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

TL;DR

This paper calculates the coefficient of the pionic chiral logarithm in $K o\pi\pi$ decays using one-loop two-flavour Chiral Perturbation Theory, providing a unique determination and cross-check with three-flavour results.

Contribution

It offers a novel calculation of the chiral logarithm coefficient in $K o\pi\pi$ decays within SU(2) Chiral Perturbation Theory, with arguments supporting its uniqueness.

Findings

Calculated the coefficient of the pionic chiral logarithm.

Validated the calculation by reducing known three-flavour results.

Provided arguments for the general applicability of the method.

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 $\logm = M^2\log M^2$ 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.