Twisted mass QCD and the $ΔI=1/2$ rule

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 $ΔI=1/2$ transitions has important advantages: the renormalisation of $K \to π$ 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 $K \to ππ$ matrix elements, which, as far as renormalisation and power subtractions are concerned, has properties analogous to the standard Wilson case.