1. Dynamics of  →       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  −  @ KLOE The decay  →   violates iso-spin invariance and it  is induced dominantly by the strong interaction via the u−d quark mass difference. The Dalitz plot density corresponding to the intrinsic  →       decay amplitude is approximately described by |A| 2 ∝ 1 + 2  z With: Z ∈ [ 0, 1 ] E i = Energy of the i-th pion in the  rest frame.  = Distance to the center of Dalitz plot.  max = Maximun value of .

4. Theory vs Experiment  −  @ KLOE Calculations for  : 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  : 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:  = −0.031 ± 0.004 KLOE, CBall and WASA consistent ChPT LO:  = 0 ChPT one and two loop:  > 0 Quark masses from  →       ? [ DeAndrea, Nehme, Talavera PRD78(2008)034032 ]

5. Frascati 19 Luglio 2007 Sample selection The cuts used to select:  →  0  0  0  are: 7 and only 7 prompt neutral clusters with 21 ° <   < 159 ° and E  > 10 MeV Opening angle between each couple of photons > 18 ° Kinematic Fit with no mass constraint P(  2 ) > 0.01 320 MeV < E  rec < 400 MeV (after kin fit) The overall common selection efficiency (trigger, reconstruction, EVCL) is  = (30.30 ± 0.01)% With these cuts the expected contribution from events other than the signal is < 0.1%

6. Matching  to   s In order to select the best       pairing, we introduce a pseudo −  2 variable for each of the 15 possible pairs, cutting on: Minimum  2 value Δ  2 between “best” and “second” combination one can obtain samples with different purity-efficiency Δ2Δ2 Δ2Δ2 min  2

7. Matching  to   s In order to select the best       pairing, we introduce a pseudo-  2 variable for each of the 15 possible pairs, cutting on: Minimum  2 value Δ  2 between “best” and “second” combination one can obtain samples with different purity-efficiency Δ2Δ2 After pairing we perform kinematic fit with  and    mass constraint  mass: M MC = 547.30 MeV /c 2 M Data = 547.822 MeV/c 2 Δ2Δ2

8. Samples LOWMED IMED IIMED IIIHIGH min   NO CUT < 10< 5< 3< 2 Δ Δ NO CUT > 1.2> 3> 4> 7 PUR75.4 %84.5 %92 %94.8 %97.6 % RES0.20030.16630.12870.10990.0871  30.3 %22 %13.6 %9.2 %4.3 % Δ  8 %14 %21 %25 %26 % N(Mevts) 1.4181.0290.64590.44530.2123

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

10. Test on fit procedure (I) We have tested the fit procedure in different ways: Looking at the result of our fit on MC (  MC = 0.) LowMed IMed IIMed IIIHigh  −0.0009 ± 0.00190.0002 ± 0.0021 0.0008 ± 0.0026 0.0022 ± 0.00300.0029 ± 0.0044

11. Test on fit procedure (II) We have tested the fit procedure in different ways: Looking at the result of our fit on MC (  MC = 0.) Using hit or miss and our reweighting we have generated samples with different values of  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 (  MC = 0.) Using hit or miss and the fit procedure we have generated samples with different values of  and then we have compared the two procedures. Parameter scan: Range  −   −   −   −   −   −   −  0 − 110 − 15 %25%16% 40% 21%12% 13%8 % 0 − 0.910 − 8 %84%75%78%59%41%26%18% 0 – 0.810 − 7 % 73% 64% 67% 52% 35% 23% 17% 0 – 0.710 − 6 % 85% 83% 71% 73% 54% 78% 0 – 0.610 − 6 % 94% 93%95% 88% 89% 83% 78%

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

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

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

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. Systematic check Idea, try to fit the WPf on DATA. To check procedure, we fit the WPf on MC: 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) % WPf  (MC) = 24.6 % WPf  (MC fit) = (24.6 ± 0.2) %

18. Systematic check On DATA: 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) % WPf (MC) = 24.6 % WPf (DATA) = (26.45 ± 0.26) %

19. Frascati 19 Luglio 2007 Systematic check

20. Results  = − 0.027 ± 0.004 stat ± 0.006 syst  2 /ndf = 13.72 / 17.

21. Dalitz plot expansion NEW approach :  7 and only 7 pnc with 21 ° 10 MeV    > 18 °  Kin Fit with  mass constraint ( on DATA M   = 547.822 MeV/c 2 )  P(  2) > 0.01  320 MeV < E  rad < 400 MeV AFTER PHOTON’S PAIRING Kinematic Fit with    mass constraint OLD approach :  7 and only 7 pnc with 21° 10 MeV    > 18°  Kin Fit with no mass constraint  P(  2) > 0.01  320 MeV < E  rad < 400 MeV AFTER PHOTON’S PAIRING  Kinematic Fit with  and  0 mass constraints (on DATA M  = 547.822 MeV/c 2 )

22. NEW vs OLD Pur % New Pur % Old Rms New Rms Old Δε % New Δε % Old Data/Mc wpf New Data/Mc wpf Old Low 82.275.4.1864.200312.481.111.07 Med I 89.484.5.1465.166315.8141.221.07 Med II 95.192.1.1141.128721.9211.531.12 Med III 97.194.8.097.109927.6251.971.15 High 99.097.6.080.087126.726 Not converge 1.35

23. Results OLD vs NEW Range Low · 10 −3 Medium I · 10 −3 Medium II · 10 −3 Medium III · 10 −3 High · 10 −3 (0, 1)− 30 ± 2− 31 ± 2− 31 ± 3− 25 ± 3− 26 ± 4 (0, 0.8)− 26 ± 2− 28 ± 2− 28 ± 3− 22 ± 4 −22 ± 5 (0, 0.7)− 26 ± 3− 28 ± 3− 27 ± 4− 21 ± 4− 23 ± 5 (0, 0.6)− 30 ± 4− 31 ± 4 − 24 ± 5 − 20 ± 6 (0, 1)− 36 ± 2− 37 ± 2 − 35 ± 3 (0, 0.8)− 36 ± 2− 37 ± 2− 34 ± 3− 32 ± 3 (0, 0.7)− 38 ± 2− 40 ± 3− 36 ± 3− 33 ± 3 (0, 0.6)− 44 ± 3− 48 ± 4− 42 ± 4− 37 ± 4

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

25. II Part MEMO 359 + x

26. Dalitz plot expansion Now we have updated the measurement of  using: Before the kinematic fit :  In the kinematic fit on data : M  = 547.874 ± 0.007 ±0.031  MeV/c 2 MC sample generated according to  = -0.027 New samples with different purity - efficiency A correction of about 2% to the photon energies in the  0 rest frame.

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

28.  > 9°

29.  >18 ° > 15 ° > 12 ° > 9 ° > 6 ° = 0 ° PUR % 9190.790.690.590.490.3  % 18.415.612.410.79.99.6 PUR % 95.495.395.295.195  % 221812.610.3108.8 PUR % 97.697.597.497.397.297.1  % 161312109.68 Low Med High

30.  > 9°  >18 ° > 15 ° > 12 ° > 9 ° > 6 ° = 0 ° PUR % 9190.790.690.590.490.3  % 18.415.612.410.79.99.6 PUR % 95.495.395.295.195  % 221812.610.3108.8 PUR % 97.697.597.497.397.1  % 1613121088 Low Med High

31. Ponza 05 June 2008 Status report on    analysis  input MC  fit on data 0 -0.028  0.004 -0.026 -0.026  0.004 -0.028 -0.028  0.004 -0.030 -0.027  0.004 -0.032 -0.027  0.004 -0.034 -0.027  0.004 -0.036 -0.027  0.004 -0.038 -0.027  0.004 -0.040 -0.027  0.004 -0.042 -0.027  0.004 -0.044 -0.027  0.004 -0.046 -0.027  0.004 -0.048 -0.027  0.004 We’ll use MC generated with:  = - 0.027. On this MC sample:  - 0.027  0.002 New MC sample We have generated MC samples with different  values in input and we have fitted  on data 

32. LOW  2 > 2.5 Pur  90.4%   21%    11% Res  0.1335 N = 948471 MEDIUM    > 5 Pur  95%   14%     10% Res  0.1108 N = 614663 HIGH   > 9 Pur  97.3%   7%     10% Res  0.096 N = 333493 3 new samples We have fix the cut on min  2 < 5 obtaining:

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

34. Correction We have corrected the Data / MC discrepancy (at level of 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:  ’ = 0.; Med:  ’= 0.6%; High:  ’ =0.9%), obtaining Range Low · 10  4 Medium · 10  4 High · 10  4 (0, 1)  288 ± 22  281 ± 26  289 ± 34 (0, 0.8)  313 ± 26  288 ± 31  295 ± 42 (0, 0.7)  319 ± 29  301 ± 35  308 ± 47 (0, 0.6)  348 ± 31  330 ± 44  343 ± 60

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

37. Systematic checks: Resolution

40. The systematic uncertainty due to the resolution is obtained considering the fluctuation in the RMSdata / RMS MC Effect LOW · 10  4 MEDIUM · 10  4 HIGH · 10  4 Res -4 +4 -2 +2

41. Systematic checks: Efficiency DATA N High / N low = 0.3516 ± 0.0007 N Medium / N low = 0.6481 ± 0.0011 MC N High / N low = 0.3511 ± 0.0003 N Medium / N low = 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 High Medium Low Effect LOW · 10  4 MEDIUM · 10  4 HIGH · 10  4 Low E  -5-3-5

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

46. On DATA: Wrong pair fraction (MC) = 5 % Wrong pair fraction (DATA) = (5.51 ± 0.68) % Wrong pair fraction (MC) = 2.7 % Wrong pair fraction (DATA) = (3.31 ± 0.90) % Wrong pair fraction (MC) = 9.59 % Wrong pair fraction (DATA) = (10.01 ± 0.45) % Systematic checks: WPF Effect LOW · 10  4 MEDIUM · 10  4 HIGH · 10  4 Bkg -7 +5-6 +5-16 +17

47. Status report on    analysis Range Low · 10  4 Medium · 10  4 High · 10  4 (0, 1)  288 ± 22  281 ± 26  289 ± 34 (0, 0.8)  313 ± 26  288 ± 31  295 ± 42 (0, 0.7)  319 ± 29  301 ± 35  308 ± 47 (0, 0.6)  348 ± 31  330 ± 44  343 ± 60 Effect LOW · 10  4 MEDIUM · 10  4 HIGH · 10  4 Res -4 +4 -2 +2 Low E  -5-3-5 Bkg -7 +5-6 +5-16 +17 MM -6 +5-2 +6-1 +5 Range -29 +31-29 +20  35 +19 Purity +15 -18  4 +11 Tot -31 +35-36 +22-40 +28 Final results 10 -4

48. Conclusion  =  0.0301 ± 0.0035 stat - 0.0036 syst + 0.0022 syst 2005: we have published this preliminary result:  =  0.027 ± 0.004 stat ± 0.006 syst 2009: we found this result: 2007: we have published this preliminary results:  =  0.013 ± 0.004 stat ± 0.005 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 ± 0.003 stat +0.012 -0.008 syst