Saturation of counterterms by resonances in $K \to πe^{+} e^{-}$ decays

Details Saturation of counterterms by resonances in $K \to πe^{+} e^{-}$ decays Saturation of counterterms by resonances in $K \to πe^{+} e^{-}$ decays

1995-05-11

arxiv.org/abs/hep-ph/9505280v1

Z.Phys. C71 (1996) 307-312

Physics

High Energy Physics

High Energy Physics - Phenomenology

24 pages, LaTeX

Scientific paper

10.1007/BF02906988

The decays $K^{+} \rightarrow \pi^{+} e^{+} e^{-}$, $K_{S} \rightarrow \pi^{0} e^{+} e^{-}$ and $K_{L} \rightarrow \pi^{0} e^{+} e^{-}$ are reinvestigated within the framework of chiral perturbation theory. The counterterms induced by strong, electromagnetic and weak interactions are determined assuming the resonance exchange. The weak deformation model, the factorization model and the large $N_{c}$ limit are used to create a weak Lagrangian. It is found that the results of the first two approaches depend on the $H_{1}$ coupling, defined in the effective chiral Lagrangian of the ${\it O} (p^{4})$ order. The set of parameters used in the extended Nambu and Jona-Lasinio model can accommodete $K^{+} \rightarrow \pi^{+} e^{+} e^{-}$ decay rate within the factorization approach. The CP violating $K_{L} \rightarrow \pi^{0} e^{+} e^{-}$ decay rate is discussed.

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