Note on the power divergence in lattice calculations ofΔI=1/2K→ππamplitudes atMK=Mπ

Abstract

In this Brief Report, we clarify a point concerning the power divergence in lattice calculations of $\ensuremath{\Delta}I=1/2\stackrel{\ensuremath{\rightarrow}}{K}\ensuremath{\pi}\ensuremath{\pi}$ decay amplitudes. There have been worries that this divergence might show up in the Minkowski amplitudes at ${M}_{K}{=M}_{\ensuremath{\pi}}$ with all the mesons at rest. Here we demonstrate, via an explicit calculation in leading-order chiral perturbation theory, that the power divergence is absent at the above kinematic point, as predicted by CPS symmetry.