Dynamics of η → π 0 π 0 π 0

1. Dynamics of η → π0π0π0 F. Ambrosino T. Capussela F. Perfetto

2. OUTLINE • KLOE Memo n. 359 • α = − 0.027 ± 0.004 stat ± 0.006 syst • (blessed 19/07/2007; KLOE preliminary arXiv 0707.4137) • Selection scheme & fit procedure & systematics evaluations • Introduction of a new selection scheme: NEW approach • NEW or OLD approach ? • KLOE Memo n. 359 + x • Update on the measurement using different samples • Final results

3. Dalitz plot expansion The decay η → 3π violates iso-spin invariance and itis induced dominantly by the strong interaction via the u−d quark mass difference. The Dalitz plot density corresponding to the intrinsic η→ π0 π0 π0 decay amplitude is approximately described by |A|2 ∝1 + 2αz With: Z ∈ [ 0 , 1 ] Ei = Energy of the i-th pion in the ηrest frame. ρ = Distance to the center of Dalitz plot. ρmax = Maximun value of ρ. η−>3π @ KLOE

4. Theory vs Experiment Calculations for α: J.Kambor et al. (1996): −0.007 or −0.0014 B.Borasoy et al. (2005): −0.031 ± 0.003 J.Bijnens et al. (2007): 0.013 ± 0.032 Experimental results for α: GAMS-2000 (1984): −0.022 ± 0.023 CBarrel at LEAR (1998): −0.052 ± 0.017 ± 0.010 CBall at AGS (2001): −0.031 ± 0.004 KLOE (prelim.2005): −0.013 ± 0.004 ± 0.005 CELSIUS-WASA (2007): −0.026 ± 0.010 ± 0.010 KLOE (prelim.2007): −0.027 ± 0.004 ± 0.005 CBall at MAMI-B (2009): −0.032 ± 0.002 ± 0.002 CBall at MAMI-C (2009): −0.032 ± 0.003 • Experiment: α = −0.031 ± 0.004 • KLOE, CBall and WASA consistent • ChPT LO: α = 0 • ChPT one and two loop: α > 0 • Quark masses from η → π0π0π0? • [ DeAndrea, Nehme, Talavera PRD78(2008)034032 ] η−>3π @ KLOE

5. Sample selection • The cuts used to select:η → π0 π0 π0are: • 7 and only 7 prompt neutral clusters with 21°<θγ<159° • and Eγ> 10 MeV • Opening angle between each couple of photons > 18° • Kinematic Fit with no mass constraint • P(χ2) > 0.01 • 320 MeV < Eγrec < 400 MeV (after kin fit) • The overall common selection efficiency (trigger, reconstruction, EVCL) is ε = (30.30 ± 0.01)% With these cuts the expected contribution from events other than the signal is < 0.1% Frascati 19 Luglio 2007

6. Matching γ to π0 s • In order to select the best π0 π0 π0 pairing, we introduce a pseudo−χ2 variable for each of the 15 possible pairs, • cutting on: • Minimum χ2 value • Δχ2 between “best” and “second” combination • one can obtain samples with different purity-efficiency Δχ2 Δχ2 min χ2 min χ2

7. Matching γ to π0 s • In order to select the best π0 π0 π0 pairing, we introduce a pseudo- χ2 variable for each of the 15 possible pairs, • cutting on: • Minimum χ2 value • Δχ2 between “best” and “second” combination • one can obtain samples with different purity-efficiency After pairing we perform kinematic fit with η andπ0 mass constraint η mass:MMC = 547.30 MeV /c2 MData = 547.822 MeV/c2 Δχ2 Δχ2

8. Samples

9. Fit procedure The fit is done using a binned likelihood approach We obtain an extimate by minimizing Where: • ni= recostructed events • νi= for each MC event (according pure phase space): • Evaluate its ztrue and its zrec (if any!) • Enter an histogram with the value of zrec • Weight the entry with 1 + 2αztrue • Weight the event with the fraction of combinatorial background, for the signal (bkg) if it has correct (wrong) pairing This procedure relies heavily on MC.

10. Test on fit procedure (I) • We have tested the fit procedure in different ways: • Looking at the result of our fit on MC (αMC = 0.)

11. Test on fit procedure (II) • We have tested the fit procedure in different ways: • Looking at the result of our fit on MC (αMC = 0.) • Using hit or miss and our reweighting we have generated • samples with different values of α and then we have • compared the two procedures.

12. Test on fit procedure (III) • We have tested the fit procedure in different ways: • Looking at the result of our fit on MC pure phase space(αMC = 0.) • Using hit or miss and the fit procedure we have generated samples with different values of α and then we have compared the two procedures. • Parameter scan:

13. Systematic checks Mean 134.2 RMS 11.83 Mean 134.2 RMS 11.99 Frascati 19 Luglio 2007

14. A further check can be done comparing the energies of the two photons in the pion rest frame as function of pion energy Systematic check vs

15. A further check can be done comparing the energies of the two photons in the pion rest frame as function of pion energy A data MC discrepancy at level of 1÷2 % is observed. Thus we fit filling a histo with: z’rec = zgen + η(zrec− zgen ). Systematic check

16. Systematic checks N2/N1 exp. = 0.7263 ± 0.0002 N3/N1 exp. = 0.4497 ± 0.0002 N4/N1 exp. = 0.3048 ± 0.0002 N5/N1 exp. = 0.1431 ± 0.0001 N2/N1 obs = 0.7258 ± 0.0004 N3/N1 obs. = 0.4556 ± 0.0004 N4/N1 obs. = 0.3140 ± 0.0004 N5/N1 obs. = 0.1498 ± 0.0003

17. Idea, try to fit the WPf on DATA. To check procedure, we fit the WPf on MC: WPf(MC) = 24.6 % WPf(MC fit) = (24.6 ± 0.2) % WPf(MC) = 15.5 % WPf(MC fit) = (15.5 ± 0.2) % WPf (MC) = 8.0 % WPf (MC fit) = (7.9 ± 0.3) % WPf (MC) = 5.2 % WPf (MC fit) = (5.2 ± 0.3) % WPf (MC) = 2.4 % WPf (MC fit) = (2.4 ± 0.4) % Systematic check

18. On DATA: WPf (MC) = 24.6 % WPf (DATA) = (26.45 ± 0.26) % WPf (MC) = 15.5 % WPf (DATA) = (16.6 ± 0.28) % WPf (MC) = 8.0 % WPf (DATA) = (8.90 ± 0.37) % WPf (MC) = 5.2 % WPf (DATA) = (6.0 ± 0.45) % WPf (MC) = 2.4 % WPf (DATA) = (3.25 ± 1.00) % Systematic check

19. Systematic check Frascati 19 Luglio 2007

20. α= − 0.027 ± 0.004stat ± 0.006 syst Results χ2/ndf = 13.72 / 17.

21. NEW approach: • 7 and only 7 pnc with • 21° < θγ< 159°and Eγ> 10 MeV • θγγ > 18° • Kin Fit with η mass constraint • (onDATAMη= 547.822 MeV/c2 ) • P(χ2) > 0.01 • 320 MeV < Eγrad < 400 MeV • AFTER PHOTON’S PAIRING • Kinematic Fit with π0mass • constraint Dalitz plot expansion • OLD approach: • 7 and only 7 pnc with • 21° < θγ< 159° and Eγ > 10 MeV • θγγ > 18° • Kin Fit with no mass constraint • P(χ2) > 0.01 • 320 MeV < Eγrad < 400 MeV • AFTER PHOTON’S PAIRING • Kinematic Fit with η and π0 mass constraints (on DATA Mη = 547.822 MeV/c2 )

22. NEW vs OLD

23. Results OLD vs NEW

24. NEW or OLD ? NEW APPROACH OLD APPROACH ……OLD APPROACH !!

25. II Part MEMO 359 + x

26. Dalitz plot expansion • Now we have updated the measurement of a using: • Before the kinematic fit : qgg > 9° • In the kinematic fit on data : Mh = 547.874± 0.007 ±0.031MeV/c2 • MC sample generated according to a = -0.027 • New samples with different purity - efficiency • A correction of about 2% to the photon energies in the p0 rest frame.

27. qgg > 9° After kinematic fit After P(2) > 0.01 After E> 10 MeV After EVCL After 320 MeV < Erad < 400 MeV Afterg > 18°

28. qgg > 9°

29. qgg > 9° Low Med High

30. qgg > 9° Low Med High

31. New MC sample We have generated MC samples with different a values in input and we have fitted a on data: • We’ll use MC generated with: • = - 0.027. On this MC sample: • a = - 0.027  0.002 Status report on  analysis Ponza 05 June 2008

32. 3 new samples We have fix the cut on min c2< 5 obtaining: LOW Dc2 > 2.5 Pur  90.4% e 21% De / e 11% Res  0.1335 N = 948471 MEDIUM Dc2> 5 Pur  95% e 14% De / e 10% Res 0.1108 N = 614663 HIGH Dc2 > 9 Pur  97.3% e 7% De / e  10% Res 0.096 N = 333493

33. Resolution & efficiency Status report on analysis

34. Correction We have corrected the Data / MC discrepancy (at level of 1.5 %) with a smearing of the photon energies, obtaining:

35. Correction We have recovered the residual discrepancy (Low: h’ = 0.; Med: h’= 0.6%; High: h’ =0.9%),obtaining

36. Residuals in [0 – 0.7] =  0.0301 ± 0.0035stat

37. Systematic checks: Resolution

38. Systematic checks: Resolution

39. Systematic checks: Resolution

40. Systematic checks: Resolution The systematic uncertainty due to the resolution is obtained considering the fluctuation in the RMSdata / RMS MC

41. Systematic checks: Efficiency DATA NHigh / Nlow = 0.3516 ± 0.0007 NMedium / Nlow = 0.6481 ± 0.0011 MC NHigh / Nlow = 0.3511 ± 0.0003 NMedium / Nlow = 0.6461± 0.0005

42. Systematic checks: Efficiency Correction to the photon efficiency is applied weighting the Montecarlo events with a Fermi Dirac function obtained fitting the photon energy spectrum Data/MC discrepancy

43. Systematic checks: Efficiency Medium High Low

44. Systematic checks: WPF On DATA: Wrong pair fraction (MC) = 9.59 % Wrong pairfraction (DATA) = (10.01 ± 0.45) % Wrong pairfraction (MC) = 5 % Wrong pairfraction (DATA) = (5.51 ± 0.68) % Wrong pair fraction (MC) = 2.7 % Wrong pairfraction (DATA) = (3.31 ± 0.90) %

45. Systematic checks: WPF

46. Systematic checks: WPF On DATA: Wrong pair fraction (MC) = 9.59 % Wrong pairfraction (DATA) = (10.01 ± 0.45) % Wrong pairfraction (MC) = 5 % Wrong pairfraction (DATA) = (5.51 ± 0.68) % Wrong pair fraction (MC) = 2.7 % Wrong pairfraction (DATA) = (3.31 ± 0.90) %

47. Final results 10-4 Status report on analysis

48. Conclusion 2005: we have published this preliminary result: = 0.013 ± 0.004stat ± 0.005 syst 2007: we have published this preliminary results: = 0.027 ± 0.004stat ± 0.006 syst 2009: we found this result: = 0.0301 ± 0.0035stat - 0.0036 syst + 0.0022 syst This result is compatible with the published Crystal Ball result: = 0.031 ± 0.004 And the calculations from the +- analysis using only the  -  rescattering in the final state. = 0.038 ± 0.003stat +0.012-0.008syst

49. To publish