Scattering amplitude from Bethe-Salpeter wave function inside the interaction range

TL;DR

This paper introduces a lattice-based method to compute scattering amplitudes from the Bethe-Salpeter wave function within the interaction range, validated by pion scattering length calculations consistent with traditional methods.

Contribution

It presents a novel approach to determine scattering amplitudes directly from the Bethe-Salpeter wave function on the lattice, expanding computational techniques in hadron physics.

Findings

Scattering length for I=2 S-wave two pions matches conventional results.

Method successfully evaluates on-shell scattering amplitude.

Half-off-shell amplitude also computed, demonstrating versatility.

Abstract

We propose a method to calculate scattering amplitudes using the Bethe-Salpeter wave function inside the interaction range on the lattice. For an exploratory study of this method, we evaluate a scattering length of $I=2$ S-wave two pions by the use of the on-shell scattering amplitude. Our result is confirmed to be consistent with the value obtained from the conventional finite volume method. The half-off-shell scattering amplitude is also evaluated.