Scattering phase shift determinations from a two-scalar field theory

TL;DR

This paper revisits a two-scalar field theory to accurately determine scattering phase shifts using improved lattice actions and Monte Carlo methods, extending previous studies beyond large coupling limits.

Contribution

It introduces a comprehensive analysis of scattering phase shifts in a two-scalar field theory with improved continuum behavior and advanced Monte Carlo techniques, beyond prior large-coupling restrictions.

Findings

Accurate phase shift determinations across various lattice sizes.

Effective use of Symanzik-improved action for continuum dispersion relations.

Successful application of Lüscher analysis with multiple partial waves.

Abstract

A field theory involving two interacting scalar fields, previously studied by Rummukainen and Gottlieb, is revisited. Our study is not restricted to the limit of large quartic couplings, and a Symanzik-improved action is used so that continuum dispersion relations work well. The Metropolis method, combined with a local microcanonical updating algorithm, is employed in our Monte Carlo calculations. Isotropic lattices ranging from $16^3 \times 48$ to $53^3 \times 48$ are used, and scattering phase shifts are determined using a L\"uscher analysis with multiple partial waves.