sudeep ghosh for the clas collaboration · - 0.04 - 0.02 0 0.02 0.04 0.06 0.08 0.1 generated...
TRANSCRIPT
Dalitz Plot Analysis of η′ → η π+ π−
Sudeep Ghosh for the CLAS Collaboration
Indian Institute of Technology Indore, India
June 17, 2016
Plan of the talk
Motivation
Introduction
Analysis
Result
Summary
Motivation
• Comparative statistics collected in the channel η′ → η π+ π− byCLAS in comparison to other experiments reported so far.
• Dalitz plot(DP) provides pure kinematic information of a three bodydecay.
• DP helps to understand the correct input in theoretical distributionof the effective chiral Lagrangian.
• The decay channel has a low Q-value, thus it will help to studyeffective chiral perturbation theory at a low Q limit.
Three body decay of a meson
DALITZ PLOT BY EYE
9
Constraints Degree of freedom
3 four-vectors 12
4-momentum conservation -4
3 masses -3
3 Euler angles -3
TOT 2
3-body decay. All particles are scalars Default in this talk
So, we can describe the 3-body state with two variables
The two variables are
• The Dalitz variables for η′(P)→η(p1)+π+(p2)+π−(p3) isdefined as
X =
√3(Tπ+ − Tπ−)
Q,Y =
(mη + 2mπ)
mπ· Tη
Q− 1, (1)
where Ti (i = π+, π−, η) is kinetic energy of a given particlein the rest frame of η′ and Q = Tπ+ + Tπ− + Tη.
• The boundary of the decay is given by
|Pη2 − Pπ+
2 − Pπ−2| ≤ 2~Pπ+.~Pπ− (2)
The Dalitz Plot Geometry
Dalitz Plot Geometry
Brian Lindquist, Dalitz Plots SASS Talk 9
QT1 Q
T2
QT3
y
x
Non-relativistically, circle is boundary of allowed events
Dalitz Plot Geometry
Brian Lindquist, Dalitz Plots SASS Talk 10
relativistically, boundary is slightly distortedy
x
T1 + T2 + T3
Q= 1 (3)
ρ(x , y) =1
2J + 1
∑mj
|A(mj)|2 (4)
g12 Experiment in Hall B at Jefferson Lab
• g12 Run : 26 x 109
production triggersrecorded
• Beam : Bremsstrahlungprocess produces a realphoton energy from 1.142to 5.425 GeV
• Target : The target waspositioned -90 cm fromthe CLAS center
Fig : CLAS detector
Event Selection of γ p → η′(→ η π+ π−) p
• The calibrated and corrected(g12 Corrections) data withone p, one π+, one π− andXn number of neutralparticles selected for analysis
• Beam Energy : 1.4553 to 3.2GeV
• Kinematic Fitting : 1C fit tothe missing mass of p, π+
and π− to be an η ie.Mx(pπ+π−)=0.547 GeV isapplied. All events with Prob< 1% are rejected.
• -0.85 < cos(θ)cm of η′ <0.85
0
500
1000
1500
2000
2500
3000
3500
4000
4500
]2-) [GeV/cπ+πMx(p0.48 0.5 0.52 0.54 0.56 0.58 0.6 0.62
]2M
x(p)
[GeV
/c
0.88
0.9
0.92
0.94
0.96
0.98
1
1.02
1.04
]2Mx(p) [GeV/c0.88 0.9 0.92 0.94 0.96 0.98 1 1.02 1.04
(Eve
nts/
2M
eV)
0
5000
10000
15000
20000
25000
30000
35000
40000
Signal = 223015Background = 79692
σ 3±Range = Error = 618
Subtraction of Background
• 15 x 15 DP bins in X and Y
• The multi pionic backgroundis subtracted with apolynomial of order 2
• Yield after non-resonantbackground subtraction isreduced by the “Percentagecontribution ofη′ → (η)π+π− → (γγ)π+π−
” DP bin
• So we have the notacceptance corrected DP
The bins with least and most number of events are
shown in Fig. (Before reducing percentage
contribution of yield)
Channel contribution
• Generated with input Bremsstrahlung beam and DPparameters.
• Normalised with differential cross section and branching ratio.
0
10
20
30
40
50
60
70
80
90
74 75 74 76 77
70 72 72 72 72 72 73 74 75
71 72 70 69 69 69 70 72 74 75 79
75 74 72 71 71 71 70 71 72 73 75 78 86
77 76 73 73 73 73 73 72 74 75 77 77 81
71 79 77 76 75 75 73 74 74 75 76 78 79 81
81 79 78 77 76 75 75 75 75 75 77 79 80 80 96
81 81 79 78 77 76 76 76 77 77 78 78 80 84
81 80 78 78 77 77 77 77 77 77 77 81 86
81 80 79 78 78 78 77 78 77 78 78 84 50
79 79 79 79 79 78 78 78 78 78 82
76 79 78 78 76
Q
)-π - T+π
(T3X=
1.5− 1− 0.5− 0 0.5 1 1.5
- 1
QηT
πm
) π+
2mη
(mY
=
1.5−
1−
0.5−
0
0.5
1
1.5
Efficiency of η′ → (η)π+π− → (γγ)π+π−
Simulation
• Using Pluto 2 x 107 eventsgenerated• Generated with input Bremsstrahlung
beam and Differential Cross sectioninformation
• Decay generated with input η′ → η
π+ π− DP parameters from BESIIImeasurement
• Simulation take care of allthe cuts and detectorresponse as in data
• 15 x 15 DP selected foranalysis, the bin-width is 0.2to both X and Y.
• Boundary bins of η′ → η π+
π− DP are rejected
TRUE - XRECX1− 0.8− 0.6− 0.4− 0.2− 0 0.2 0.4 0.6 0.8 1
Eve
nts
/ 0.0
066
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
20000
22000Mean 0.004058−
RMS 0.06679
Resolution = 0.067
TRUE - YRECY1− 0.8− 0.6− 0.4− 0.2− 0 0.2 0.4 0.6 0.8 1
Eve
nts
/ 0.0
066
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
20000
22000
24000
Mean 0.003692
RMS 0.08498
Resolution = 0.060
Comparison of Momentum, θ and φ of Proton
[GeV]pP0 0.5 1 1.5 2 2.5 3
0
2000
4000
6000
8000
10000
Simulation
g12 Data
]° [pθ0 20 40 60 80 100 120
0
2000
4000
6000
8000
10000
Simulation
g12 Data
]° [p
φ150− 100− 50− 0 50 100 150
0
200
400
600
800
1000
1200
1400
1600
1800
Simulation
g12 Data
Comparison of Momentum, θ and φ of π+
[GeV]+πP0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
0
5000
10000
15000
20000
25000
Simulation
g12 Data
]° [+πθ0 20 40 60 80 100 120
0
1000
2000
3000
4000
5000
6000
7000
Simulation
g12 Data
]° [+π
φ150− 100− 50− 0 50 100 150
0
200
400
600
800
1000
1200
1400
1600
1800
2000
Simulation
g12 Data
Comparison of Momentum, θ and φ of π-
[GeV]-πP0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
20000
22000
Simulation
g12 Data
]° [-πθ0 20 40 60 80 100 120
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
Simulation
g12 Data
]° [-πφ150− 100− 50− 0 50 100 150
0
500
1000
1500
2000
2500
Simulation
g12 Data
Fit to the Dalitz Plot
χ2 =∑Nbins
n=1
(Nn−
∑Nbinsm=1 εn,mNtheory ,m
σn
)2
• Nn is no. of η′ → η π+ π− events in the nth DP bin.
• εn,m is acceptance with smearing matrix, ie. it gives acceptance ofmth bin when events are generated in nth bin.
• Ntheory ,m =∫Boundary
A(1 + aY + bY2 + cX + dX 2)dXdY
• σn is the error associated with nth DP bin.
Cross check to the analysis
902 1210 1017 910 848 797 466
1151 1200 1068 989 899 773 731 532 420
1033 1198 1169 1067 1045 886 806 622 516 376 189
575 1120 1113 1120 1044 993 854 760 622 462 298 172
963 1078 1165 1139 1060 1008 969 750 629 449 316 137 44
1093 1170 1178 1111 1128 1009 894 818 695 452 272 101 23
1230 1168 1190 1158 1157 1058 928 824 615 432 233 88 16
970 1260 1151 1170 1108 1030 935 772 571 364 203 68
1157 1330 1202 1095 1054 866 757 543 347 193 46
1041 1238 1083 936 789 508 290
Q)-π - T+π
(T31.5− 1− 0.5− 0 0.5 1 1.5
- 1
QηT π
m) π
+2m
η(m
1.5−
1−
0.5−
0
0.5
1
1.5 Boundary
Reconstructed events inside the Dalitz plot theboundary.
Dalitz Plot Parametersa b c d
0.1−
0.08−
0.06−
0.04−
0.02−
0
0.02
0.04
0.06
0.08
0.1
GENERATED (BESIII)
= 0.68(NDF)126)862χ(RECONSTRUCTED
Comparison of generated and reconstructed DPparameters.
Parameters Gen BESIII CLAS Reco
a -0.047±0.012 -0.043±0.005b -0.069±0.021 -0.075±0.010c +0.019±0.012 0.019±0.006d -0.073±0.013 -0.079±0.009
ConclusionWe obtain the Generated input parameters from thesimulated events, which cross-checks our analysisprocedure.
Preliminary Result
CLAS
BESIII1 2 3 4
0.15−
0.1−
0.05−
0
0.05
0.1
CLAS
BESIII
VESBorasoy
a b c d
Preliminary Result
Parameter Theory [1] VES [2] BESIII [3] Present Worka -0.116 ± 0.011 -0.127 ± 0.018 -0.047 ± 0.012 -0.157 ± 0.010b -0.042 ± 0.034 -0.106 ± 0.032 -0.069 ± 0.021 -0.043 ± 0.019c ... 0.015 ± 0.018 0.019 ± 0.012 0.019 ± 0.012d +0.010 ± 0.019 -0.082 ± 0.019 -0.073 ± 0.013 -0.048 ± 0.016�2
NDF129.3114
= 1.13 504476
= 1.05 29197
= 3
[1]B.BorasoyandR.Nissler, Eur.Phys.J.A26, 383(2005).[2]V. Dorofeev et al., Phys. Lett. B 651, 22 (2007).[3]M. Ablikim et al., [BESIII Collaboration], Phys. Rev. D 83, 012003 (2011).
Dalitz Plot Fit Parameters
⌘0 ! ⇡+⇡�⌘
Parameter Theory [1] VES [2] BESIII [3] Present Worka -0.116 ± 0.011 -0.127 ± 0.018 -0.047 ± 0.012 -0.157 ± 0.010b -0.042 ± 0.034 -0.106 ± 0.032 -0.069 ± 0.021 -0.043 ± 0.019c ... 0.015 ± 0.018 0.019 ± 0.012 0.019 ± 0.012d +0.010 ± 0.019 -0.082 ± 0.019 -0.073 ± 0.013 -0.048 ± 0.016χ2
NDF129.3114
= 1.13 504476
= 1.05 29197
= 3
[1]B.Borasoy and R. Nissler, Eur. Phys. J. A 26, 383 (2005).[2]V. Dorofeev et al., Phys. Lett. B 651, 22 (2007).[3]M. Ablikim et al., [BESIII Collaboration], Phys. Rev. D 83, 012003 (2011).
Summary
Conclusion
• We have reported the Dalitz plot parameters with 87245events, which is approximately twice than BESIII.
• The parameters are consistent with predictions from theory.
• An overall cross check of the whole analysis is also presentedwith simulation.
Future Plans
• Improving the χ2
NDF for the fits
• Study the systematics
Thank you
Email ID : [email protected]
Backup :Comparison of the incident photon beamenergy in center-of-mass
[GeV]s1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
Simulationg12 Data
Backup : In Peak contribution
• η′ → ηπ+π− decay generated with DP parameters a=-0.047,b=-0.069, c=0.019, d=-0.073 from BESIII[1]
• Signal Channel : η′ → (η)π+π− [42.9] → (γγ)π+π− [72.90]
[BR1= (42.9∗72.09)100 = 30.92]
• In Peak background Channel : η′ → (η)π+π− [42.9]
→ (π+π−π0)π+π− [27.14] [BR2= (42.9∗27.14)100 = 11.64]
• Secondary decay η→π+π−π0 are produced in phasespace.
• Channel produces combinatorics and has differentacceptance to signal
• Background Channel : η′ → (η)π0π0 [22.2] → (π+π−π0)π0π0
[27.14] [BR3= (22.2∗27.14)100 = 6.02] is generated with DP parameters
a=-0.067, b=-0.064, c=0.0, d=-0.067 from GAMP[2]
• Secondary decay η→π+π−π0 are produced in phase space.• Channel produces in peak contribution
[1] M. Ablikim et al. [BESIII Collaboration], Phys. Rev. D 83, 012003 (2011)
[2] A.M.Blik et al.,“Measurement of the matrix element for the decay η′ → ηπ0π0 with the GAMS-4πspectrometer,”Phys.Atom.Nucl.72, 231(2009)