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

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Simulation

g12 Data

]° [p

φ150− 100− 50− 0 50 100 150

0

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1400

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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

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7000

Simulation

g12 Data

]° [+π

φ150− 100− 50− 0 50 100 150

0

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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

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Simulation

g12 Data

]° [-πθ0 20 40 60 80 100 120

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9000

Simulation

g12 Data

]° [-πφ150− 100− 50− 0 50 100 150

0

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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 : sghosh@jlab.org

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

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3000

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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)