The ΔS = 1 weak chiral lagrangian as the effective theory of the chiral quark model

Abstract

We use the chiral quark model to estimate the coefficients of the weak chiral lagrangian as obtained from the bosonization of the ten relevant operators of the ΔS=1 effective quark lagrangian. All contributions of order N2c as well as Nc and αsNc are included. The chiral coefficients are given in terms of fπ, the quark and gluon condensates and the scale-dependent NLO Wilson coefficients of the corresponding operators. In addition, they depend on the constituent quark mass M, a parameter characteristic of the model. The γ5-scheme dependence of the chiral coefficients, computed via dimensional regularization, and the Fierz transformation properties of the operator basis are discussed in detail. We apply our result to the evaluation of the hadronic matrix elements for the decay K0→2π, consistently including the renormalization induced by the meson loops. The effect of this renormalization is sizable and introduces a long-distance scale dependence that matches in the physical amplitudes the short-distance scale dependence of the Wilson coefficients.