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 0  fit update

 0  fit update. P.Gauzzi. Outline. Kaon Loop S ystematics 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. KL. Correlation coefficients. M a 0 1.000

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 0  fit update

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  1. 0 fit update P.Gauzzi

  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. KL Correlation coefficients Ma0 1.000 ga0KK0.931 1.000 ga0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

  4. KL Systematics • Sensitivity to fixed parameters • ga0' = -1.13 ga0KK (4q) vs ga0' = 1.2 ga0KK (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. Systematics (KL) • Relative variations

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

  7. NS Systematics • Sensitivity to fixed parameters Ma0 = 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. NS Correlation coefficients ga0KK 1.000 ga00.849 1.000 ga00.885 0.971 1.000 R-0.226 -0.261 -0.309 1.000 a00.858 0.793 0.905 -0.275 1.000 00.584 0.787 0.805 -0.283 0.768 1.000 a1 0.684 0.707 0.813 -0.253 0.933 0.836 1.000 10.807 0.912 0.936 -0.294 0.868 0.931 0.816 1.000 • Large correlations

  9. NS • Relative variations • Large correlations also with the a0 mass • Strange behaviour for N  1

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

  13. NS with Adler zeros • The fit convergence improves: no need to fix the a0 mass • However according to Gino no Adler zeros should be put in the model, but…

  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 f0 • All couplings are written in terms of 2 parameters: cf and cI (|cI|<<| cf |) • 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. New NS fit • The mass is in agreement with KL and with PDG • cf=6.6 GeV-1 cI=1.6 GeV-1 (cf= 22 GeV-1 cI= -2.6 GeV-1 best fit by t’Hooft et al.)

  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. Systematics from photon pairing • Data • Right p. • Wrong p. • C(a0) is the difference between the • first and the second photon combination • for the a0 hypothesis • Two component (right and wrong pairing) • fit to the  C(a0) distribution of the data • (final sample) • Right and wrong pairing shapes from MC • wrong pairings = (11.5 ± 0.70) % • (from MC 14 %)  C(a0)

  18. Systematics from photon pairing • From C(a0) 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 Mrec (MeV) Mgen (MeV)

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