Scattering length from BS wave function inside the interaction range

TL;DR

This paper computes the I=2 two-pion scattering length using Bethe-Salpeter wave functions in quenched lattice QCD, and compares results with traditional methods and chiral perturbation theory for validation.

Contribution

It introduces a novel approach to evaluate scattering lengths directly from the wave function within the interaction range, enhancing the analysis of lattice QCD data.

Findings

Scattering length results are consistent with finite size method and chiral perturbation theory.

Effective range is extracted from half-off-shell amplitude.

Method provides an alternative way to analyze scattering in lattice QCD.

Abstract

We evaluate $I=2$ two-pion scattering length through the scattering amplitude obtained by the Bethe-Salpeter wave function inside the interaction range. The scattering length is computed with $m_\pi = 0.52-0.86$ GeV in the quenched lattice QCD. Furthermore, the half-off-shell amplitude is calculated, from which the effective range is extracted. Our results are compared with those by the conventional finite size method and by chiral perturbation theory to confirm consistency.