Twisted mass QCD and lattice approaches to the $\Delta I=1/2$ rule

Abstract

Twisted mass lattice QCD (tmQCD), generalised to four Wilson quark flavours, can be used for the computation of some weak matrix elements related to $\Delta I=1/2$ transitions. Besides eliminating unphysical zero modes, tmQCD may alleviate long-standing renormalisation problems of the four-quark operators which contribute to CP-conserving $K\to \pi$ transitions. With an active charm quark, the renormalisation of the $K\to \pi$ matrix elements requires at most the subtraction of a linearly divergent counterterm. Furthermore, in the (partially) quenched approximation the twist angles can be chosen so that only a finite counterterm needs to be subtracted.

Comments: 35 pages;final version with references added