$\pi-\pi$ scattering, QED and finite-volume quantization

TL;DR

This paper introduces a lattice QCD method in Coulomb gauge to compute $^+^+$ scattering phase shifts, including Coulomb effects, aiming to improve understanding of electromagnetic contributions to CP violation in kaon decays.

Contribution

It develops a novel lattice QCD procedure that incorporates Coulomb interactions and relativistic effects, avoiding finite-volume corrections in scattering calculations.

Findings

First lattice QCD calculation including Coulomb effects in $^+^+$ scattering.

Method accounts for relativity and reduces finite-volume corrections.

Lays groundwork for electromagnetic and isospin-breaking contributions to $'$.

Abstract

Using the Coulomb gauge formulation of QED we present a lattice QCD procedure to calculate the $\pi^+\pi^+$ scattering phase shift including the effects of the Coulomb potential which appears in this formulation. The approach described here incorporates the effects of relativity and avoids finite-volume corrections that vanish as a power of the volume in which the lattice calculation is performed. This is the first step in developing a complete lattice QCD calculation of the electromagnetic and isospin-breaking light-quark mass contributions to $\varepsilon'$, the parameter describing direct CP violating effects in $K_L\to\pi\pi$ decay.