Testing a new method for scattering in finite volume in the $\phi^4$ theory

TL;DR

This paper evaluates an alternative finite-volume scattering method in lattice simulations using a scalar 4 theory, finding comparable results to the L"uscher method but with reduced statistical uncertainties at larger volumes.

Contribution

It introduces and tests a new approach for extracting scattering lengths in lattice simulations, demonstrating its effectiveness compared to established methods.

Findings

Results are comparable to L"uscher method

Smaller statistical uncertainties at larger volumes

Validates the new method in 4 theory

Abstract

We test an alternative proposal by Bruno and Hansen [1] to extract the scattering length from lattice simulations in a finite volume. For this, we use a scalar $\phi^4$ theory with two mass nondegenerate particles and explore various strategies to implement this new method. We find that the results are comparable to those obtained from the L\"uscher method, with somewhat smaller statistical uncertainties at larger volumes.