Studying $\varepsilon '/\varepsilon$ in the Chiral Quark Model: $\gamma_5$-Scheme Independence and NLO Hadronic Matrix Elements

We study the $CP$-violating, $|\Delta S| =1$ parameter $\varepsilon '/\varepsilon$ by computing the hadronic matrix elements in the chiral quark model. We estimate the coefficients of the next-to-leading order terms in the chiral expansion that correspond to the operators $Q_6$ and $Q_{11}$. We consider the impact of these corrections on the value of $\varepsilon '/\varepsilon$. We also investigate the possibility that the chiral quark model might drastically reduce the dimensional regularization $\gamma_5$-scheme dependence of current evaluations of $\varepsilon '/\varepsilon$.