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

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 $\mathcal{O}(p^4)$. We examine the contributions of the order $\mathcal{O}(N_c)$ to the ratio $g_{\underline{8}}/g_{\underline{27}}$, considering e.g. the quark axial-vector constant $g_{\mathrm{A}}$ different from unity. The low energy constants of the counterterms are also presented and discussed.

Comments: 25 pages. RevTex is used. 3 postscript figures. Final version for publication in Nucl. Phys. B