GLUON FROM BBAR (intermediate state
OF MAX PT GLUON FROM BBAR",100,-8.0,8.0,0.);
gH->Hbook1(131,"PHI OF GLUONS FROM INITIAL Q (initial/final states)",100,0.0
,6.3,0.);
gH->Hbook1(132,"PHI OF GLUONS FROM INITIAL Q (intermediate states)",100,0.0,
6.3,0.);
gH->Hbook1(133,"PHI OF GLUONS FROM INITIAL Q",100,0.0,6.3,0.);
48
A
CODE
gH->Hbook1(134,"PHI
0.0,6.3,0.);
gH->Hbook1(135,"PHI
.0,6.3,0.);
gH->Hbook1(136,"PHI
gH->Hbook1(137,"PHI
.);
gH->Hbook1(138,"PHI
);
gH->Hbook1(139,"PHI
gH->Hbook1(140,"PHI
0.);
gH->Hbook1(141,"PHI
.);
gH->Hbook1(142,"PHI
gH->Hbook1(143,"PHI
;
gH->Hbook1(144,"PHI
gH->Hbook1(145,"PHI
gH->Hbook1(146,"PHI
0.);
gH->Hbook1(147,"PHI
.);
gH->Hbook1(148,"PHI
OF GLUONS FROM INITIAL QBAR (initial/final states)",100,
gH->Hbook1(149,"PHI
00,0.0,6.3,0.);
gH->Hbook1(150,"PHI
0,0.0,6.3,0.);
gH->Hbook1(151,"PHI
gH->Hbook1(152,"PHI
",100,0.0,6.3,0.);
gH->Hbook1(153,"PHI
,100,0.0,6.3,0.);
gH->Hbook1(154,"PHI
gH->Hbook1(155,"PHI
,6.3,0.);
gH->Hbook1(156,"PHI
6.3,0.);
gH->Hbook1(157,"PHI
gH->Hbook1(158,"PHI
0,6.3,0.);
gH->Hbook1(159,"PHI
,6.3,0.);
gH->Hbook1(160,"PHI
gH->Hbook1(161,"PHI
.3,0.);
gH->Hbook1(162,"PHI
3,0.);
gH->Hbook1(163,"PHI
OF MAX PT GLUON FROM INITIAL Q (initial/final states)",1
OF GLUONS FROM INITIAL QBAR (intermediate states)",100,0
OF GLUONS FROM INITIAL QBAR",100,0.0,6.3,0);
OF GLUONS FROM TOP (initial/final states)",100,0.0,6.3,0
OF GLUONS FROM TOP (intermediate states)",100,0.0,6.3,0.
OF GLUONS FROM TOP",100,0.0,6.3,0.);
OF GLUONS FROM TBAR (initial/final states)",100,0.0,6.3,
OF GLUONS FROM TBAR (intermediate states)",100,0.0,6.3,0
OF GLUONS FROM TBAR",100,0.0,6.3,0.);
OF GLUONS FROM B (initial/final states)",100,0.0,6.3,0.)
OF GLUONS FROM B (intermediate states)",100,0.0,6.3,0.);
OF GLUONS FROM B",100,0.0,6.3,0.);
OF GLUONS FROM BBAR (initial/final states)",100,0.0,6.3,
OF GLUONS FROM BBAR (intermediate states)",100,0.0,6.3,0
OF GLUONS FROM BBAR",100,0.0,6.3,0.);
OF MAX PT GLUON FROM INITIAL Q (intermediate states)",10
OF MAX PT GLUON FROM INITIAL Q",100,0.0,6.3,0.);
OF MAX PT GLUON FROM INITIAL QBAR (initial/final states)
OF MAX PT GLUON FROM INITIAL QBAR (intermediate states)"
OF MAX PT GLUON FROM INITIAL QBAR",100,0.0,6.3,0.);
OF MAX PT GLUON FROM TOP (initial/final states)",100,0.0
OF MAX PT GLUON FROM TOP (intermediate states)",100,0.0,
OF MAX PT GLUON FROM TOP",100,0.0,6.3,0.);
OF MAX PT GLUON FROM TBAR (initial/final states)",100,0.
OF MAX PT GLUON FROM TBAR (intermediate states)",100,0.0
OF MAX PT GLUON FROM TBAR",100,0.0,6.3,0.);
OF MAX PT GLUON FROM B (initial/final states)",100,0.0,6
OF MAX PT GLUON FROM B (intermediate states)",100,0.0,6.
OF MAX PT GLUON FROM B",100,0.0,6.3,0.);
A.1
49
gH->Hbook1(164,"PHI OF MAX PT GLUON FROM BBAR (initial/final states)",100,0.
0,6.3,0.);
gH->Hbook1(165,"PHI OF MAX PT GLUON FROM BBAR (intermediate states)",100,0.0
,6.3,0.);
gH->Hbook1(166,"PHI OF MAX PT GLUON FROM BBAR",100,0.0,6.3,0.);
//Set axis titles:
for (int j = 1; j < 95; j++){
TH1D *h=gH->get1d(j);
h->GetXaxis()->SetTitle("PT (GeV)");
h->GetYaxis()->SetTitle("# Events");
}
for (int j = 95; j < 131; j++){
h->GetXaxis()->SetTitle("Pseudorapidity");
h->GetYaxis()->SetTitle("# Gluons");
}
for (int j = 131; j < 167; j++){
h->GetXaxis()->SetTitle("Phi (radians)");
}
//2D Histos___________________________________________________
gH->Hbook2(167,"DISTRIBUTION OF GLUONS
ates)",70,-7.0,7.0,63,0.0,6.3,0.0);
gH->Hbook2(168,"DISTRIBUTION OF MAX PT
inal states)",70,-7.0,7.0,63,0.0,6.3,0.0);
tes)",70,-7.0,7.0,63,0.0,6.3,0.0);
ate states)",70,-7.0,7.0,63,0.0,6.3,0.0);
.0,6.3,0.0);
.0,63,0.0,6.3,0.0);
FROM INITIAL QUARKS (initial/final st
GLUONS FROM INITIAL QUARKS (Initial/f
FROM INITIAL QUARKS (intermediate sta
GLUONS FROM INITIAL QUARKS (intermedi
FROM INITIAL QUARKS",70,-7.0,7.0,63,0
GLUONS FROM INITIAL QUARKS",70,-7.0,7
gH->Hbook2(173,"DISTRIBUTION OF GLUONS FROM INITIAL ANTIQUARKS (initial/fina
l states)",70,-7.0,7.0,63,0.0,6.3,0.0);
gH->Hbook2(174,"DISTRIBUTION OF MAX PT GLUONS FROM INITIAL ANTIQUARKS (initi
al/final states)",70,-7.0,7.0,63,0.0,6.3,0.0);
gH->Hbook2(175,"DISTRIBUTION OF GLUONS FROM INITIAL ANTIQUARKS (intermediate
states)",70,-7.0,7.0,63,0.0,6.3,0.0);
gH->Hbook2(176,"DISTRIBUTION OF MAX PT GLUONS FROM INITIAL ANTIQUARKS (inter
mediate states)",70,-7.0,7.0,63,0.0,6.3,0.0);
gH->Hbook2(177,"DISTRIBUTION OF GLUONS FROM INITIAL ANTIQUARKS",70,-7.0,7.0,
50
A
CODE
63,0.0,6.3,0.0);
gH->Hbook2(178,"DISTRIBUTION OF MAX PT GLUONS FROM INITIAL ANTIQUARKS",70,-7
.0,7.0,63,0.0,6.3,0.0);
)",70,-7.0,7.0,63,0.0,6.3,0.0);
states)",70,-7.0,7.0,63,0.0,6.3,0.0);
",70,-7.0,7.0,63,0.0,6.3,0.0);
states)",70,-7.0,7.0,63,0.0,6.3,0.0);
.3,0.0);
3,0.0,6.3,0.0);
FROM TOP QUARKS (initial/final states
s)",70,-7.0,7.0,63,0.0,6.3,0.0);
l states)",70,-7.0,7.0,63,0.0,6.3,0.0);
)",70,-7.0,7.0,63,0.0,6.3,0.0);
6.3,0.0);
63,0.0,6.3,0.0);
FROM TBAR QUARKS (initial/final state
ates)",70,-7.0,7.0,63,0.0,6.3,0.0);
inal states)",70,-7.0,7.0,63,0.0,6.3,0.0);
70,-7.0,7.0,63,0.0,6.3,0.0);
ates)",70,-7.0,7.0,63,0.0,6.3,0.0);
,0.0);
0.0,6.3,0.0);
FROM INITIAL QUARKS (initial/final st
s)",70,-7.0,7.0,63,0.0,6.3,0.0);
l states)",70,-7.0,7.0,63,0.0,6.3,0.0);
)",70,-7.0,7.0,63,0.0,6.3,0.0);
states)",70,-7.0,7.0,63,0.0,6.3,0.0);
FROM BBAR QUARKS (initial/final state
GLUONS FROM TOP QUARKS (initial/final
FROM TOP QUARKS (intermediate states)
GLUONS FROM TOP QUARKS (intermediate
FROM TOP QUARKS",70,-7.0,7.0,63,0.0,6
GLUONS FROM TOP QUARKS",70,-7.0,7.0,6
GLUONS FROM TBAR QUARKS (initial/fina
FROM TBAR QUARKS (intermediate states
GLUONS FROM TBAR QUARKS (intermediate states)",70
FROM TBAR QUARKS",70,-7.0,7.0,63,0.0,
GLUONS FROM TBAR QUARKS",70,-7.0,7.0,
GLUONS FROM INITIAL QUARKS (initial/f
FROM B QUARKS (intermediate states)",
GLUONS FROM B QUARKS (intermediate st
FROM B QUARKS",70,-7.0,7.0,63,0.0,6.3
GLUONS FROM B QUARKS",70,-7.0,7.0,63,
GLUONS FROM BBAR QUARKS (initial/fina
FROM BBAR QUARKS (intermediate states
GLUONS FROM BBAR QUARKS (intermediate
A.1
51
gH->Hbook2(201,"DISTRIBUTION OF GLUONS FROM BBAR QUARKS",70,-7.0,7.0,63,0.0,
6.3,0.0);
gH->Hbook2(202,"DISTRIBUTION OF MAX PT GLUONS FROM BBAR QUARKS",70,-7.0,7.0,
63,0.0,6.3,0.0);
gH->Hbook2(1001,"GLUONS RADIATING FROM Q + QBAR",70,-7.0,7.0,63,0.0,6.3,0.0)
;
gH->Hbook2(1002,"GLUONS
0.0);
.0,6.3,0.0);
63,0.0,6.3,0.0);
.3,0.0);
.0,6.3,0.0);
.0,63,0.0,6.3,0.0);
.0,7.0,63,0.0,6.3,0.0);
RADIATING FROM Q + QBAR + T",70,-7.0,7.0,63,0.0,6.3,
RADIATING FROM Q + QBAR + T + TBAR",70,-7.0,7.0,63,0
RADIATING FROM Q + QBAR + T + TBAR + B",70,-7.0,7.0,
RADIATING FROM MAX PT Q + QBAR",70,-7.0,7.0,63,0.0,6
RADIATING FROM MAX PT Q + QBAR + T",70,-7.0,7.0,63,0
RADIATING FROM MAX PT Q + QBAR + T + TBAR",70,-7.0,7
RADIATING FROM MAX PT Q + QBAR + T + TBAR + B",70,-7
gH->Hbook2(1009,"GLUONS RADIATING FROM T + TBAR",70,-7.0,7.0,63,0.0,6.3,0.0)
;
gH->Hbook2(1010,"GLUONS RADIATING FROM B + BBAR",70,-7.0,7.0,63,0.0,6.3,0.0)
;
.3,0.0);
.3,0.0);
.0,6.3,0.0);
.0,63,0.0,6.3,0.0);
RADIATING FROM MAX PT B + BBAR",70,-7.0,7.0,63,0.0,6
RADIATING FROM MAX PT B + BBAR",70,-7.0,7.0,63,0.0,6
RADIATING FROM T + TBAR + B + BBAR",70,-7.0,7.0,63,0
RADIATING FROM MAX PT T + TBAR + B + BBAR",70,-7.0,7
gH->Hbook2(203,"DISTRIBUTION OF GLUONS FROM INITIAL, TOP AND B QUARKS",70,-7
.0,7.0,63,0.0,6.3,0.0);
gH->Hbook2(204,"DISTRIBUTION OF MAX PT GLUONS FROM INITIAL, TOP AND B QUARKS
",70,-7.0,7.0,63,0.0,6.3,0.0);
gH->Hbook2(205,"RATIO OF TOP QUARK GLUONS TO INITIAL QUARK GLUONS",70,-7.0,7
.0,63,0.0,6.3,0.0);
gH->Hbook2(206,"RATIO OF TOP QUARK GLUONS TO BOTTOM QUARK GLUONS",70,-7.0,7.
0,63,0.0,6.3,0.0);
gH->Hbook2(207,"RATIO OF TOP QUARK GLUONS TO INITIAL AND BOTTOM QUARK GLUONS
",70,-7.0,7.0,63,0.0,6.3,0.0);
for (int j = 167; j < 208; j++){
52
A
CODE
h->GetYaxis()->SetTitle("Phi (radians)");
}
for (int j = 1001; j < 1015; j++){
h->GetYaxis()->SetTitle("Phi (radians)");
}
//Calculating the angle of radiation from top quarks_______________________
gH->Hbook1(208,"ANGLE
,0.);
OF GLUON RADIATION FROM TOP QUARK",320,0.0,3.2,0.);
OF GLUON RADIATION FROM TBAR QUARK",320,0.0,3.2,0.);
OF GLUON RADIATION FROM T AND TBAR QUARKS",320,0.0,3.2
OF GLUON RADIATION FROM INITIAL QUARKS",320,0.0,3.2,0.
);
gH->Hbook1(212,"MOMENTUM
OF
OF
OF
OF
TOP QUARKS",700,0.0,700.0,0.);
TBAR QUARKS",700,0.0,700.0,0.);
TOP AND TBAR QUARKS",700,0.0,700.0,0.);
INITIAL QUARKS",900,0.0,900.0,0.);
for (int j = 208; j < 212; j++){
h->GetXaxis()->SetTitle("Angle of Radiation (radians)");
}
for (int j = 212; j < 216; j++){
h->GetXaxis()->SetTitle("P (GeV)");
h->GetYaxis()->SetTitle("# Top quarks");
}
A.2
A.2
Variables
Variables
53
54
A
int np =
_HepEvtBlock.hepevt.nhep;
//Select the initial state quarks:
double
double
double
double
pxQI = _HepEvtBlock.hepevt.px[3];
pyQI = _HepEvtBlock.hepevt.py[3];
pxQBarI = _HepEvtBlock.hepevt.px[4];
pyQBarI = _HepEvtBlock.hepevt.py[4];
//define and set variables for calculating difference in PT and evaluating
the effects of the ’cone’ and hadronisation (b and bbar only)
double
double
double
double
double
ptQ = 0.0;
pxQCone = 0.0;
pyQCone = 0.0;
ptQCone = 0.0;
ptQMinusCone = 0.0;
double
double
double
double
double
ptQBar = 0.0;
pxQBarCone = 0.0;
pyQBarCone = 0.0;
ptQBarCone = 0.0;
ptQBarMinusCone = 0.0;
double
double
double
double
double
ptTQ = 0.0;
pxTQCone = 0.0;
pyTQCone = 0.0;
ptTQCone = 0.0;
ptTQMinusCone = 0.0;
double
double
double
double
double
ptTQBar = 0.0;
pxTQBarCone = 0.0;
pyTQBarCone = 0.0;
ptTQBarCone = 0.0;
ptTQBarMinusCone = 0.0;
double
double
double
double
double
double
double
double
double
double
double
double
ptB = 0.0;
pxBCone = 0.0;
pyBCone = 0.0;
ptBCone = 0.0;
pxBHadrons = 0.0;
pyBHadrons = 0.0;
ptBHadrons = 0.0;
ptBMinusCone = 0.0;
ptBMinusHadrons = 0.0;
ptBMinusHadronsAndCone = 0.0;
ptBInitial = 0.0;
ptBFinal = 0.0;
CODE
A.2
Variables
double
double
double
double
double
double
double
double
double
double
double
double
ptBBar = 0.0;
pxBBarCone = 0.0;
pyBBarCone = 0.0;
ptBBarCone = 0.0;
pxBBarHadrons = 0.0;
pyBBarHadrons = 0.0;
ptBBarHadrons = 0.0;
ptBBarMinusCone = 0.0;
ptBBarMinusHadrons = 0.0;
ptBBarMinusHadronsAndCone = 0.0;
ptBBarInitial = 0.0;
ptBBarFinal = 0.0;
double totalPtGluons = 0.0;
double totalPtGluonsMinusCone = 0.0;
double totalPtTQGluons = 0.0;
double totalPtTQGluonsMinusCone = 0.0;
double totalPtBGluons = 0.0;
double totalPtBGluonsMinusHadrons = 0.0;
double totalPtBGluonsMinusHadronsAndCone = 0.0;
//Test variables to check arithmetic of code:
double Qtest = 0.0;
double TQtest = 0.0;
double Btest = 0.0;
//Define variables for the calculations based on first B mesons:
double
double
double
double
double
double
ptBmeson = 0.0;
ptBBarmeson = 0.0;
totalPtBLost = 0.0;
totalPtBBarLost = 0.0;
totalPtBLostMinusHadrons = 0.0;
totalPtBBarLostMinusHadrons = 0.0;
//Define variables for the calculations made directly from the gluons:
double
double
double
double
double
double
double
double
double
double
transverseQGluon1 = 0.0;
transverseQGluon2 = 0.0;
transverseQBarGluon1 = 0.0;
transverseQBarGluon2 = 0.0;
transverseTQGluon1 = 0.0;
transverseTQGluon2 = 0.0;
transverseTQBarGluon1 = 0.0;
transverseTQBarGluon2 = 0.0;
transverseBGluon1 = 0.0;
transverseBGluon2 = 0.0;
55
56
A
double transverseBBarGluon1 = 0.0;
double transverseBBarGluon2 = 0.0;
double
double
double
double
double
double
double
double
double
double
double
double
sumPtQGluons1 = 0.0;
sumPtQGluons2 = 0.0;
sumPtQBarGluons1 = 0.0;
sumPtQBarGluons2 = 0.0;
sumPtTQGluons1 = 0.0;
sumPtTQGluons2 = 0.0;
sumPtTQBarGluons1 = 0.0;
sumPtTQBarGluons2 = 0.0;
sumPtBGluons1 = 0.0;
sumPtBGluons2 = 0.0;
sumPtBBarGluons1 = 0.0;
sumPtBBarGluons2 = 0.0;
double
double
double
double
double
double
double
double
double
double
double
double
ptQMax1 = 0.0;
ptQMax2 = 0.0;
ptQBarMax1 = 0.0;
ptQBarMax2 = 0.0;
ptTQMax1 = 0.0;
ptTQMax2 = 0.0;
ptTQBarMax1 = 0.0;
ptTQBarMax2 = 0.0;
ptBMax1 = 0.0;
ptBMax2 = 0.0;
ptBBarMax1 = 0.0;
ptBBarMax2 = 0.0;
double
double
double
double
double
double
double
double
double
double
double
double
psRapQGluon1 = 0.0;
psRapQGluon2 = 0.0;
psRapQBarGluon1 = 0.0;
psRapQBarGluon2 = 0.0;
psRapTQGluon1 = 0.0;
psRapTQGluon2 = 0.0;
psRapTQBarGluon1 = 0.0;
psRapTQBarGluon2 = 0.0;
psRapBGluon1 = 0.0;
psRapBGluon2 = 0.0;
psRapBBarGluon1 = 0.0;
psRapBBarGluon2 = 0.0;
double
double
double
double
double
double
double
double
pseudorapidityQMax1 = 0.0;
pseudorapidityQMax2 = 0.0;
pseudorapidityQBarMax1 = 0.0;
pseudorapidityQBarMax2 = 0.0;
pseudorapidityTQMax1 = 0.0;
pseudorapidityTQMax2 = 0.0;
pseudorapidityTQBarMax1 = 0.0;
pseudorapidityTQBarMax2 = 0.0;
CODE
A.2
Variables
double
double
double
double
pseudorapidityBMax1 = 0.0;
pseudorapidityBMax2 = 0.0;
pseudorapidityBBarMax1 = 0.0;
pseudorapidityBBarMax2 = 0.0;
double
double
double
double
double
double
double
double
double
double
double
double
phiQGluon1 = 0.0;
phiQGluon2 = 0.0;
phiQBarGluon1 = 0.0;
phiQBarGluon2 = 0.0;
phiTQGluon1 = 0.0;
phiTQGluon2 = 0.0;
phiTQBarGluon1 = 0.0;
phiTQBarGluon2 = 0.0;
phiBGluon1 = 0.0;
phiBGluon2 = 0.0;
phiBBarGluon1 = 0.0;
phiBBarGluon2 = 0.0;
double
double
double
double
double
double
double
double
double
double
double
double
QMaxPtPhi1 = 0.0;
QMaxPtPhi2 = 0.0;
QBarMaxPtPhi1 = 0.0;
QBarMaxPtPhi2 = 0.0;
TQMaxPtPhi1 = 0.0;
TQMaxPtPhi2 = 0.0;
TQBarMaxPtPhi1 = 0.0;
TQBarMaxPtPhi2 = 0.0;
BMaxPtPhi1 = 0.0;
BMaxPtPhi2 = 0.0;
BBarMaxPtPhi1 = 0.0;
BBarMaxPtPhi2 = 0.0;
//Define variables to be used in dead cone calculations:
double
double
double
double
double
double
alpha = 0.0;
alphabar = 0.0;
quarkalpha = 0.0;
topmom = 0.0;
topbarmom = 0.0;
quarkmom = 0.0;
//Set index numbers to be either the maximum or zero:
int
int
int
int
TQi = np;
TQBari = np;
TQFi = 0;
TQBarFi = 0;
int Bi = np;
int BBari = np;
int BFi = 0;
57
58
A
int BBarFi = 0;
int Bmesoni = np;
int BBarmesoni = np;
CODE
A.3
A.3
Calculating PT Loss
Calculating PT Loss
59
60
A
CODE
//loop over all of the particles in the event:
for (int i = 0; i < np; i++){
int idpdg = _HepEvtBlock.hepevt.id_pdg[i];
int mother = _HepEvtBlock.hepevt.mother[i][0];
double xmom = _HepEvtBlock.hepevt.px[i];
double ymom = _HepEvtBlock.hepevt.py[i];
//look for the initial state quarks after they have radiated gluons:
if (idpdg == 94 && mother == 4){
double pxQF = xmom;
double pyQF = ymom;
double pxQGluon = pxQI-pxQF;
double pyQGluon = pyQI-pyQF;
ptQ = TMath::Sqrt((pxQGluon*pxQGluon)+(pyQGluon*pyQGluon));
}
//Calculate the PT lost in the cone:
pxQCone = xmom;
pyQCone = ymom;
ptQCone = TMath::Sqrt((pxQCone*pxQCone)+(pyQCone*pyQCone));
ptQMinusCone = ptQ - ptQCone;
}
//Look for the initial state antiquarks after they have radiated gluons:
double
double
double
double
ptQBar
pxQBarF = xmom;
pyQBarF = ymom;
pxQBarGluon = pxQBarI-pxQBarF;
pyQBarGluon = pyQBarI-pyQBarF;
= TMath::Sqrt((pxQBarGluon*pxQBarGluon)+(pyQBarGluon*pyQBarGluon))
;
}
pxQBarCone = xmom;
pyQBarCone = ymom;
ptQBarCone = TMath::Sqrt((pxQBarCone*pxQBarCone)+(pyQBarCone*pyQBarCone));
ptQBarMinusCone = ptQBar - ptQBarCone;
A.3
Calculating PT Loss
61
}
//Look for the initial and final top quark entries:
if (idpdg == 6){
if (i < TQi){
TQi = i;
}
if (i > TQFi){
TQFi = i;
}
}
double
double
double
double
double
double
ptTQ =
pxTQI = _HepEvtBlock.hepevt.px[TQi];
pyTQI = _HepEvtBlock.hepevt.py[TQi];
pxTQF = _HepEvtBlock.hepevt.px[TQFi];
pyTQF = _HepEvtBlock.hepevt.py[TQFi];
pxTQGluon = pxTQI-pxTQF;
pyTQGluon = pyTQI-pyTQF;
TMath::Sqrt((pxTQGluon*pxTQGluon)+(pyTQGluon*pyTQGluon));
if ((_HepEvtBlock.hepevt.mother[i][0] == TQi + 1) && (idpdg == 0)){
pxTQCone = xmom;
pyTQCone = ymom;
ptTQCone = TMath::Sqrt((pxTQCone*pxTQCone)+(pyTQCone*pyTQCone));
}
ptTQMinusCone = ptTQ - ptTQCone;
//Look for the initial and final tbar entries:
if (idpdg == -6){
if (i < TQBari){
TQBari = i;
}
if (i > TQBarFi){
TQBarFi = i;
}
}
double pxTQBarI = _HepEvtBlock.hepevt.px[TQBari];
double pyTQBarI = _HepEvtBlock.hepevt.py[TQBari];
double pxTQBarF = _HepEvtBlock.hepevt.px[TQBarFi];
double pyTQBarF = _HepEvtBlock.hepevt.py[TQBarFi];
double pxTQBarGluon = pxTQBarI-pxTQBarF;
double pyTQBarGluon = pyTQBarI-pyTQBarF;
ptTQBar = TMath::Sqrt((pxTQBarGluon*pxTQBarGluon)+(pyTQBarGluon*pyTQBarGluon
));
62
A
CODE
if ((_HepEvtBlock.hepevt.mother[i][0] == TQBari + 1) && (idpdg == 0)){
pxTQBarCone = xmom;
pyTQBarCone = ymom;
ptTQBarCone = TMath::Sqrt((pxTQBarCone*pxTQBarCone)+(pyTQBarCone*pyTQBarCo
ne));
}
ptTQBarMinusCone = ptTQBar - ptTQBarCone;
//Look for the initial and final b entries:
if (idpdg == 5){
if (i < Bi){
Bi = i;
}
if (i > BFi){
BFi = i;
}
}
double pxBI = _HepEvtBlock.hepevt.px[Bi];
double pyBI = _HepEvtBlock.hepevt.py[Bi];
ptBInitial = TMath::Sqrt((pxBI*pxBI)+(pyBI*pyBI));
double pxBF = _HepEvtBlock.hepevt.px[BFi];
double pyBF = _HepEvtBlock.hepevt.py[BFi];
ptBFinal = TMath::Sqrt((pxBF*pxBF)+(pyBF*pyBF));
double pxBGluon = pxBI-pxBF;
double pyBGluon = pyBI-pyBF;
ptB = TMath::Sqrt((pxBGluon*pxBGluon)+(pyBGluon*pyBGluon));
if ((_HepEvtBlock.hepevt.mother[i][0] == Bi + 1) && (idpdg == 0)){
pxBCone = xmom;
pyBCone = ymom;
ptBCone = TMath::Sqrt((pxBCone*pxBCone)+(pyBCone*pyBCone));
}
ptBMinusCone = ptB - ptBCone;
//Calculate the PT lost to hadronisation processes:
if ((_HepEvtBlock.hepevt.mother[i][0] == _HepEvtBlock.hepevt.mother[BFi][0])
&& (idpdg != 5) && (idpdg != -5)){
pxBHadrons = pxBHadrons + _HepEvtBlock.hepevt.px[i];
pyBHadrons = pyBHadrons + _HepEvtBlock.hepevt.py[i];
ptBHadrons = TMath::Sqrt((pxBHadrons*pxBHadrons)+(pyBHadrons*pyBHadrons));
A.3
Calculating PT Loss
63
}
ptBMinusHadrons = ptB - ptBHadrons;
ptBMinusHadronsAndCone = ptBMinusHadrons - ptBCone;
//Look for the initial and final bbar entries:
if (idpdg == -5){
if (i < BBari){
BBari = i;
}
if (i > BBarFi){
BBarFi = i;
}
}
double pxBBarI = _HepEvtBlock.hepevt.px[BBari];
double pyBBarI = _HepEvtBlock.hepevt.py[BBari];
ptBBarInitial = TMath::Sqrt((pxBBarI*pxBBarI)+(pyBBarI*pyBBarI));
double pxBBarF = _HepEvtBlock.hepevt.px[BBarFi];
double pyBBarF = _HepEvtBlock.hepevt.py[BBarFi];
ptBBarFinal = TMath::Sqrt((pxBBarF*pxBBarF)+(pyBBarF*pyBBarF));
double pxBBarGluon = pxBBarI-pxBBarF;
double pyBBarGluon = pyBBarI-pyBBarF;
ptBBar = TMath::Sqrt((pxBBarGluon*pxBBarGluon)+(pyBBarGluon*pyBBarGluon));
if ((_HepEvtBlock.hepevt.mother[i][0] == BBari + 1) && (idpdg == 0)){
pxBBarCone = _HepEvtBlock.hepevt.px[i];
pyBBarCone = _HepEvtBlock.hepevt.py[i];
ptBBarCone = TMath::Sqrt((pxBBarCone*pxBBarCone)+(pyBBarCone*pyBBarCone));
}
ptBBarMinusCone = ptBBar - ptBBarCone;
//Calculate the PT lost to hadronisation processes:
if ((_HepEvtBlock.hepevt.mother[i][0] == _HepEvtBlock.hepevt.mother[BBarFi][
0]) && (idpdg != 5) && (idpdg != -5)){
pxBBarHadrons = pxBBarHadrons + _HepEvtBlock.hepevt.px[i];
pyBBarHadrons = pyBBarHadrons + _HepEvtBlock.hepevt.py[i];
ptBBarHadrons = TMath::Sqrt((pxBBarHadrons*pxBBarHadrons)+(pyBBarHadrons*p
yBBarHadrons));
}
ptBBarMinusHadrons = ptBBar - ptBBarHadrons;
ptBBarMinusHadronsAndCone = ptBBarMinusHadrons - ptBCone;
//Locate the first appearances of B0bar and B- mesons (from b quark)
64
A
CODE
if (idpdg == 511 || idpdg == 521 || idpdg ==10511 || idpdg == 10521 || idpdg
== 513
|| idpdg == 523 || idpdg == 10513 || idpdg == 10523 || idpdg == 20513 ||
idpdg == 20523
|| idpdg == 515 || idpdg == 525 || idpdg == 531 || idpdg == 10531 || idp
dg == 533
|| idpdg == 10533 || idpdg == 20533 || idpdg == 535 || idpdg ==541 || id
pdg == 10541
|| idpdg == 543 || idpdg == 10543 || idpdg == 20543 || idpdg == 545){
if (i < Bmesoni){
Bmesoni = i;
}
}
double pxBmeson = _HepEvtBlock.hepevt.px[Bmesoni];
double pyBmeson = _HepEvtBlock.hepevt.py[Bmesoni];
ptBmeson = TMath::Sqrt((pxBmeson*pxBmeson)+(pyBmeson*pyBmeson));
//Locate the first appearances of B0 and B+ mesons (from bbar quark)
if (idpdg ==-511 || idpdg ==-521 || idpdg ==-10511 || idpdg ==-10521 || idpd
g ==-513
|| idpdg ==-523 || idpdg ==-10513 || idpdg ==-10523 || idpdg ==-20513 || i
dpdg ==-20523
|| idpdg ==-515 || idpdg ==-525 || idpdg ==-531 || idpdg ==-10531 || idpdg
==-533
|| idpdg ==-10533 || idpdg ==-20533 || idpdg ==-535 || idpdg ==-541 || idp
dg ==-10541
|| idpdg ==-543 || idpdg ==-10543 || idpdg ==-20543 || idpdg ==-545){
if (i < BBarmesoni){
BBarmesoni = i;
}
}
double pxBBarmeson = _HepEvtBlock.hepevt.px[Bmesoni];
double pyBBarmeson = _HepEvtBlock.hepevt.py[Bmesoni];
ptBBarmeson = TMath::Sqrt((pxBBarmeson*pxBBarmeson)+(pyBBarmeson*pyBBarmeson
));
//add the transverse momenta together:
totalPtGluons = ptQ + ptQBar;
totalPtGluonsMinusCone = ptQMinusCone + ptQBarMinusCone;
totalPtTQGluons = ptTQ + ptTQBar;
totalPtTQGluonsMinusCone = ptTQMinusCone + ptTQBarMinusCone;
totalPtBGluons = ptB + ptBBar;
totalPtBGluonsMinusHadrons = ptBMinusHadrons + ptBBarMinusHadrons;
A.3
Calculating PT Loss
65
totalPtBGluonsMinusHadronsAndCone = ptBMinusHadrons + ptBBarMinusHadrons - p
tBCone - ptBBarCone;
totalPtBLost = ptBInitial - ptBmeson;
totalPtBBarLost = ptBBarInitial - ptBBarmeson;
totalPtBLostMinusHadrons = totalPtBLost - ptBHadrons;
totalPtBBarLostMinusHadrons = totalPtBBarLost - ptBBarHadrons;
//Test to see if arithmetic is correct:
Qtest = ptQ - ptQMinusCone - ptQCone;
TQtest = ptTQ - ptTQMinusCone - ptTQCone;
Btest = ptB - ptBMinusCone - ptBCone;
}
66
A.4
A
CODE
Momentum and Spatial Calculations Directly From HERWIG Gluon Entries
A.4
67
//Calculate Pt, eta and phi of the gluons as they appear in HERWIG
for (int i = 0; i < np; i++){
//Select gluons which have not radiated from other gluons:
if (idpdg == 21 && _HepEvtBlock.hepevt.id_pdg[_HepEvtBlock.hepevt.mother[0][
i]-1] != 21){
//initial u,d or s
//limit the search to particles with i=0 to i=27:
if (i<28){
//Look for the intermediate states i.e those with an idpdg of 94, whose
//mother is a u,d or s:
if((_HepEvtBlock.hepevt.id_pdg[mother-1] == 94) &&
(_HepEvtBlock.hepevt.id_pdg[_HepEvtBlock.hepevt.mother[mother-1][0]-1
]==1 ||
_HepEvtBlock.hepevt.id_pdg[_HepEvtBlock.hepevt.mother[mother-1][0]-1
]==2 ||
_HepEvtBlock.hepevt.id_pdg[_HepEvtBlock.hepevt.mother[mother-1][0]-1
]==3 ||
_HepEvtBlock.hepevt.id_pdg[_HepEvtBlock.hepevt.mother[_HepEvtBlock.h
epevt.mother[mother-1][0]-1][0]-1]==1 ||
epevt.mother[mother-1][0]-1][0]-1]==2 ||
epevt.mother[mother-1][0]-1][0]-1]==3)){
//Extract momentum components:
Double_t qx = _HepEvtBlock.hepevt.px[i];
Double_t qy = _HepEvtBlock.hepevt.py[i];
Double_t qz = _HepEvtBlock.hepevt.pz[i];
//Calculate PT
transverseQGluon1 = TMath::Sqrt((qx*qx)+(qy*qy));
gH->Hf1(42,transverseQGluon1);
//Add each gluon PT to the sum for the event:
sumPtQGluons1 = sumPtQGluons1 + transverseQGluon1;
gH->Hf1(60,sumPtQGluons1);
68
A
//Create new TLorentzVector object with momentum components as arguments
:
TLorentzVector *lorentz = new TLorentzVector(qx,qy,qz);
Double_t qEta = lorentz->PseudoRapidity();
//Assign the correct phi value according to position in the transverse p
lane:
if(qy<0.0){
Double_t qPhi = TMath::ACos(-qx/transverseQGluon1) + TMath::Pi();
phiQGluon1 = qPhi;
gH->Hf1(132,phiQGluon1);
}
if(qy>=0.0){
Double_t qPhi = TMath::ACos(qx/transverseQGluon1);
phiQGluon1 = qPhi;
}
//Define pseudorapidity of each gluon:
psRapQGluon1 = qEta;
gH->Hf1(96,psRapQGluon1);
//Fill 2D histogram with eta and phi for each gluon:
gH->Hf2(169,psRapQGluon1, phiQGluon1);
//Select mother quark’s momentum components:
Double_t quarkx = _HepEvtBlock.hepevt.px[mother-1];
Double_t quarky = _HepEvtBlock.hepevt.py[mother-1];
Double_t quarkz = _HepEvtBlock.hepevt.pz[mother-1];
//Calculate the complete momentum of the quark and the gluon:
quarkmom = TMath::Sqrt((quarkx*quarkx)+(quarky*quarky)+(quarkz*quarkz));
Double_t quarkgluonmom = TMath::Sqrt((qx*qx)+(qy*qy)+(qz*qz));
//Calculate the angle between the two vectors:
Double_t dotproduct = ((qx*quarkx)+(qy*quarky)+(qz*quarkz));
Double_t cosalpha = (dotproduct/(quarkmom*quarkgluonmom));
quarkalpha = TMath::ACos(cosalpha);
gH->Hf1(211,quarkalpha);
gH->Hf1(215,quarkmom);
//Select the highest PT gluon in the event:
CODE
A.4
69
if (transverseQGluon1 > ptQMax1){
//PT of highest PT gluon:
ptQMax1 = transverseQGluon1;
gH->Hf1(78,ptQMax1);
//eta of highest PT gluon:
pseudorapidityQMax1 = qEta;
gH->Hf1(114,pseudorapidityQMax1);
//Assign correct phi value for highest PT gluon:
if(qy<0.0){
QMaxPtPhi1 = qPhi;
gH->Hf1(150,QMaxPtPhi1);
}
if(qy>=0.0){
QMaxPtPhi1 = qPhi;
}
//Fill 2D histo with eta and phi of highest PT gluon:
gH->Hf2(170,pseudorapidityQMax1,QMaxPtPhi1);
}
}
//Select gluons from initial and final state u,d,s:
if (_HepEvtBlock.hepevt.id_pdg[mother-1] == 1 || _HepEvtBlock.hepevt.id_pd
g[mother-1] == 2
|| _HepEvtBlock.hepevt.id_pdg[mother-1] == 3){
Double_t qx = _HepEvtBlock.hepevt.px[i];
Double_t qy = _HepEvtBlock.hepevt.py[i];
Double_t qz = _HepEvtBlock.hepevt.pz[i];
transverseQGluon2 = TMath::Sqrt((qx*qx)+(qy*qy));
gH->Hf1(41,transverseQGluon2);
sumPtQGluons2 = sumPtQGluons2 + transverseQGluon2;
gH->Hf1(59,sumPtQGluons2);
TLorentzVector *lorentz = new TLorentzVector(qx,qy,qz);
Double_t qEta = lorentz->PseudoRapidity();
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A
CODE
if(qy<0.0){
phiQGluon2 = qPhi;
}
if(qy>=0.0){
phiQGluon2 = qPhi;
}
psRapQGluon2 = qEta;
gH->Hf1(95,psRapQGluon2);
gH->Hf2(167,psRapQGluon2, phiQGluon2);
if (transverseQGluon2 > ptQMax2){
ptQMax2 = transverseQGluon2;
gH->Hf1(77,ptQMax2);
pseudorapidityQMax2 = qEta;
gH->Hf1(113,pseudorapidityQMax2);
if(qy<0.0){
QMaxPtPhi2 = qPhi;
}
if(qy>=0.0){
QMaxPtPhi2 = qPhi;
}
gH->Hf2(168,pseudorapidityQMax2,QMaxPtPhi2);
}
}
//initial ubar, dbar or sbar
(_HepEvtBlock.hepevt.id_pdg[_HepEvtBlock.hepevt.mother[mother-1][0]-1]=
=-1 ||
_HepEvtBlock.hepevt.id_pdg[_HepEvtBlock.hepevt.mother[mother-1][0]-1]=
=-2 ||
_HepEvtBlock.hepevt.id_pdg[_HepEvtBlock.hepevt.mother[mother-1][0]-1]=
A.4
71
=-3 ||
_HepEvtBlock.hepevt.id_pdg[_HepEvtBlock.hepevt.mother[_HepEvtBlock.hep
evt.mother[mother-1][0]-1][0]-1]==-1 ||
evt.mother[mother-1][0]-1][0]-1]==-2 ||
evt.mother[mother-1][0]-1][0]-1]==-3)){
Double_t qbarx = _HepEvtBlock.hepevt.px[i];
Double_t qbary = _HepEvtBlock.hepevt.py[i];
Double_t qbarz = _HepEvtBlock.hepevt.pz[i];
transverseQBarGluon1 = TMath::Sqrt((qbarx*qbarx)+(qbary*qbary));
gH->Hf1(45,transverseQBarGluon1);
sumPtQBarGluons1 = sumPtQBarGluons1 + transverseQBarGluon1;
gH->Hf1(63,sumPtQBarGluons1);
TLorentzVector *lorentz = new TLorentzVector(qbarx,qbary,qbarz);
Double_t qbarEta = lorentz->PseudoRapidity();
if(qbary<0.0){
Double_t qbarPhi = TMath::ACos(-qbarx/transverseQBarGluon1) + TMath::Pi(
);
phiQBarGluon1 = qbarPhi;
gH->Hf1(135,phiQBarGluon1);
}
if(qbary>=0.0){
Double_t qbarPhi = TMath::ACos(qbarx/transverseQBarGluon1);
}
psRapQBarGluon1 = qbarEta;
gH->Hf1(99,psRapQBarGluon1);
gH->Hf2(175,psRapQBarGluon1,phiQBarGluon1);
if (transverseQBarGluon1 > ptQBarMax1){
ptQBarMax1 = transverseQBarGluon1;
gH->Hf1(81,ptQBarMax1);
pseudorapidityQBarMax1 = qbarEta;
gH->Hf1(117,pseudorapidityQBarMax1);
if(qbary<0.0){
Double_t qbarPhi = TMath::ACos(-qbarx/transverseQBarGluon1) + TMath::P
i();
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CODE
QBarMaxPtPhi1 = qbarPhi;
gH->Hf1(153,QBarMaxPtPhi1);
}
if(qbary>=0.0){
}
gH->Hf2(176,pseudorapidityQBarMax1, QBarMaxPtPhi1);
}
}
if (_HepEvtBlock.hepevt.id_pdg[mother-1] == -1 || _HepEvtBlock.hepevt.id_p
dg[mother-1] == -2 || _HepEvtBlock.hepevt.id_pdg[mother-1] == -3){
Double_t qbarx = _HepEvtBlock.hepevt.px[i];
Double_t qbary = _HepEvtBlock.hepevt.py[i];
Double_t qbarz = _HepEvtBlock.hepevt.pz[i];
transverseQBarGluon2 = TMath::Sqrt((qbarx*qbarx)+(qbary*qbary));
gH->Hf1(44,transverseQBarGluon2);
sumPtQBarGluons2 = sumPtQBarGluons2 + transverseQBarGluon2;
gH->Hf1(62,sumPtQBarGluons2);
TLorentzVector *lorentz = new TLorentzVector(qbarx,qbary,qbarz);
Double_t qbarEta = lorentz->PseudoRapidity();
if(qbary<0.0){
Double_t qbarPhi = TMath::ACos(-qbarx/transverseQBarGluon2) + TMath::Pi(
);
}
if(qbary>=0.0){
}
psRapQBarGluon2 = qbarEta;
gH->Hf1(98,psRapQBarGluon2);
gH->Hf2(173,psRapQBarGluon2,phiQBarGluon2);
if (transverseQBarGluon2 > ptQBarMax2){
ptQBarMax2 = transverseQBarGluon2;
A.4
73
gH->Hf1(80,ptQBarMax2);
pseudorapidityQBarMax2 = qbarEta;
gH->Hf1(116,pseudorapidityQBarMax2);
if(qbary<0.0){
Double_t qbarPhi = TMath::ACos(-qbarx/transverseQBarGluon2) + TMath::P
i();
}
if(qbary>=0.0){
}
gH->Hf2(174,pseudorapidityQBarMax2,QBarMaxPtPhi2);
}
}
}
//t
(_HepEvtBlock.hepevt.id_pdg[_HepEvtBlock.hepevt.mother[mother-1][0]-1]=
=6 ||
evt.mother[mother-1][0]-1][0]-1]==6)){
Double_t tx = _HepEvtBlock.hepevt.px[i];
Double_t ty = _HepEvtBlock.hepevt.py[i];
Double_t tz = _HepEvtBlock.hepevt.pz[i];
transverseTQGluon1 = TMath::Sqrt((tx*tx)+(ty*ty));
gH->Hf1(48,transverseTQGluon1);
sumPtTQGluons1 = sumPtTQGluons1 + transverseTQGluon1;
gH->Hf1(66,sumPtTQGluons1);
TLorentzVector *lorentz = new TLorentzVector(tx,ty,tz);
Double_t tEta = lorentz->PseudoRapidity();
if(ty<0.0){
Double_t tPhi = TMath::ACos(-tx/transverseTQGluon1) + TMath::Pi();
phiTQGluon1 = tPhi;
gH->Hf1(138,phiTQGluon1);
}
if(ty>=0.0){
74
A
Double_t tPhi = TMath::ACos(tx/transverseTQGluon1);
phiTQGluon1 = tPhi;
}
psRapTQGluon1 = tEta;
gH->Hf1(102,psRapTQGluon1);
gH->Hf2(181,psRapTQGluon1,phiTQGluon1);
Double_t topx = _HepEvtBlock.hepevt.px[mother-1];
Double_t topy = _HepEvtBlock.hepevt.py[mother-1];
Double_t topz = _HepEvtBlock.hepevt.pz[mother-1];
topmom = TMath::Sqrt((topx*topx)+(topy*topy)+(topz*topz));
Double_t gluonmom = TMath::Sqrt((tx*tx)+(ty*ty)+(tz*tz));
Double_t dotproduct = ((tx*topx)+(ty*topy)+(tz*topz));
Double_t cosalpha = (dotproduct/(topmom*gluonmom));
alpha = TMath::ACos(cosalpha);
gH->Hf1(208,alpha);
gH->Hf1(212,topmom);
if (transverseTQGluon1 > ptTQMax1){
ptTQMax1 = transverseTQGluon1;
gH->Hf1(84,ptTQMax1);
pseudorapidityTQMax1 = tEta;
gH->Hf1(120,pseudorapidityTQMax1);
if(ty<0.0){
TQMaxPtPhi1 = tPhi;
gH->Hf1(156,TQMaxPtPhi1);
}
if(ty>=0.0){
TQMaxPtPhi1 = tPhi;
}
gH->Hf2(182,pseudorapidityTQMax1,TQMaxPtPhi1);
}
}
if(_HepEvtBlock.hepevt.id_pdg[mother-1] == 6){
Double_t tx = _HepEvtBlock.hepevt.px[i];
CODE
A.4
Double_t ty = _HepEvtBlock.hepevt.py[i];
Double_t tz = _HepEvtBlock.hepevt.pz[i];
transverseTQGluon2 = TMath::Sqrt((tx*tx)+(ty*ty));
gH->Hf1(47,transverseTQGluon2);
sumPtTQGluons2 = sumPtTQGluons2 + transverseTQGluon2;
gH->Hf1(65,sumPtTQGluons2);
TLorentzVector *lorentz = new TLorentzVector(tx,ty,tz);
Double_t tEta = lorentz->PseudoRapidity();
if (ty<0.0){
phiTQGluon2 = tPhi;
}
if (ty>=0.0){
phiTQGluon2 = tPhi;
}
Double_t topx = _HepEvtBlock.hepevt.px[mother-1];
Double_t topy = _HepEvtBlock.hepevt.py[mother-1];
Double_t topz = _HepEvtBlock.hepevt.pz[mother-1];
topmom = TMath::Sqrt((topx*topx)+(topy*topy)+(topz*topz));
Double_t gluonmom = TMath::Sqrt((tx*tx)+(ty*ty)+(tz*tz));
Double_t dotproduct = ((tx*topx)+(ty*topy)+(tz*topz));
Double_t cosalpha = (dotproduct/(topmom*gluonmom));
alpha = TMath::ACos(cosalpha);
gH->Hf1(208,alpha);
gH->Hf1(212,topmom);
psRapTQGluon2 = tEta;
gH->Hf1(101,psRapTQGluon2);
gH->Hf2(179,psRapTQGluon2,phiTQGluon2);
if (transverseTQGluon2 > ptTQMax2){
ptTQMax2 = transverseTQGluon2;
gH->Hf1(83,ptTQMax2);
pseudorapidityTQMax2 = tEta;
gH->Hf1(119,pseudorapidityTQMax2);
75
76
A
if (ty<0.0){
TQMaxPtPhi2 = tPhi;
}
if (ty>=0.0){
TQMaxPtPhi2 = tPhi;
}
gH->Hf2(180,pseudorapidityTQMax2,TQMaxPtPhi2);
}
}
//tbar
]==-6 ||
epevt.mother[mother-1][0]-1][0]-1]==-6)){
Double_t tbarx = _HepEvtBlock.hepevt.px[i];
Double_t tbary = _HepEvtBlock.hepevt.py[i];
Double_t tbarz = _HepEvtBlock.hepevt.pz[i];
transverseTQBarGluon1 = TMath::Sqrt((tbarx*tbarx)+(tbary*tbary));
gH->Hf1(51,transverseTQBarGluon1);
sumPtTQBarGluons1 = sumPtTQBarGluons1 + transverseTQBarGluon1;
gH->Hf1(69,sumPtTQBarGluons1);
TLorentzVector *lorentz = new TLorentzVector(tbarx,tbary,tbarz);
Double_t tbarEta = lorentz->PseudoRapidity();
if(tbary<0.0){
Double_t tbarPhi = TMath::ACos(-tbarx/transverseTQBarGluon1) + TMath::Pi
();
phiTQBarGluon1 = tbarPhi;
gH->Hf1(141,phiTQBarGluon1);
}
if(tbary>=0.0){
Double_t tbarPhi = TMath::ACos(tbarx/transverseTQBarGluon1);
}
CODE
A.4
Double_t topbarx = _HepEvtBlock.hepevt.px[mother-1];
Double_t topbary = _HepEvtBlock.hepevt.py[mother-1];
Double_t topbarz = _HepEvtBlock.hepevt.pz[mother-1];
topbarmom = TMath::Sqrt((topbarx*topbarx)+(topbary*topbary)+(topbarz*top
barz));
Double_t topbargluonmom = TMath::Sqrt((tbarx*tbarx)+(tbary*tbary)+(tbarz
*tbarz));
Double_t dotproduct = ((tbarx*topbarx)+(tbary*topbary)+(tbarz*topbarz));
Double_t cosalpha = (dotproduct/(topbarmom*topbargluonmom));
alphabar = TMath::ACos(cosalpha);
gH->Hf1(209,alphabar);
gH->Hf1(213,topbarmom);
psRapTQBarGluon1 = tbarEta;
gH->Hf1(105,psRapTQBarGluon1);
gH->Hf2(187,psRapTQBarGluon1,phiTQBarGluon1);
if (transverseTQBarGluon1 > ptTQBarMax1){
ptTQBarMax1 = transverseTQBarGluon1;
gH->Hf1(87,ptTQBarMax1);
pseudorapidityTQBarMax1 = tbarEta;
gH->Hf1(123,pseudorapidityTQBarMax1);
if(tbary<0.0){
Double_t tbarPhi = TMath::ACos(-tbarx/transverseTQBarGluon1) + TMath::
Pi();
TQBarMaxPtPhi1 = tbarPhi;
gH->Hf1(159,TQBarMaxPtPhi1);
}
if(tbary>=0.0){
}
gH->Hf2(188,pseudorapidityTQBarMax1,TQBarMaxPtPhi1);
}
}
if(_HepEvtBlock.hepevt.id_pdg[mother-1] == -6){
Double_t tbarx = _HepEvtBlock.hepevt.px[i];
Double_t tbary = _HepEvtBlock.hepevt.py[i];
Double_t tbarz = _HepEvtBlock.hepevt.pz[i];
77
78
A
transverseTQBarGluon2 = TMath::Sqrt((tbarx*tbarx)+(tbary*tbary));
gH->Hf1(50,transverseTQBarGluon2);
sumPtTQBarGluons2 = sumPtTQBarGluons2 + transverseTQBarGluon2;
gH->Hf1(68,sumPtTQBarGluons2);
TLorentzVector *lorentz = new TLorentzVector(tbarx,tbary,tbarz);
Double_t tbarEta = lorentz->PseudoRapidity();
if(tbary<0.0){
Double_t tbarPhi = TMath::ACos(-tbarx/transverseTQBarGluon2) + TMath::Pi
();
}
if(tbary>=0.0){
}
Double_t topbarx = _HepEvtBlock.hepevt.px[mother-1];
Double_t topbary = _HepEvtBlock.hepevt.py[mother-1];
Double_t topbarz = _HepEvtBlock.hepevt.pz[mother-1];
topbarmom = TMath::Sqrt((topbarx*topbarx)+(topbary*topbary)+(topbarz*top
barz));
Double_t topbargluonmom = TMath::Sqrt((tbarx*tbarx)+(tbary*tbary)+(tbarz
*tbarz));
Double_t dotproduct = ((tbarx*topbarx)+(tbary*topbary)+(tbarz*topbarz));
Double_t cosalpha = (dotproduct/(topbarmom*topbargluonmom));
alphabar = TMath::ACos(cosalpha);
gH->Hf1(209,alphabar);
gH->Hf1(213,topbarmom);
psRapTQBarGluon2 = tbarEta;
gH->Hf1(104,psRapTQBarGluon2);
gH->Hf2(185,psRapTQBarGluon2,phiTQBarGluon2);
if (transverseTQBarGluon2 > ptTQBarMax2){
ptTQBarMax2 = transverseTQBarGluon2;
gH->Hf1(86,ptTQBarMax2);
pseudorapidityTQBarMax2 = tbarEta;
gH->Hf1(122,pseudorapidityTQBarMax2);
CODE
A.4
if(tbary<0.0){
Double_t tbarPhi = TMath::ACos(-tbarx/transverseTQBarGluon2) + TMath::
Pi();
}
if(tbary>=0.0){
}
gH->Hf2(186,pseudorapidityTQBarMax2,TQBarMaxPtPhi2);
}
}
//b
]==5 ||
epevt.mother[mother-1][0]-1][0]-1]==5)){
Double_t bx = _HepEvtBlock.hepevt.px[i];
Double_t by = _HepEvtBlock.hepevt.py[i];
Double_t bz = _HepEvtBlock.hepevt.pz[i];
transverseBGluon1 = TMath::Sqrt((bx*bx)+(by*by));
gH->Hf1(54,transverseBGluon1);
sumPtBGluons1 = sumPtBGluons1 + transverseBGluon1;
gH->Hf1(72,sumPtBGluons1);
TLorentzVector *lorentz = new TLorentzVector(bx,by,bz);
Double_t bEta = lorentz->PseudoRapidity();
if(by<0.0){
Double_t bPhi = TMath::ACos(-bx/transverseBGluon1) + TMath::Pi();
phiBGluon1 = bPhi;
gH->Hf1(144,phiBGluon1);
}
if(by>=0.0){
Double_t bPhi = TMath::ACos(bx/transverseBGluon1);
phiBGluon1 = bPhi;
79
80
A
}
psRapBGluon1 = bEta;
gH->Hf1(108,psRapBGluon1);
gH->Hf2(193,psRapBGluon1,phiBGluon1);
if (transverseBGluon1 > ptBMax1){
ptBMax1 = transverseBGluon1;
gH->Hf1(90,ptBMax1);
pseudorapidityBMax1 = bEta;
gH->Hf1(126,pseudorapidityBMax1);
if(by<0.0){
BMaxPtPhi1 = bPhi;
gH->Hf1(162,BMaxPtPhi1);
}
if(by>=0.0){
BMaxPtPhi1 = bPhi;
}
gH->Hf2(194,pseudorapidityBMax1,BMaxPtPhi1);
}
}
if(_HepEvtBlock.hepevt.id_pdg[mother-1] == 5){
Double_t bx = _HepEvtBlock.hepevt.px[i];
Double_t by = _HepEvtBlock.hepevt.py[i];
Double_t bz = _HepEvtBlock.hepevt.pz[i];
transverseBGluon2 = TMath::Sqrt((bx*bx)+(by*by));
gH->Hf1(53,transverseBGluon2);
sumPtBGluons2 = sumPtBGluons2 + transverseBGluon2;
gH->Hf1(71,sumPtBGluons2);
TLorentzVector *lorentz = new TLorentzVector(bx,by,bz);
Double_t bEta = lorentz->PseudoRapidity();
if(by<0.0){
phiBGluon2 = bPhi;
CODE
A.4
}
if(by>=0.0){
phiBGluon2 = bPhi;
}
psRapBGluon2 = bEta;
gH->Hf1(107,psRapBGluon2);
gH->Hf2(191,psRapBGluon2,phiBGluon2);
if (transverseBGluon2 > ptBMax2){
ptBMax2 = transverseBGluon2;
gH->Hf1(89,ptBMax2);
pseudorapidityBMax2 = bEta;
gH->Hf1(125,pseudorapidityBMax2);
if(by<0.0){
BMaxPtPhi2 = bPhi;
}
if(by>=0.0){
BMaxPtPhi2 = bPhi;
}
gH->Hf2(192,pseudorapidityBMax2,BMaxPtPhi2);
}
}
//bbar
]==-5 ||
epevt.mother[mother-1][0]-1][0]-1]==-5)){
Double_t bbarx = _HepEvtBlock.hepevt.px[i];
Double_t bbary = _HepEvtBlock.hepevt.py[i];
Double_t bbarz = _HepEvtBlock.hepevt.pz[i];
81
82
A
transverseBBarGluon1 = TMath::Sqrt((bbarx*bbarx)+(bbary*bbary));
gH->Hf1(57,transverseBBarGluon1);
sumPtBBarGluons1 = sumPtBBarGluons1 + transverseBBarGluon1;
gH->Hf1(75,sumPtBBarGluons1);
TLorentzVector *lorentz = new TLorentzVector(bbarx,bbary,bbarz);
Double_t bbarEta = lorentz->PseudoRapidity();
if(bbary<0.0){
Double_t bbarPhi = TMath::ACos(-bbarx/transverseBBarGluon1) + TMath::Pi(
);
phiBBarGluon1 = bbarPhi;
gH->Hf1(147,phiBBarGluon1);
}
if(bbary>=0.0){
Double_t bbarPhi = TMath::ACos(bbarx/transverseBBarGluon1);
}
psRapBBarGluon1 = bbarEta;
gH->Hf1(111,psRapBBarGluon1);
gH->Hf2(199,psRapBBarGluon1,phiBBarGluon1);
if (transverseBBarGluon1 > ptBBarMax1){
ptBBarMax1 = transverseBBarGluon1;
gH->Hf1(93,ptBBarMax1);
pseudorapidityBBarMax1 = bbarEta;
gH->Hf1(129,pseudorapidityBBarMax1);
if(bbary<0.0){
Double_t bbarPhi = TMath::ACos(-bbarx/transverseBBarGluon1) + TMath::P
i();
BBarMaxPtPhi1 = bbarPhi;
gH->Hf1(165,BBarMaxPtPhi1);
}
if(bbary>=0.0){
}
gH->Hf2(200,pseudorapidityBBarMax1,BBarMaxPtPhi1);
}
CODE
A.4
}
if(_HepEvtBlock.hepevt.id_pdg[mother-1] == -5){
Double_t bbarx = _HepEvtBlock.hepevt.px[i];
Double_t bbary = _HepEvtBlock.hepevt.py[i];
Double_t bbarz = _HepEvtBlock.hepevt.pz[i];
transverseBBarGluon2 = TMath::Sqrt((bbarx*bbarx)+(bbary*bbary));
gH->Hf1(56,transverseBBarGluon2);
sumPtBBarGluons2 = sumPtBBarGluons2 + transverseBBarGluon2;
gH->Hf1(74,sumPtBBarGluons2);
TLorentzVector *lorentz = new TLorentzVector(bbarx,bbary,bbarz);
Double_t bbarEta = lorentz->PseudoRapidity();
if(bbary<0.0){
Double_t bbarPhi = TMath::ACos(-bbarx/transverseBBarGluon2) +TMath::Pi()
;
}
if(bbary>=0.0){
}
psRapBBarGluon2 = bbarEta;
gH->Hf1(110,psRapBBarGluon2);
gH->Hf2(197,psRapBBarGluon2,phiBBarGluon2);
if (transverseBBarGluon2 > ptBBarMax2){
ptBBarMax2 = transverseBBarGluon2;
gH->Hf1(92,ptBBarMax2);
pseudorapidityBBarMax2 = bbarEta;
gH->Hf1(128,pseudorapidityBBarMax2);
if(bbary<0.0){
Double_t bbarPhi = TMath::ACos(-bbarx/transverseBBarGluon2) +TMath::Pi
();
}
83
84
A
if(bbary>=0.0){
}
gH->Hf2(198,pseudorapidityBBarMax2,BBarMaxPtPhi2);
}
}
}
}
CODE
A.5
A.5
Filling and Adding Histograms
85
86
A
// Get the ROOT histogram objects by passing in the integer id of histogram
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
*h41=
*h42=
*h43=
*h44=
*h45=
*h46=
*h47=
*h48=
*h49=
*h50=
*h51=
*h52=
*h53=
*h54=
*h55=
*h56=
*h57=
*h58=
*h59=
*h60=
*h61=
*h62=
*h63=
*h64=
*h65=
*h66=
*h67=
*h68=
*h69=
*h70=
*h71=
*h72=
*h73=
*h74=
*h75=
*h76=
*h77=
*h78=
*h79=
*h80=
*h81=
*h82=
*h83=
*h84=
*h85=
*h86=
*h87=
gH->get1d(41);
gH->get1d(42);
gH->get1d(43);
gH->get1d(44);
gH->get1d(45);
gH->get1d(46);
gH->get1d(47);
gH->get1d(48);
gH->get1d(49);
gH->get1d(50);
gH->get1d(51);
gH->get1d(52);
gH->get1d(53);
gH->get1d(54);
gH->get1d(55);
gH->get1d(56);
gH->get1d(57);
gH->get1d(58);
gH->get1d(59);
gH->get1d(60);
gH->get1d(61);
gH->get1d(62);
gH->get1d(63);
gH->get1d(64);
gH->get1d(65);
gH->get1d(66);
gH->get1d(67);
gH->get1d(68);
gH->get1d(69);
gH->get1d(70);
gH->get1d(71);
gH->get1d(72);
gH->get1d(73);
gH->get1d(74);
gH->get1d(75);
gH->get1d(76);
gH->get1d(77);
gH->get1d(78);
gH->get1d(79);
gH->get1d(80);
gH->get1d(81);
gH->get1d(82);
gH->get1d(83);
gH->get1d(84);
gH->get1d(85);
gH->get1d(86);
gH->get1d(87);
CODE
A.5
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
*h88= gH->get1d(88);
*h89= gH->get1d(89);
*h90= gH->get1d(90);
*h91= gH->get1d(91);
*h92= gH->get1d(92);
*h93= gH->get1d(93);
*h94= gH->get1d(94);
*h95= gH->get1d(95);
*h96= gH->get1d(96);
*h97= gH->get1d(97);
*h98= gH->get1d(98);
*h99= gH->get1d(99);
*h100= gH->get1d(100);
*h101= gH->get1d(101);
*h102= gH->get1d(102);
*h103= gH->get1d(103);
*h104= gH->get1d(104);
*h105= gH->get1d(105);
*h106= gH->get1d(106);
*h107= gH->get1d(107);
*h108= gH->get1d(108);
*h109= gH->get1d(109);
*h110= gH->get1d(110);
*h111= gH->get1d(111);
*h112= gH->get1d(112);
*h113= gH->get1d(113);
*h114= gH->get1d(114);
*h115= gH->get1d(115);
*h116= gH->get1d(116);
*h117= gH->get1d(117);
*h118= gH->get1d(118);
*h119= gH->get1d(119);
*h120= gH->get1d(120);
*h121= gH->get1d(121);
*h122= gH->get1d(122);
*h123= gH->get1d(123);
*h124= gH->get1d(124);
*h125= gH->get1d(125);
*h126= gH->get1d(126);
*h127= gH->get1d(127);
*h128= gH->get1d(128);
*h129= gH->get1d(129);
*h130= gH->get1d(130);
*h131= gH->get1d(131);
*h132= gH->get1d(132);
*h133= gH->get1d(133);
*h134= gH->get1d(134);
*h135= gH->get1d(135);
*h136= gH->get1d(136);
*h137= gH->get1d(137);
87
88
A
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
TH1D
*h138=
*h139=
*h140=
*h141=
*h142=
*h143=
*h144=
*h145=
*h146=
*h147=
*h148=
*h149=
*h150=
*h151=
*h152=
*h153=
*h154=
*h155=
*h156=
*h157=
*h158=
*h159=
*h160=
*h161=
*h162=
*h163=
*h164=
*h165=
*h166=
gH->get1d(138);
gH->get1d(139);
gH->get1d(140);
gH->get1d(141);
gH->get1d(142);
gH->get1d(143);
gH->get1d(144);
gH->get1d(145);
gH->get1d(146);
gH->get1d(147);
gH->get1d(148);
gH->get1d(149);
gH->get1d(150);
gH->get1d(151);
gH->get1d(152);
gH->get1d(153);
gH->get1d(154);
gH->get1d(155);
gH->get1d(156);
gH->get1d(157);
gH->get1d(158);
gH->get1d(159);
gH->get1d(160);
gH->get1d(161);
gH->get1d(162);
gH->get1d(163);
gH->get1d(164);
gH->get1d(165);
gH->get1d(166);
// add histos
h43->Add(h41,h42,1.0,1.0);
h46->Add(h44,h45,1.0,1.0);
h49->Add(h47,h48,1.0,1.0);
h52->Add(h50,h51,1.0,1.0);
h55->Add(h53,h54,1.0,1.0);
h58->Add(h56,h57,1.0,1.0);
h61->Add(h59,h60,1.0,1.0);
h64->Add(h62,h63,1.0,1.0);
h67->Add(h65,h66,1.0,1.0);
h70->Add(h68,h69,1.0,1.0);
h73->Add(h71,h72,1.0,1.0);
h76->Add(h74,h75,1.0,1.0);
h79->Add(h77,h78,1.0,1.0);
h82->Add(h80,h81,1.0,1.0);
h85->Add(h83,h84,1.0,1.0);
h88->Add(h86,h87,1.0,1.0);
h91->Add(h89,h90,1.0,1.0);
h94->Add(h92,h93,1.0,1.0);
CODE
A.5
h97->Add(h95,h96,1.0,1.0);
h100->Add(h98,h99,1.0,1.0);
h103->Add(h101,h102,1.0,1.0);
h106->Add(h104,h105,1.0,1.0);
h109->Add(h107,h108,1.0,1.0);
h112->Add(h110,h111,1.0,1.0);
h115->Add(h113,h114,1.0,1.0);
h118->Add(h116,h117,1.0,1.0);
h121->Add(h119,h120,1.0,1.0);
h124->Add(h122,h123,1.0,1.0);
h127->Add(h125,h126,1.0,1.0);
h130->Add(h128,h129,1.0,1.0);
h133->Add(h131,h132,1.0,1.0);
h136->Add(h134,h135,1.0,1.0);
h139->Add(h137,h138,1.0,1.0);
h142->Add(h140,h141,1.0,1.0);
h145->Add(h143,h144,1.0,1.0);
h148->Add(h146,h147,1.0,1.0);
h151->Add(h149,h150,1.0,1.0);
h154->Add(h152,h153,1.0,1.0);
h157->Add(h155,h156,1.0,1.0);
h160->Add(h158,h159,1.0,1.0);
h163->Add(h161,h162,1.0,1.0);
h166->Add(h164,h165,1.0,1.0);
TH2D
TH2D
TH2D
TH2D
TH2D
TH2D
*h167=
*h168=
*h169=
*h170=
*h171=
*h172=
gH->get2d(167);
gH->get2d(168);
gH->get2d(169);
gH->get2d(170);
gH->get2d(171);
gH->get2d(172);
TH2D
TH2D
TH2D
TH2D
TH2D
TH2D
*h173=
*h174=
*h175=
*h176=
*h177=
*h178=
gH->get2d(173);
gH->get2d(174);
gH->get2d(175);
gH->get2d(176);
gH->get2d(177);
gH->get2d(178);
TH2D
TH2D
TH2D
TH2D
TH2D
TH2D
*h179=
*h180=
*h181=
*h182=
*h183=
*h184=
gH->get2d(179);
gH->get2d(180);
gH->get2d(181);
gH->get2d(182);
gH->get2d(183);
gH->get2d(184);
TH2D
TH2D
TH2D
*h185= gH->get2d(185);
*h186= gH->get2d(186);
*h187= gH->get2d(187);
89
90
A
TH2D
TH2D
TH2D
*h188= gH->get2d(188);
*h189= gH->get2d(189);
*h190= gH->get2d(190);
TH2D
TH2D
TH2D
TH2D
TH2D
TH2D
*h191=
*h192=
*h193=
*h194=
*h195=
*h196=
gH->get2d(191);
gH->get2d(192);
gH->get2d(193);
gH->get2d(194);
gH->get2d(195);
gH->get2d(196);
TH2D
TH2D
TH2D
TH2D
TH2D
TH2D
*h197=
*h198=
*h199=
*h200=
*h201=
*h202=
gH->get2d(197);
gH->get2d(198);
gH->get2d(199);
gH->get2d(200);
gH->get2d(201);
gH->get2d(202);
TH2D
TH2D
TH2D
TH2D
TH2D
TH2D
TH2D
TH2D
TH2D
TH2D
TH2D
TH2D
TH2D
TH2D
*h1001=
*h1002=
*h1003=
*h1004=
*h1005=
*h1006=
*h1007=
*h1008=
*h1009=
*h1010=
*h1011=
*h1012=
*h1013=
*h1014=
TH2D
TH2D
TH2D
TH2D
TH2D
*h203=
*h204=
*h205=
*h206=
*h207=
gH->get2d(1001);
gH->get2d(1002);
gH->get2d(1003);
gH->get2d(1004);
gH->get2d(1005);
gH->get2d(1006);
gH->get2d(1007);
gH->get2d(1008);
gH->get2d(1009);
gH->get2d(1010);
gH->get2d(1011);
gH->get2d(1012);
gH->get2d(1013);
gH->get2d(1014);
gH->get2d(203);
gH->get2d(204);
gH->get2d(205);
gH->get2d(206);
gH->get2d(207);
h171->Add(h167,h169,1.0,1.0);
h172->Add(h168,h170,1.0,1.0);
h177->Add(h173,h175,1.0,1.0);
h178->Add(h174,h176,1.0,1.0);
h183->Add(h179,h181,1.0,1.0);
h184->Add(h180,h182,1.0,1.0);
h189->Add(h185,h187,1.0,1.0);
h190->Add(h186,h188,1.0,1.0);
CODE
A.5
h195->Add(h191,h193,1.0,1.0);
h196->Add(h192,h194,1.0,1.0);
h201->Add(h197,h199,1.0,1.0);
h202->Add(h198,h200,1.0,1.0);
h1001->Add(h171,h177,1.0,1.0);
h1002->Add(h1001,h183,1.0,1.0);
h1003->Add(h1002,h189,1.0,1.0);
h1004->Add(h1003,h195,1.0,1.0);
h203->Add(h1004,h201,1.0,1.0);
h1005->Add(h172,h178,1.0,1.0);
h1006->Add(h1005,h184,1.0,1.0);
h1007->Add(h1006,h190,1.0,1.0);
h1008->Add(h1007,h196,1.0,1.0);
h204->Add(h1008,h202,1.0,1.0);
h1009->Add(h183,h189,1.0,1.0);
h1010->Add(h184,h190,1.0,1.0);
h1011->Add(h195,h201,1.0,1.0);
h1012->Add(h196,h202,1.0,1.0);
h1013->Add(h1009,h1010,1.0,1.0);
h1014->Add(h1011,h1012,1.0,1.0);
h205->Divide(h1009,h1003,1.0,1.0);
h206->Divide(h1009,h1013,1.0,1.0);
h207->Divide(h1009,h203,1.0,1.0);
TH1D
TH1D
TH1D
*h208= gH->get1d(208);
*h209= gH->get1d(209);
*h210= gH->get1d(210);
h210->Add(h208,h209,1.0,1.0);
//TH1D
TH1D
TH1D
TH1D
*h211= gH->get1d(211);
*h212= gH->get1d(212);
*h213= gH->get1d(213);
*h214= gH->get1d(214);
h214->Add(h212,h213,1.0,1.0);
//TH1D
*h215= gH->get1d(215);
91
92
B.1
Gluon PT Histograms
Mean PT
h1_46
Entries
20083
Mean
3.905
RMS
5.331
PT OF GLUONS RADIATING FROM INITIAL QBAR
# Events
B
B
7000
6000
5000
4000
3000
2000
1000
0
0
20
40
60
80
100
120
140
160
180 200
PT (GeV)
GLUON PT HISTOGRAMS
Mean PT
93
h1_52
Entries
12749
Mean
7.702
RMS
9.781
# Events
PT OF GLUONS RADIATING FROM TBAR
1800
1600
1400
1200
1000
800
600
400
200
0
0
20
40
60
80
100
120
140
160
180 200
PT (GeV)
h1_58
Entries
9725
Mean
7.631
RMS
8.493
PT OF GLUONS RADIATING FROM BBAR
# Events
B.1
1200
1000
800
600
400
200
0
0
20
40
60
80
100
120
140
160
180 200
PT (GeV)
94
Total PT Radiated From Each Quark
h1_61
Entries
23180
Mean
13.54
RMS
17.98
TOTAL PT OF GLUONS RADIATING FROM EACH INITIAL Q
# Events
B.2
B
2500
2000
1500
1000
500
0
0
20
40
60
80
100
120
140
160
180 200
PT (GeV)
GLUON PT HISTOGRAMS
Total PT Radiated From Each Quark
95
h1_64
Entries
20083
Mean
9.405
RMS
12.88
# Events
TOTAL PT OF GLUONS RADIATING FROM EACH INITIAL QBAR
3500
3000
2500
2000
1500
1000
500
0
0
20
40
60
80
100
120
140
160
180 200
PT (GeV)
h1_67
Entries
13045
14.42
Mean
RMS
15.66
TOTAL PT OF GLUONS RADIATING FROM EACH TOP
# Events
B.2
900
800
700
600
500
400
300
200
100
0
0
20
40
60
80
100
120
140
160
180 200
PT (GeV)
96
B
h1_70
Entries
12749
Mean
13.43
RMS
15.7
# Events
TOTAL PT OF GLUONS RADIATING FROM EACH TBAR
1200
1000
800
600
400
200
0
0
20
40
60
80
100
120
140
160
h1_73
Entries
10017
Mean
13.78
14.4
RMS
TOTAL PT OF GLUONS RADIATING FROM EACH B
# Events
180 200
PT (GeV)
600
500
400
300
200
100
0
0
20
40
60
80
100
120
140
160
180 200
PT (GeV)
GLUON PT HISTOGRAMS
B.3
PT of Maximum PT Gluon
97
h1_76
Entries
9725
Mean
12.43
RMS
13.9
# Events
TOTAL PT OF GLUONS RADIATING FROM EACH BBAR
900
800
700
600
500
400
300
200
100
0
0
B.3
20
40
60
80
100
120
140
160
180 200
PT (GeV)
98
B
h1_79
Entries
12366
Mean
5.178
RMS
7.119
PT OF MAX PT GLUON FROM INITIAL Q
# Events
3500
3000
2500
2000
1500
1000
500
0
0
20
40
60
80
100
120
140
160
180 200
PT (GeV)
h1_82
Entries
13053
Mean
4.582
RMS
6.198
PT OF MAX PT GLUON FROM INITIAL QBAR
# Events
4500
4000
3500
3000
2500
2000
1500
1000
500
0
0
20
40
60
80
100
120
140
160
180 200
PT (GeV)
GLUON PT HISTOGRAMS
99
h1_85
Entries
8717
Mean
9.34
RMS
11.06
PT OF MAX PT GLUON FROM TOP
# Events
1000
800
600
400
200
0
0
20
40
60
80
100
120
140
160
180 200
PT (GeV)
h1_88
Entries
9684
Mean
8.692
RMS
10.76
PT OF MAX PT GLUON FROM TQBAR
# Events
B.3
1200
1000
800
600
400
200
0
0
20
40
60
80
100
120
140
160
180 200
PT (GeV)
100
B
h1_91
Entries
6833
Mean
9.2
RMS
9.642
# Events
PT OF MAX PT GLUON FROM B
700
600
500
400
300
200
100
0
0
20
40
60
80
100
120
140
160
h1_94
Entries
7764
Mean
8.284
RMS
9.119
PT OF MAX PT GLUON FROM BBAR
# Events
180 200
PT (GeV)
900
800
700
600
500
400
300
200
100
0
0
20
40
60
80
100
120
140
160
180 200
PT (GeV)
GLUON PT HISTOGRAMS
101
η Distributions of Max Pt Gluons
h1_115
Entries
12366
Mean
-1.778
RMS
1.343
PSEUDORAPIDITY OF MAX PT GLUON FROM INITIAL Q
# Gluons
C
600
500
400
300
200
100
0
-8
-6
-4
-2
0
2
4
6
8
Pseudorapidity
102
C η DISTRIBUTIONS OF MAX PT GLUONS
# Gluons
PSEUDORAPIDITY OF MAX PT GLUON FROM INITIAL QBAR
500
h1_118
Entries
13053
Mean
2.639
RMS
1.549
400
300
200
100
0
-8
-6
-4
-2
0
2
4
# Gluons
PSEUDORAPIDITY OF MAX PT GLUON FROM TOP
600
6
8
Pseudorapidity
h1_121
Entries
8717
Mean
0.0023
RMS
1.008
500
400
300
200
100
0
-8
-6
-4
-2
0
2
4
6
8
Pseudorapidity
103
# Gluons
PSEUDORAPIDITY OF MAX PT GLUON FROM TBAR
h1_124
Entries
9684
Mean
0.02732
RMS
0.9868
600
500
400
300
200
100
0
-8
-6
-4
-2
0
2
4
h1_127
Entries
6833
Mean
0.01093
RMS
1.033
PSEUDORAPIDITY OF MAX PT GLUON FROM B
# Gluons
6
8
Pseudorapidity
500
400
300
200
100
0
-8
-6
-4
-2
0
2
4
6
8
Pseudorapidity
104
C η DISTRIBUTIONS OF MAX PT GLUONS
# Gluons
PSEUDORAPIDITY OF MAX PT GLUON FROM BBAR
500
h1_130
Entries
7764
Mean
0.02209
RMS
1.003
400
300
200
100
0
-8
-6
-4
-2
0
2
4
6
8
Pseudorapidity

Final Report: pdf

Transcription

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