$K\to \pi \pi$ Decays in SU(2) Chiral Perturbation Theory

Abstract

We study the decays $K\to \pi \pi$ in one-loop two-flavour Chiral Perturbation Theory. We provide arguments why the calculation of the coefficient of the pionic chiral logarithm $\text{logm}=M^2\log M^2$ is unique and then perform the calculation. As a check we perform the reduction of the known three-flavour result. The underlying arguments are expected to be valid for heavier particles and other processes as well.

Comments: 11 pages, Section 3 expanded and made more structured. Comments on lattice and relation to FSI added