I=2 Pion Scattering Length with the Wilson Fermion

TL;DR

This paper recalculates the I=2 pion scattering length using quenched lattice QCD with Wilson fermions across multiple lattice spacings, achieving results consistent with chiral perturbation theory.

Contribution

It provides a continuum limit calculation of the I=2 pion scattering length using Wilson fermions and finite size scaling, improving previous lattice QCD estimates.

Findings

Result consistent with chiral perturbation theory

Continuum limit value of a0mπ = -0.0410(69)

Lattice spacings range from 0.12 to 0.07 fm

Abstract

The calculation of the I=2 pion scattering length in quenched lattice QCD is revisited. The calculation is carried out with the Wilson fermion action employing L\"uscher's finite size scaling method at $\beta=5.9$, 6.1, and 6.3 corresponding to the range of lattice spacing $a\simeq 0.12 - 0.07$ fm. We obtain in the continuum limit $a_0m_\pi = -0.0410(69)$, which is consistent with the prediction of chiral perturbation theory $a_0m_\pi=-0.0444(10)$.