Saturation of counterterms by resonances inK →πe + e ? decays

The decaysK ⁺→π ⁺ e ⁺ e ^?,K _S→π ⁰ e ⁺ e ^? andK _L→π 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 largeN _c limit are used to create a weak Lagrangian. It is found that the results of the first two approaches depend on theH ₁ coupling, defined in the effective chiral Lagrangian of theO(p ⁴) order. The set of parameters used in the extended Nambu and Jona-Lasinio model can accommodeteK ⁺→π ⁺ e ⁺ e ^? decay rate within the factorization approach. The CP violatingK _L→π ⁰ e ⁺ e ^? decay rate is discussed.