Studying ${\epsilon }^{\prime }/\epsilon$ in the Chiral Quark Model: ${\gamma }_5$-Scheme Independence and NLO Hadronic Matrix Elements

Abstract

We study the $CP$-violating, $|\Delta S|=1$ parameter ${\epsilon }^{\prime }/\epsilon$ 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 ${\epsilon }^{\prime }/\epsilon$. We also investigate the possibility that the chiral quark model might drastically reduce the dimensional regularization ${\gamma }_5$-scheme dependence of current evaluations of ${\epsilon }^{\prime }/\epsilon$.

Comments: 38 pages, LATEX, including 4 eps figures