2. F. AmbrosinoEuridice Midterm Meeting LNF 11/02/05 1 F.Ambrosino Università e Sezione INFN, Napoli for the KLOE collaboration Study of  Dalitz plot at KLOE Motivations             Conclusions and outlook

3. F. AmbrosinoEuridice Midterm Meeting LNF 11/02/05 2 The decay    occours primarily on account of the d-u quark mass differences and the result arising from lowest order chiral pertubation theory is well known: With: A good understanding of M(s,t,u) can in principle lead to a very accurate determination of Q:  in chiral theory And, at l.o.

4. F. AmbrosinoEuridice Midterm Meeting LNF 11/02/05 3 Still there are some intriguing questions for this decay : Why is it experimental width so large (270 eV) w.r.t theoretical calculation ? (Tree level: 66 eV (!!!); 1 loop : 160 eV ) Possible answers: Final state interaction Scalar intermediate states Violation of Dashen theorem Is the dynamics of the decay correctly described by theoretical calculations ? …and its open questions

5. F. AmbrosinoEuridice Midterm Meeting LNF 11/02/05 4 The usual expansion of square modulus of the decay amplitude about the center of the Dalitz plot is: |A(s,t,u)| 2 = 1 + aY + bY 2 + cX + dX 2 + eXY Where: Dalitz plot expansion

6. F. AmbrosinoEuridice Midterm Meeting LNF 11/02/05 5 Tabella sperimentale di Bijnens Calculation a b d Tree One-loop[1] Dispersive[2] Tree dispersive Absolute dispersive -1.00 0.25 0.00 -1.33 0.42 0.08 -1.16 0.26 0.10 -1.10 0.31 0.001 -1.21 0.33 0.04 MeasurementNN a b d Layter Gormley Crystal Barrel 80884 30000 1077 3230 -1.08  0.14 0.034  0.027 0.046  0.031 -1.17  0.02 0.21  0.03 0.06  0.04 -0.94  0.15 0.11  0.27 -1.22  0.07 0.22  0.11 0.06 fixed [1] Gasser,J. and Leutwyler, H., Nucl. Phys. B 250, 539 (1985) [2] Kambor, J., Wiesendanger, C. and Wyler, D., Nucl. Phys. B 465, 215 (1996) Dalitz expansion: theory vs experiment

7. F. AmbrosinoEuridice Midterm Meeting LNF 11/02/05 6 At KLOE  is produced in the process . The final state for       is thus     , and the final state for       is 7 , both with almost no physical background.  at KLOE Selection: 2 track vertex+3  candidates Kinematic fit

8. F. AmbrosinoEuridice Midterm Meeting LNF 11/02/05 7 Resolutions and efficiency “core”  X = 0.018 “core”  Y = 0.027 Efficiency almost flat, and  36%

9. F. AmbrosinoEuridice Midterm Meeting LNF 11/02/05 8 Comparison Data-MC:  

10. F. AmbrosinoEuridice Midterm Meeting LNF 11/02/05 9 Comparison Data-MC:  

11. F. AmbrosinoEuridice Midterm Meeting LNF 11/02/05 10 Signal B/S  0.8%

12. F. AmbrosinoEuridice Midterm Meeting LNF 11/02/05 11 The analysis has been applied on 450 pb –1 corresponding to: N(  +  -  0 ) = 1,425,131 events in the Dalitz plot, fitted with function: fit is stable… …but the model seems not to fit adeguately data (BAD P  2 ). We have added the cubic terms: |A(X,Y)| 2 = 1+aY+bY 2 +cX+dX 2 +eXY+fY 3 +gX 3 +hX 2 Y+lXY 2 |A(X,Y)| 2 = 1+aY+bY 2 +cX+dX 2 +eXY Fitting function

13. F. AmbrosinoEuridice Midterm Meeting LNF 11/02/05 12 Fit stability

14. F. AmbrosinoEuridice Midterm Meeting LNF 11/02/05 13 ndf P2%P2% abcdef 14760 -1.072  0.006 -0.007 +0.005 0.117  0.006 -0.006 +0.004 0.0001  0.0029 -0.0021 +0.0003 0.047  0.006 -0.005 +0.004 -0.006  0.008 -0. +0.013 0.13  0.01 -0.01 +0.02 15063 -1.072  0.005 -0.008 +0.005 0.117  0.006 -0.006 +0.004 --- 0.047  0.006 -0.005 +0.004  0.13  0.01 -0.01 +0.02 1500.02 -1.055  0.004 -0.007 +0.006 0.100  0.005 -0.002 +0.004 --- 0.12  0.01 -0.02 +0.02 1500 -1.013  0.003 -0.007 +0.004 0.120  0.005 -0.023 +0. --- 0.043  0.006 -0.003 +0.004 --- Results 15063 -1.072  0.005 -0.008 +0.005 0.117  0.006 -0.006 +0.004 --- 0.047  0.006 -0.005 +0.004  0.13  0.01 -0.01 +0.02 |A(X,Y)| 2 = 1+aY+bY 2 +cX+dX 2 +eXY+fY 3

15. F. AmbrosinoEuridice Midterm Meeting LNF 11/02/05 14 Results (II) |A(X,Y)| 2 = 1-1.072 Y+0.117 Y 2 +0.047 X 2 +0.13Y 3 Using preliminary KLOE results shown at ICHEP 04 B.V. Martemyanov and V.S. Sopov (hep-ph\0502023) have extracted: Q = 22.8 ± 0.4 against Q dashen = 24.2 (as already argued for example in J. Bijnens and J. Prades, Nucl. Phys. B490, 239 (1997)

16. F. AmbrosinoEuridice Midterm Meeting LNF 11/02/05 15 The dynamics of the       decay can be studied analysing the Dalitz plot distribution. The Dalitz plot density ( |A| 2 ) is specified by a single parameter: |A| 2  1 + 2  z with: E i = Energy of the i-th pion in the  rest frame.  = Distance to the center of Dalitz plot.  max = Maximun value of . Z  [ 0, 1 ]   Dalitz plot expansion

17. F. AmbrosinoEuridice Midterm Meeting LNF 11/02/05 16 Alde (1984) -0.022  0.023 Crystal Barrel (1998) -0.052  0.020 Crystal Ball (2001) -0.031  0.004 Dalitz expansion: theory vs experiment Calculation  Tree One-loop[1] Dispersive[2] Tree dispersive Absolute dispersive 0.00 0.0015 -0.007 - -0.014 -0.006 -0.007 [1] Gasser,J. and Leutwyler, H., Nucl. Phys. B 250, 539 (1985) [2] Kambor, J., Wiesendanger, C. and Wyler, D., Nucl. Phys. B 465, 215 (1996)

18. F. AmbrosinoEuridice Midterm Meeting LNF 11/02/05 17 Recoil  is the most energetic cluster. In order to match every couple of photon to the right  0 we build a  2 -like variable for each of the 15 combinations: With: is the invariant mass of  i 0 for j-th combination = 134.98 MeV is obtained as function of photon energies Photons pairing

19. F. AmbrosinoEuridice Midterm Meeting LNF 11/02/05 18 Cutting on: Minimum  2 value  2 between “best” and “second” combination One can obtain samples with different purity-efficiency Purity= Fraction of events with all photons correctly matched to   ‘s Combination selection Pur  85 % Eff  22 % Pur  92 % Eff  14 % Pur  98 % Eff  4.5 %

20. F. AmbrosinoEuridice Midterm Meeting LNF 11/02/05 19 The problem of resolution Phase space MC reconstructed ResolutionEfficiency

21. F. AmbrosinoEuridice Midterm Meeting LNF 11/02/05 20 Results on MC

22. F. AmbrosinoEuridice Midterm Meeting LNF 11/02/05 21 Results on MC

23. F. AmbrosinoEuridice Midterm Meeting LNF 11/02/05 22 Results on MC

24. F. AmbrosinoEuridice Midterm Meeting LNF 11/02/05 23 The agreement is good on all spectra Comparison Data - MC

25. F. AmbrosinoEuridice Midterm Meeting LNF 11/02/05 24 = -0.0ZZ  0.004 Low purity Medium purity High purity = -0.0XX  0.002= -0.0YY  0.002 Fitting Data Systematics are at the same level of the statistical error

26. F. AmbrosinoEuridice Midterm Meeting LNF 11/02/05 25 Conclusions KLOE is analyzing an unprecedented statistics of  decays with negligible background For       channel the analysis is almost completed and finds evidence for an unexpected large y 3 term 3   analysis is much harder, we expect to provide soon a result at the same level of the Crystal Ball one.

27. F. AmbrosinoEuridice Midterm Meeting LNF 11/02/05 26 SPARE SLIDES

28. F. AmbrosinoEuridice Midterm Meeting LNF 11/02/05 27 Kinematic fit with no mass constrains

29. F. AmbrosinoEuridice Midterm Meeting LNF 11/02/05 28 Tests of the fit procedure on MC Generator slopes in MC rad-04: a = -1.04 b = 0.14 c = 0. d = 0.06 e = 0. KLOE measure (100 pb -1 )

30. F. AmbrosinoEuridice Midterm Meeting LNF 11/02/05 29 Comparison Data-MC  data  MC A.U.

31. F. AmbrosinoEuridice Midterm Meeting LNF 11/02/05 30 Comparison Data-MC: Y ch – Y 0 Shift  1.33 MeV Shift  0.03 MeV NA48: 547.843  0.030 st  0.041 sys Physica Scripta T99 140-142, 2002

32. F. AmbrosinoEuridice Midterm Meeting LNF 11/02/05 31  i is for each bin: the efficiency as a function of Dalitz-plot. N i is for each bin: the number of events of Dalitz-plot.  i is the statistical error on the ratio N i /  i All the bins are included in the fit apart from the bins crossed by the Dalitz plot contour. The fit is done using a binned  2 approach Fit procedure

33. F. AmbrosinoEuridice Midterm Meeting LNF 11/02/05 32 Comparison Data-MC: X & Y

34. F. AmbrosinoEuridice Midterm Meeting LNF 11/02/05 33 Comparison between efficiency corrected data and fitted function as function of the bin number. The structure observed is due to the Y distribution for X slices P(  2   0 2 )  60% Goodness of fit

35. F. AmbrosinoEuridice Midterm Meeting LNF 11/02/05 34 A = (-0.009  0.093)  10 -2         A q = (-0.02  0.09)  10 -2       A s = (0.07  0.09)  10 -2 Asymmetries

36. F. AmbrosinoEuridice Midterm Meeting LNF 11/02/05 35        We have tested the effect of radiative corrections to the Dalitz plot density. The ratio of the two plots has been fitted with the usual expansion: corrections to parameters are compatible with zero

37. F. AmbrosinoEuridice Midterm Meeting LNF 11/02/05 36        time stability To check stability wrt data taking conditions we fit the integrated Dalitz plot in samples of 4 pb -1 each

38. F. AmbrosinoEuridice Midterm Meeting LNF 11/02/05 37 Check on cubic term No cubic dependence in |A(X,Y)| 2 |A(X,Y)| 2 = 1 + aY + bY 2 + dX 2 with a  -1. Can evaluate  such as to mimic the cubic term. Fitted function is actually :  Real (X,Y)  MC (X,Y)  |A(X,Y)| 2 Assume:  Real (X,Y)  MC (X,Y)  1+  Y+  X 2

39. F. AmbrosinoEuridice Midterm Meeting LNF 11/02/05 38   MC MC weighted MC MC weighted

40. F. AmbrosinoEuridice Midterm Meeting LNF 11/02/05 39 The cuts used to select:       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 320 MeV < E  rad < 400 MeV P(  2) > 0.01 Sample selection

41. F. AmbrosinoEuridice Midterm Meeting LNF 11/02/05 40

42. F. AmbrosinoEuridice Midterm Meeting LNF 11/02/05 41 Once a combination has been selected, one can do a second kinematic fit imposing  0 mass for each couple of photons. Second kinematic fit

43. F. AmbrosinoEuridice Midterm Meeting LNF 11/02/05 42 But now: n i = recostructed events i = from each single MC recostructed event weighted with the theoretical function Still we minimize: Doing it the hard way..

44. F. AmbrosinoEuridice Midterm Meeting LNF 11/02/05 43 The center of Dalitz plot correspond to 3 pions with the same energy (E i = M  /3 = 182.4 MeV). A good check of the MC performance in evaluating the energy resolution of  0 comes from the distribution of E  0 - E i for z = 0 Comparison Data – MC (II)

45. F. AmbrosinoEuridice Midterm Meeting LNF 11/02/05 44 E*  1 - E*  2 Vs. E  Comparison Data – MC (II)