Effective Weak Chiral Lagrangian to ${\cal O} (p^4)$ in the Chiral Quark Model

TL;DR

This paper derives the effective weak chiral Lagrangian to order ${ m O}(p^4)$ within the chiral quark model, providing insights into weak interactions and low energy constants relevant for kaon decays.

Contribution

It presents a derivation of the weak chiral Lagrangian to ${ m O}(p^4)$ in the chiral quark model, including ${ m O}(N_c)$ contributions and low energy constants.

Findings

Derived the ${ m O}(p^4)$ weak chiral Lagrangian

Analyzed ${ m O}(N_c)$ contributions to $g_{8}/g_{27}$ ratio

Presented low energy constants of counterterms

Abstract

We investigate the $\Delta S = 1,2$ effective weak chiral Lagrangian within the framework of the chiral quark model. Starting from the effective four-quark operators, we derive the effective weak chiral action by integrating out the constituent quark fields. Employing the derivative expansion, we obtain the effective weak chiral Lagrangian to order ${\cal O} (p^4)$. We examine the contributions of the order ${\cal O} (N_c)$ to the ratio $g_{\underline{8}}/g_{\underline{27}}$, considering e.g. the quark axial-vector constant $g_{\rm A}$ different from unity. The low energy constants of the counterterms are also presented and discussed.