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Rare Decays

RENCONTRES DE MORIOND March 2005. Rare Decays. David GREYNAT. in collaboration with S. FRIOT and E. de RAFAEL. arXiv:hep-ph/0404136 or PLB 595 (2004) 301. Motivations. 1- New experimental results for the rare decays. [NA48 ’03]. Those results allow for a.

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Rare Decays

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  1. RENCONTRES DE MORIOND March 2005 Rare Decays David GREYNAT in collaboration with S. FRIOT and E. de RAFAEL arXiv:hep-ph/0404136 or PLB 595 (2004) 301

  2. Motivations 1- New experimental results for the rare decays [NA48 ’03] Those results allow for a Re-analysis of the CP violating rare decay 2- Computation of some of the coupling constants of the effective to leading and next-to-leading orders in Large NC QCD

  3.  CP Direct Short Distance Contribution  CP indirect directly from CP Conservingpart CP Violating part Constructive ? InterferenceTerm Destructive

  4. which can be rewritten in a more convenient way (Large NC counting) is where is Experimental constraints on this coupling constants via Chiral Lagrangians The nature of the interference is strongly linked to coupling constants of chiral Lagrangians Precisely to and in their combination In fact the usual chiral electro-weak order p4 Lagrangian is[EPdeR ’87]

  5. [PDG ’02] [NA48 ’03] Constraints from Branching Ratios Key-quantities Order p4

  6. Octet Dominance Hypothesis and Large-NC Predictions  OctetDominanceHypothesis[EPdR ‘87]: Large-NcPredictions : Through the bosonization of the factorized part of the operator matched to O(p4) chiral Lagrangian gives See also [Bruno Prades ’93]

  7. Results Conclusion: in both cases thenCONSTRUCTIVE INTERFERENCE But the sign of is not clearly predicted: Need for a Large NC next-to-leading order calculation

  8. Order p4: where is given by the pion chiral loop. Clearly, the O(p4) is not sufficient Constraints from the form factor

  9. Beyond order p4 Strategies:  Guess of dominantO(p6 ) contributions [Isidori et al. ’03] • O(p4 )+ Chiral resummation (inspired by M.H.A of Large NC) « NarrowResonance Minimal Structure » 

  10. Narrow resonances dynamical framework K K K     K NRD Hyp. MHA chiral limit In agreement with Octet Dominance assumption [EPdeR ’87]

  11. Minimal Narrow Resonances Saturation of the Form Factor The form factor is now

  12. Fit

  13. Predictions

  14. Prediction for CP Conserving Part[Buchalla et al. ‘03] CP Direct Violating Part[Buchalla et al. ‘03] CP Indirect Violating Part[NA48 ‘03] Interference term[this work]

  15. Conclusions and Outlook • This analysis which combined chiral perturbation theory at order p4 with a model inspired by Large NC gives very good results for the known branching ratios of • We obtain a prediction for the golden mode closed to reachable experimental determination • Next-to-leading order calculation in Large-NC QCD of In the framework of [Hambye et al. ’03]

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