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

TL;DR

This paper demonstrates that twisted mass QCD with four quark flavors simplifies the calculation of weak matrix elements related to the $$ rule, reducing renormalization issues and avoiding exceptional configurations.

Contribution

The study shows that tmQCD offers significant advantages for computing $$ transition matrix elements, including simplified renormalization and better behavior at small pion masses.

Findings

Renormalization of $K o \pi$ matrix elements is simplified.

Quenched simulations avoid exceptional configurations at small pion mass.

Properties of $K o \pi ext{ extbackslash}pi$ matrix elements are similar to standard Wilson case.

Abstract

We show that the application of twisted mass QCD (tmQCD) with four (Wilson) quark flavours to the computation of lattice weak matrix elements relevant to $\Delta I=1/2$ transitions has important advantages: the renormalisation of $K \to \pi$ matrix elements does not require the subtraction of other dimension six operators, the divergence arising from the subtraction of lower dimensional operators is softened by one power of the lattice spacing and quenched simulations do not suffer from exceptional configurations at small pion mass. This last feature is also retained in the tmQCD computation of $K \to \pi\pi$ matrix elements, which, as far as renormalisation and power subtractions are concerned, has properties analogous to the standard Wilson case.