1.  0  fit update P.Gauzzi

2. 2 Outline Kaon Loop – Systematics on the fit parameters – Fit with fixed VDM No Structure –systematics – fit with free VDM KL and NS fits with Adler zeros New version of NS model

3. 3 KL M a0 1.000 g a0KK 0.931 1.000 g a0  0.584 0.550 1.000  0.277 0.236 0.156 1.000 Br(VDM) -0.252 -0.327 -0.513 0.130 1.000 R  0.004 -0.180 -0.111 0.008 -0.038 1.000 Correlation coefficients

4. 4 KL Systematics Sensitivity to fixed parameters –g a0  '  = -1.13 g a0KK (4q) vs g a0  '  = 1.2 g a0KK (qq) –g  K+K─ = 4.49  0.07 Normalization (N   1  ) Data-MC discrepancy for the wrong pairing fraction 11.5% (data) vs 14%(MC) Sensitivity to the starting values of the parameters (  10%  variations < 0.1%)

5. 5 Systematics (KL) Relative variations

6. 6 KL with fixed VDM Br(VDM) = 4  10 -6 (same as NS fit) Worse  2 probability

7. 7 NS Systematics Sensitivity to fixed parameters M a0 = 982.5 MeV (KL fit) vs 985.1 MeV (PDG) Normalization (N   1  ) Data-MC discrepancy for the wrong pairing fraction 11.5% (data) vs 14%(MC) Sensitivity to the starting values of the parameters (  10%  variations < 0.2%)

8. 8 NS g a0KK 1.000 g a0  0.849 1.000 g  a0  0.885 0.971 1.000 R  -0.226 -0.261 -0.309 1.000 a 0 0.858 0.793 0.905 -0.275 1.000  0 0.584 0.787 0.805 -0.283 0.768 1.000 a 1 0.684 0.707 0.813 -0.253 0.933 0.836 1.000  1 0.807 0.912 0.936 -0.294 0.868 0.931 0.816 1.000 Correlation coefficients Large correlations

9. 9 NS Relative variations Large correlations also with the a 0 mass Strange behaviour for N   1 

10. 10 NS with free VDM Br(VDM) as free parameter (as for KL) No sensitivity to VDM Better fit quality Couplings more similar to KL results (g  a0  still compatible)

11. 11 Fit with Adler zeros According to some theoreticians the Adler zero is needed as a consequence of Chiral Symmetry (however there is no general consensus) It forces the PP interaction to vanish close to threshold: I tried to include them into the fit functions: in order not to change the meaning of the parameters I used:

12. 12 KL fit with Adler zeros —With A.z. —Without A.z. M  (MeV) Fit quality improves All relevant parameters become larger

13. 13 NS with Adler zeros The fit convergence improves: no need to fix the a 0 mass However according to Gino no Adler zeros should be put in the model, but…

14. 14 New model t’Hooft, Isidori, Maiani …. “A theory of Scalar Mesons” arXiv:0801.2288 Scalars are “tetraquarks” “Instanton” induced transitions to explain decays like f 0  All couplings are written in terms of 2 parameters: c f and c I (|c I |<<| c f |) Pseudoscalars appear in the effective lagrangian with derivative couplings: From the technical point of view of the fit, the effect is very similar to the Adler zero

15. 15 New NS fit The mass is in agreement with KL and with PDG  c f =6.6 GeV -1 c I =1.6 GeV -1 (c f = 22 GeV -1 c I = -2.6 GeV -1 best fit by t’Hooft et al.)

16. 16 Conclusions We should decide which fit show in the paper KL fit is stable NS has some problems; what systematics should we quote ? NS with VDM free goes in the same direction as KL –Very small VDM contribution Adler zeros improve the convergence; are they really needed ? New NS model: we should discuss the results with the authors (we are in contact with A.Polosa in Rome)

17. 17 Systematics from photon pairing  C(a 0  )  C(a 0  ) is the difference between the first and the second photon combination for the a 0  hypothesis Two component (right and wrong pairing) fit to the  C(a 0  ) distribution of the data (final sample) Right and wrong pairing shapes from MC wrong pairings = (11.5 ± 0.70) % (from MC 14 %) Data ─Right p. ─Wrong p.

18. 18 M gen (MeV) M rec (MeV) Systematics from photon pairing From  C(a 0  ) between the first and the second best combination Wrong pairings: data  (11.5 ± 0.70) % MC  14 % Check done by scaling the off-diagonal part of the efficiency matrix by 0.115/0.14 and the diagonal region accordingly to conserve normalization