Residual meson-meson interaction from lattice gauge simulation in a simple QED model

TL;DR

This paper introduces a cumulant expansion method to compute residual meson-meson interactions from lattice gauge simulations, demonstrating its effectiveness in a simple confining QED model with results consistent with previous phase shift analyses.

Contribution

It presents a new cumulant expansion approach to define and compute effective meson-meson interactions from lattice simulations, applicable to other hadron-hadron systems.

Findings

Effective interaction shows a repulsive core and intermediate attraction.

Results align with previous phase shift studies.

Method is straightforward to apply to other models.

Abstract

The residual interaction for a meson-meson system is computed utilizing the cumulant, or cluster, expansion of the momentum-space time correlation matrix. The cumulant expansion serves to define asymptotic, or free, meson-meson operators. The definition of an effective interaction is then based on a comparison of the full (interacting) and the free (noninteracting) time correlation matrices. The proposed method, which may straightforwardly be transcribed to other hadron-hadron systems, here is applied to a simple 2+1 dimensional U(1) lattice gauge model tuned such that it is confining. Fermions are treated in the staggered scheme. The effective interaction exhibits a repulsive core and attraction at intermediate relative distances. These findings are consistent with an earlier study of the same model utilizing L\"{u}scher's method where scattering phase shifts are obtained directly.