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.