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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. 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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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

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


Rare decays

 CP Direct

Short Distance Contribution

 CP indirect

directly from

CP Conservingpart

CP Violating part

Constructive

?

InterferenceTerm

Destructive


Chiral lagrangians

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]


Constraints from branching ratios

[PDG ’02]

[NA48 ’03]

Constraints from Branching Ratios

Key-quantities

Order p4


Octet dominance hypothesis and large n c predictions

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]


Results

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


Constraints from the form factor

Order p4:

where is given by the pion chiral loop.

Clearly, the O(p4) is not sufficient

Constraints from the form factor


Rare decays

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 » 


Narrow resonances dynamical framework

Narrow resonances dynamical framework

K

K

K

K

NRD Hyp.

MHA

chiral limit

In agreement with Octet Dominance assumption [EPdeR ’87]


Minimal narrow resonances saturation of the form factor

Minimal Narrow Resonances Saturation of the Form Factor

The form factor is now


Rare decays

Fit


Predictions

Predictions


Rare decays

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]


Rare decays

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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