Analysis of theΔI=1/2rule andε′/εwith overlap fermions

Abstract

We study the renormalization of the $\ensuremath{\Delta}S=1$ effective weak Hamiltonian with overlap fermions. The mixing coefficients among dimension-6 operators are computed at one loop in perturbation theory. As a consequence of the chiral symmetry at finite lattice spacing and of the GIM mechanism, which is quadratic in the masses, the $\stackrel{\ensuremath{\rightarrow}}{K}\ensuremath{\pi}\ensuremath{\pi}$ and $\stackrel{\ensuremath{\rightarrow}}{K}\ensuremath{\pi}$ matrix elements relevant for the $\ensuremath{\Delta}I=1/2$ rule can be computed without any power subtractions. The analogous amplitudes for ${\ensuremath{\epsilon}}^{\ensuremath{'}}/\ensuremath{\epsilon}$ require one divergent subtraction only, which can be performed nonperturbatively using $\stackrel{\ensuremath{\rightarrow}}{K}0$ matrix elements.