Rafael A. Badui Jason S. Bono Lei Guo Brian A. Raue

Transcription

The Beam-Helicity Asymmetry
+
+
for p ! pK K and p ! p⇡ ⇡
Rafael A. Badui
Jason S. Bono
Lei Guo
Brian A. Raue
Purpose and Status
• Purpose is to demonstrate details of analysis and receive feedback
• Emphasis on procedures
• Currently writing draft of paper and analysis note
2/29
g12 Experiment
+
• Analysis of p ! pK K
the g12 experiment
+
and p ! p⇡ ⇡
using data collected from
• All final state particles were required to be detected
• Photoproduction experiment on proton target with luminosity 68pb
1
• Photon beam was circularly polarized (max polarization ⇡ 80%) with an
energy range 1.1 5.5 GeV
• Proton target was not polarized
3/29
Event Selection
10
8
• No detached vertices for either reaction
10
6
10
5
6
• Reconstructed vertex required to lie
inside target cylinder
4
y (cm)
2
r < 2.0 cm
0
−2
110 < z <
104
70 cm
−4
−6
−8
−10
−10
10
−8
−6
−4
−2
0
x (cm)
4/29
2
4
6
8
10
3
Event Selection
10
10
9
5
8
104
7
r (cm)
6
r < 2.0 cm
10
3
10
2
5
4
110 < z <
70 cm
3
2
10
1
0
−140
−130
−120
−110
−100
−90
z (cm)
4/29
−80
−70
−60
−50
−40
1
Event Selection
r < 2.0 cm
110 < z <
70 cm
• Vertex time as determined by RF and TOF
were required to be 1 ns from each other
5/29
Event Selection
r < 2.0 cm
110 < z <
70 cm
• Vertex time as determined by RF and TOF
were required to be 1 ns from each other
5/29
Event Selection
• Multiple photons were sometimes tagged
• Several algorithms were considered
Select random photon
Select more energetic photon
Select photon with larger
probability from kinematic fitting
Remove events with multiple
tagged photons
• Analysis simply removed events with
multiple tagged photons
6/29
g12 Corrections Applied
+
p ! p⇡ ⇡
• Beam Energy Corrections
• Energy Loss
• Momentum Corrections
• Kinematic Fitting
7/29
g12 Corrections Applied
+
p ! pK K
• Beam Energy Corrections
• Energy Loss
• Momentum Corrections
• Kinematic Fitting
7/29
Invariant Mass Plots
8/29
8/29
8/29
Beam-Helicity Asymmetry
• In a given kinematic bin, ⌧ , the beam-helicity asymmetry is defined as
1
I (⌧ ) =
P (⌧ )
+
(⌧ )
+ (⌧ ) +
(⌧ )
(⌧ )
• It is measured experimentally as
Y
Iexp (⌧ ) =
+
(⌧ )
↵+
N + (⌧ )
↵+
9/29
Y
+
(⌧ )
↵
N (⌧ )
↵
Y
Iexp (⌧ ) =
+
(⌧ )
↵+
N + (⌧ )
↵+
Y
+
(⌧ )
↵
N (⌧ )
↵
±
• N (⌧ ) number of events in ⌧ coming from a ± photon helicity
• ↵
±
=
• a¯c =
1
(1
2
± a¯c )
+
N⇡ N⇡
N⇡+ +N⇡
= 0.0028 ± 0.0008 is the beam-charge asymmetry
Beam-charge asymmetry was measured using the reactions p ! p⇡
+
and p ! n⇡
10/29
0
Y
Iexp (⌧ ) =
+
(⌧ )
↵+
N + (⌧ )
↵+
±
Y
+
N (⌧ )
±
Y (⌧ ) =
X
i=1
P =
E
2
Ee
+ (Ee
(⌧ )
↵
N (⌧ )
↵
1
±
P ,i
Ee E
(Ee + 3 )
2
2
E )
E
(E
e
e
3
Each event is weighted by
inverse polarization
E )
Pe
11/29
Electron beam polarization measured
by Moller polarimeter
• Beam-Helicity asymmetry was
measured with respect to the angle
between two predefined planes
p
0
X
p
• Figure on right defines the “MesonMeson Plane Configuration”
z
X
12/29
+
x
0.3
• Comparison of I between
kaon and pion channels in Meson-Meson
Plane Configuration as function of
0.2
0.1
I
• Kaon channel has larger
asymmetry amplitude and dominated
by sin(2 )
0
−0.1
γ p → p π+ π −0.2
Fourier Fit for Iπ
+
γ p → p K K−0.3
Fourier Fit for IK
−3
−2
−1
0
φ (rad)
13/29
1
2
3
• Fourier fit is to
I ( )=
3
X
0.3
0.2
cn sin(n )
0.1
I
n=1
• Coefficients stopped at 3
after significance testing
0
−0.1
γ p → p π+ π −0.2
Hypothesis Tests
Fourier Fit for Iπ
+
γ p → p K K-
LASSO
−0.3
Fourier Fit for IK
−3
−2
−1
0
φ (rad)
14/29
1
2
3
0.4
• Investigated Fourier coefficients as
function of di↵erent kinematics
I⇡ ( ; W ) =
3
X
0.3
0.2
0.1
cn (W ) sin(n )
0
n=1
−0.1
• Pion asymmetry dominated by sin(2 )
for most of the energy range
c1
c2
c3
−0.2
−0.3
−0.4
1.8
2
2.2
2.4
2.6
W (GeV)
15/29
2.8
3
3.2
0.4
IK ( ; W ) =
3
X
0.3
0.2
0.1
cn (W ) sin(n )
0
n=1
−0.1
• Kaon asymmetry dominated by
sin( ) for most of the energy range
−0.2
c1
c2
c3
−0.3
−0.4
2.2
2.4
2.6
2.8
W (GeV)
16/29
3
3.2
Interesting peak
but probably
due to threshold effects
0.5
0.4
+
IK ( ; M (K K )) =
3
X
0.3
0.2
0.1
cn (M ) sin(n )
n=1
0
−0.1
−0.2
+
• Overall amplitude decreases as M (K K )
increases
−0.3
−0.4
−0.5
c1
c2
c3
1
1.2
1.4
1.6
+
1.8
M(K K - ) (GeV)
17/29
2
2.2
0.8
0.6
IK ( ; M (pK )) =
3
X
0.4
0.2
cn (M ) sin(n )
0
n=1
−0.2
• Overall amplitude increases as M (pK )
increases
−0.4
c1
c2
c3
−0.6
−0.8
1.4
1.6
1.8
2
2.2
M(pK - ) (GeV)
18/29
2.4
2.6
0.6
0.4
0.2
+
IK ( ; M (pK )) =
3
X
cn (M ) sin(n )
0
n=1
−0.2
c1
c2
c3
+
• Overall amplitude increases as M (pK )
increases
−0.4
−0.6
1.4
1.6
1.8
2
+
2.2
M(pK ) (GeV)
19/29
2.4
2.6
0.5
0.4
IK ( ; t
!K + )
=
3
X
0.3
0.2
0.1
cn ( t) sin(n )
0
n=1
−0.1
c1
c2
c3
−0.2
−0.3
−0.4
−0.5
0.5
1
1.5
+
2
2
-t(γ → K ) (GeV )
20/29
2.5
0.5
0.4
IK ( ; t
!K + K
)=
3
X
0.3
0.2
0.1
cn ( t) sin(n )
n=1
0
−0.1
−0.2
−0.3
−0.4
−0.5
c1
c2
c3
0.5
1
1.5
2
+
-
2.5
2
-t(γ → K K ) (GeV )
21/29
3
0.5
0.4
0.3
0.2
• Thorough study
0.1
• Repeated for other plane
configurations
0
−0.1
−0.2
−0.3
−0.4
−0.5
c1
c2
c3
0.5
1
1.5
2
+
-
2.5
2
-t(γ → K K ) (GeV )
21/29
3
X
• Figure on right defines the “Neutral
Baryon Plane Configuration”
+
p
p
z
X
22/29
0
x
X
• Figure on right defines the “Positive
Baryon Plane Configuration”
X
p
z
p
23/29
0
+
x
0.5
mm
c1
nb
-c1
pb
-c1
0.4
• Apparent agreement among leading
coefficients for different plane/angle
configurations across all kinematics
(up to sign of the permutation)
0.3
0.2
0.1
• Also true for pion channel
0
• Not true for other coefficients
−0.1
−0.2
1
1.2
1.4
1.6
1.8
M(K+K- ) (GeV)
24/29
2
2.2
0.8
0.7
0.6
0.5
mm
c1
nb
-c1
pb
-c1
0.4
0.3
0.2
0.1
0
−0.1
−0.2
1.4
1.6
1.8
2
M(pK- ) (GeV)
24/29
2.2
2.4
2.6
0.6
0.5
0.4
mm
c1
nb
-c1
pb
-c1
0.3
0.2
0.1
0
−0.1
1.4
1.6
1.8
2
M(pK+) (GeV)
24/29
2.2
2.4
2.6
0.5
mm
c1
nb
-c1
pb
-c1
0.4
0.3
0.2
0.1
0
−0.1
−0.2
0.5
1
1.5
-t(γ → K+) (GeV2 )
24/29
2
2.5
0.5
0.4
0.3
mm
c1
nb
-c1
pb
-c1
0.2
0.1
0
−0.1
−0.2
0.5
1
1.5
2
-t(γ → K+K- ) (GeV2 )
24/29
2.5
3
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
2.2
2.4
2.6
2.8
W (GeV)
24/29
3
mm
c1
nb
-c1
pb
-c1
3.2
0.4
0.3
0.2
0.1
0
−0.1
mm
c2
nb
c2
pb
c2
−0.2
−0.3
−0.4
2.2
2.4
2.6
2.8
W (GeV)
23/28
3
3.2
0.4
0.3
0.2
0.1
0
−0.1
mm
c3
nb
c3
pb
c3
−0.2
−0.3
−0.4
2.2
2.4
2.6
2.8
W (GeV)
24/29
3
3.2
Statistical Uncertainties
• Statistical uncertainties treated each event following a Bernoulli-type distribution, weighted by inverse polarization and adjusted by the beamcharge asymmetry
• For N Bernoulli trials (trial can yield either ±1), the standard error on
the average number of successes (defining +1 to be a success) is given by
p
✓
◆
2 N (+1)N ( 1)
N (+1)
=
3
N
N2
25/29
Statistical Uncertainties
• In this study, N (±1) is replaced by
±
N
↵±
= N̄
±
• Due to each event weighted by the inverse polarization, the standard error
is multiplied by the root-mean-square of the inverse polarization over all
events
• The standard error on I
is given by
p
2 N̄ + N̄
stat (I ) =
3
N̄ 2
25/29
⌧
1
P2
1
2
Systematic Uncertainties
• The systematic uncertainties were estimated by varying each cut used in
the event selection process
• The cuts were varied by 10% in each direction
• Radial Vertex Cut
r < 2.0 cm ! r < 2.2 cm
r < 2.0 cm ! r < 1.8 cm
26/29
• Longitudinal Vertex Cut
|z
|z
90| < 20.0 cm ! |z
90| < 20.0 cm ! |z
90| < 22.0 cm
90| < 18.0 cm
26/29
• Timing Cut
| t| < 1.0 ns ! | t| < 1.1 ns
| t| < 1.0 ns ! | t| < 0.9 ns
26/29
• Multiple Photon Cut
Multiple photon cut ! no multiple photon cut
26/29
• Binning
16
16
bins ! 17
bins ! 15
bins
bins
26/29
• The systematic uncertainty from an arbitrary source is estimated by
v
uX ✓
◆2
u
I
(
)
I
(
)
i
i
nom
alt
u
u
Inom ( i )
u i
✓
◆
sys = u
2
u
X
1
t
I
(
)
nom
i
i
26/29
• The total systematic uncertainty was obtained by adding the uncertainties
from the di↵erent sources in quadrature
s
X
2
=
sys,tot
sys,src
src
26/29
• Systematic uncertainties for pion
channel in the meson-meson plane
configuration
27/29
• Systematic uncertainties for kaon
channel in the meson-meson plane
configuration
27/29
channel in the neutral baryon plane
configuration
27/29
channel in the positive baryon plane
configuration
27/29
• Compared to Irms , the systematic uncertainty is ⇡ 10%
v
◆2
uX ✓
u
I
(
)
i
u
u
I
(
)
i
u i
Irms = u
✓
◆
2
uX
1
t
I
(
)
i
i
28/29
Conclusions
• Thorough study on the beam-helicity asymmetry
• Its angular dependence was studied
• Fourier coefficients studied as functions of key kinematic variables
• Procedures, results, and uncertainty estimation presented
• Systematic uncertainties on fiducial cuts and TOF knockouts to be
conducted
29/29

Rafael A. Badui Jason S. Bono Lei Guo Brian A. Raue

Transcription

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