Dalitz Decays of Pseudo-calar Mesons Michael Kunkel On behalf on the CLA collaboration
Outline 1 Introduction Constituent Quark Model Form Factors 2 CLA etup 3 G12 Experiment 4 Current tate of the Art 5 Results 6 Conclusion
Constituent Quark Model Hadrons are colorless particle formed of quarks/anti-quarks that are held together by the strong force: aryons 3 valence quarks (qqq) Half integer spin ( 1 2, 3 2, 5 2...) particles (fermions) Mesons 2 valence quarks(qq) Integer spin (, 1, 2...) particles (bosons) Valence quarks in hadrons produce the quantum numbers J P J = L P = ( 1) L1
Constituent Quark Model Table: Types of Mesons Type J P L J P Pseudoscalar - calar 1 1 Vector 1-1 1 Axial Vector 1 1 1 Tensor 2 1 1 2 Figure: Nonet of Pseudoscalar Mesons
Constituent Quark Model π = 1 2 (uu dd) η and η are linear combinations of the singlet and octet states. ( ) ( ) ( ) η sin θmix cos θ η = mix η cos θ mix sin θ mix η 8 η η 8 1 (uu dd ss) 6 2 (uu dd 2ss) 3 θ mix = 16.54 ±.71
Form Factors If a particle is not point-like, then: dσ [ ] dσ dq 2 = F dq 2 (q 2 ) 2 measured pointlike q momentum transfer F (q 2 ) is the form factor, which contains information about the electromagnetic structure of the hadron F (q 2 ) is the ratio of the measured differential cross section to the Q.E.D. pointlike differential cross section
Neutral Mesons A neutral meson is it s own antiparticle and has charge = magnetic moment = wave function is unaffected by charge conjugation or only reverses sign C(M) = M Charge parity is conserved in strong and e&m processes Particle Type Charge Parity Reason γ - quanta of e &m field Pseudoscalar can decay to γγ Vector - same quantum numbers as γ
Definition of Dalitz Decay Consider charge-conjugation parity of the radiative decay of neutral meson A to neutral meson : A γ C A C γ y conservation of charge-conjugation C A = C If γ is "off shell" γ, then Dalitz decay A γ e e q 2 = m 2 (γ ) = m 2 l l > time-like probability of emitting γ is caused by the cloud of virtual states in the region of A. This dynamic structure is encoded in the transition form factor.
Neutral Meson Dalitz Decays Decay Amplitude: M = 4παı[f A (q 2 )ε αβγδ p α q β ɛ γ ] }{{} A γ transition 1 q 2 }{{} ūγ δ u }{{} leptonic current photon propagator
ack to the Form Factor For pseudoscalar meson P { π, η, η } Dalitz decay P l l γ, the decay rate is proportional to the form factor dγ(p l l γ) dqγ(p γγ) = 4α [ ] 1 [ ] ] 1 4m2 2 3 l 3πq q 2 1 2 m2 l [1 q 2 q2 m 2 F (q 2 ) 2 P F (q 2 ) can be fit to the dipole form: F (q 2 ) = [1 q2 Λ 2 ] 1 In the limit of small momentum transfer lim F q 2 (q2 ) = 1 1 6 q2 r 2 Determining the transition form factor or the charge radius from Dalitz decay has been a challenge due to low statistics...until now
Dalitz Event In
G12 Overview Data was taken in Hall experiment G12 Running Time: 4/28 6/28 44 Days of eam Time 6 65 na of 5.6 5.7 GeV e E γ up to 5.5 GeV 126 T Raw Data 4 cm lh 2 target Raw sensitivity of 53 pb 1 26 x1 9 production triggers (3 x 1 6 triggers) Calorimeter Čerenkov counter cleanly identify e e pairs ad reject π π pairs by factor of 1 6 gold radiator 1 4 X
Identifying p e ± and γ events For e ±, particle had to pass CC and EC cut Detect p, e e γ for reaction p(γ, p, e e γ) Identify e e and reject π π pairs by # of Čerenkov counter photoelectrons 2.5 per particle Calorimeter energy particle momentum Geometric match in the azimuthal angle between the CC and a DC hits. Identify & measure γ Energy deposition in EC Time of flight No missing mass or missing energy Also look at p(γ, p, e e ) γ, identifying the γ with missing mass and energy
Many collaborations and η factories have produced results for TFF s For π INDRUM I: 53,955 FERMILA: 63,693 For η WAA: 526 ± 25 TAP: 1345 ± 59 For η NONE
π Dalitz Decay tatistics FNAL E832 events Entries / 1.2 MeV 1 Mean:.135 ±.1 GeV σ:.9 ±.1 GeV 8 6 4 Yield: 1565 ackground: 1472 = 46.7 This experiment s p(,pe e ) events h3 Entries 26867 Mean.1347 RM.1311 2 M(e e )[GeV] M(e e )[GeV].8.1.12.14.16.18.2 M(e e )[GeV] Comparison of FNAL Dalitz decay spectrum (left), to the CLA G12 Dalitz decay spectrum (right)
η Dalitz Decay tatistics Counts / 5 MeV TAP events Entries / 6 MeV 5 4 Yield: 294 3 ackground: 311 2 This experiment s p(,pe e Mean:.5478 ±.2 GeV σ:.115 ±.2 GeV = 164.7 ) events h3 Entries 26867 Mean.5496 RM.256 1 M(e e )[MeV].46.48.5.52.54.56.58.6.62.64 M(e e )[GeV] Comparison of TAP Dalitz decay spectrum (left), to the CLA G12 Dalitz decay spectrum (right)
η Dalitz Decay tatistics CLEO events Data MC Entries / 6 MeV 45 4 35 3 25 2 15 1 5 This experiment s p(,pe e Mean:.9574 ±.14 GeV σ:.112 ±.13 GeV Yield: 131 ackground: 77 = 14.9 ) events h3 Entries 27638 Mean 1.12 RM.7597.9.95 1 1.5 1.1 1.15 1.2 M(e e )[GeV] M(e e )[GeV] CLEO search of Dalitz decay (left), First observation of Dalitz decay from CLA G12 experiment (right)
imulation Acceptance is complete due to PLUTO event simulator, which I implemented for CLA for Dalitz decays Generates Dalitz spectrum using conserving production angles
Results Entries 3 1 2 1 Data Preliminary Uncorrected.1.2.3.4.5 - M(e e - ) [GeV] Problem: Anomalous point at q 2
Results 8 7 6 5 4 3 2 1 3 25 2 15 1 5 3 25 2 15 1 5 4 35 3 25 2 15 1 5.46.48.5.52.54.56.58.6.62.64.46.48.5.52.54.56.58.6.62.64.46.48.5.52.54.56.58.6.62.64.46.48.5.52.54.56.58.6.62.64 12 1 8 6 4 2 18 16 14 12 1 8 6 4 2 3 25 2 15 1 5.46.48.5.52.54.56.58.6.62.64.46.48.5.52.54.56.58.6.62.64.46.48.5.52.54.56.58.6.62.64 8 7 6 5 4 3 2 1 3 25 2 15 1 5 25 2 15 1 5.46.48.5.52.54.56.58.6.62.64.46.48.5.52.54.56.58.6.62.64.46.48.5.52.54.56.58.6.62.64 Entries / 1 MeV < q <.125 Yield 24 ackground 172 Mean.5467 ±. σ:.1153 ±.32 = 11.9 Range: ± 2.5 σ Entries / 1 MeV.125 < q <.25 Yield 41 ackground 3 Mean.5494 ±. σ :.1373 ±.89 = 13.4 Entries / 1 MeV.25 < q <.65 Yield 188 ackground 31 Mean.5499 ±.1217 GeV σ :.1344 ±.1459 GeV = 6.1 Entries / 1 MeV.65 < q <.15 Yield 56 ackground 8 Mean.5511 ±.1398 GeV σ :.8748 ±.1319 GeV = 7. Entries / 1 MeV.15 < q <.145 Yield 29 ackground 4 Mean.5492 ±.1823 GeV σ :.8142 ±.153 GeV = 7.2 Entries / 1 MeV.145 < q <.2 Yield 51 ackground 6 Mean.5498 ±.165 GeV σ :.8937 ±.1851 GeV = 8.5 Entries / 1 MeV.2 < q <.26 Yield 39 ackground 4 Mean.5476 ±.1264 GeV σ :.6293 ±.151 GeV = 9.8 Entries / 1 MeV.26 < q <.32 Yield 35 ackground 4 Mean.5474 ±.1148 GeV σ :.5851 ±.185 GeV = 8.8 Entries / 1 MeV.32 < q <.38 Yield 38 ackground 9 Mean.5465 ±.169 GeV σ :.7687 ±.1227 GeV = 4.2 Entries / 1 MeV.38 < q <.56 Yield 32 ackground 39 Mean.5435 ±.199 GeV σ :.5725 ±.158 GeV =.8
ackground @ q 2 ackground due to η γγ and γ e e in the target olution simulate this process using GEMC, a GEANT4 based simulation
GEMC imulation Used PLUTO to simulate 1 7 η γγ events meared γ vertex to be uniformly distributed within GEMC target - η γγ γe e Conversion Probability -1 1-2 1-3 1-4 1 Preliminary.1.2.3.4.5 M(e e - ) [GeV]
Acceptance 22 2 18 16 14 12 1 8 6 4 2 7 6 5 4 3 2 1 6 5 4 3 2 1 22 2 18 16 14 12 1 8 6 4 2.46.48.5.52.54.56.58.6.62.64.46.48.5.52.54.56.58.6.62.64.46.48.5.52.54.56.58.6.62.64.46.48.5.52.54.56.58.6.62.64 7 6 5 4 3 2 1 7 6 5 4 3 2 1 45 4 35 3 25 2 15 1 5.46.48.5.52.54.56.58.6.62.64.46.48.5.52.54.56.58.6.62.64.46.48.5.52.54.56.58.6.62.64 12 1 8 6 4 2 8 7 6 5 4 3 2 1 3 25 2 15 1 5.46.48.5.52.54.56.58.6.62.64.46.48.5.52.54.56.58.6.62.64.46.48.5.52.54.56.58.6.62.64 Used PLUTO to simulate 5 1 6 η e e γ Dalitz events Used same cuts and binning as data Entries / 1 MeV < q <.125 Yield 433 ackground 142 Mean.5495 ±. σ :.8333 ±.1 = 3.3 Entries / 1 MeV.125 < q <.25 Yield 1484 ackground 94 Mean.552 ±. σ :.9182 ±.2 = 15.8 Entries / 1 MeV.25 < q <.65 Yield 197 ackground 1 Mean.5492 ±. σ :.6955 ±.2 = 19.7 Entries / 1 MeV.65 < q <.15 Yield 1168 ackground 3 Mean.5483 ±.23 GeV σ:.61 ±.1973 GeV = 38.9 Range: ± 2.5 σ Entries / 1 MeV.15 < q <.145 Yield ackground 181 16 Mean.5487 ±.1891 GeV σ :.5674 ±.1879 GeV = 67.6 Entries / 1 MeV.145 < q <.2 Yield 115 ackground 11 Mean.548 ±.1567 GeV σ:.5319 ±.1422 GeV = 14.5 Range: ± 2.5 σ Entries / 1 MeV.2 < q <.26 Yield ackground 84 8 Mean.5476 ±.1873 GeV σ :.5392 ±.161 GeV = 15. Entries / 1 MeV.26 < q <.32 Yield 618 ackground 3 Mean.5478 ±.253 GeV σ :.587 ±.1739 GeV = 26. Entries / 1 MeV.32 < q <.38 Yield 383 ackground 9 Mean.547 ±.2867 GeV σ:.5322 ±.2146 GeV = 42.6 Range: ± 2.5 σ Entries / 1 MeV.38 < q <.56 Yield 266 ackground 12 Mean.5466 ±.3648 GeV σ :.5357 ±.2637 GeV = 22.2
Acceptance Acceptance Acceptance Probability.3.25.2.15.1.5.1.2.3.4.5 M(e e )[GeV]
Corrected Eta Dalitz pectrum Accepted hdalitz_conv Corrected d dm 6 1 5 1 Preliminary Q.E.D Fit to Data Fit to TAP Λ 4 1.1.2.3.4.5 M(e e )[GeV] Anomalous points in bins 4 & 5 Currently studying causes of these anomalies
What we will to contribute to Form Factor Preliminary F 2 M(e e )[GeV] Hope to update current picture with better error bars
Conclusion Works in Progress tudy anomalous points in data spectrum Investigating acceptance corrections Invariant mass of e e γ exceeds worlds statistics in P(η, η ) Dalitz decay of η seen for first time A significant contribution will be made from this work