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

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 ${\epsilon }^{\prime }$, the parameter describing direct CP violating effects in $K_L\to \pi \pi$ decay.

Comments: 51 pages, 10 figures