A note on the power divergence in lattice calculations of $\Delta I=1/2$ $K\to \pi \pi$ amplitudes at $M_K=M_{\pi }$

Abstract

In this note, we clarify a point concerning the power divergence in lattice calculations of $\Delta I=1/2$ $K\to \pi \pi$ decay amplitudes. There have been worries that this divergence might show up in the Minkowski amplitudes at $M_K=M_{\pi }$ 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.

Comments: 5 pages, 2 figures