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Rare Decays

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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

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

CP Direct

Short Distance Contribution

CP indirect

directly from

CP Conservingpart

CP Violating part

Constructive

?

InterferenceTerm

Destructive

which can be rewritten in a more convenient way (Large NC counting)

is

where

is

Experimental constraints on this coupling constants via

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]

[PDG ’02]

[NA48 ’03]

Key-quantities

Order p4

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]

Conclusion: in both cases thenCONSTRUCTIVE INTERFERENCE

But the sign of is not clearly predicted: Need for a Large NC next-to-leading order calculation

Order p4:

where is given by the pion chiral loop.

Clearly, the O(p4) is not sufficient

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 »

K

K

K

K

NRD Hyp.

MHA

chiral limit

In agreement with Octet Dominance assumption [EPdeR ’87]

The form factor is now

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]

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]