Two- and three-body interactions in $\varphi^4$ theory from lattice simulations

TL;DR

This paper uses lattice simulations to analyze two- and three-particle interactions in $\

Contribution

It introduces a method to accurately extract multi-particle interaction parameters in $\

Findings

Finite-volume effects can be mitigated using the single particle mass.

Reliable extraction of scattering length, effective range, and three-body coupling is demonstrated.

The effective three-body coupling is found to be significantly non-zero.

Abstract

We calculate the one-, two- and three-particle energy levels for different lattice volumes in the complex $\varphi^4$ theory on the lattice. We argue that the exponentially suppressed finite-volume corrections for the two- and three-particle energy shifts can be reduced significantly by using the single particle mass, which includes the finite-size effects. We show numerically that, for a set of bare parameters, corresponding to the weak repulsive interaction, one can reliably extract the two- and three-particle energy shifts. From those, we extract the scattering length, the effective range and the effective three-body coupling. We show that the parameters, extracted from the two- and three-particle energy shifts, are consistent. Moreover, the effective three-body coupling is significantly different from zero.