Unstable particles in finite volume: The broken phase of the $4$-d $O(4)$ non-linear $\sigma$-model

TL;DR

This paper demonstrates how L"uscher's method can be used in a Monte-Carlo study of the 4D $O(4)$ non-linear sigma model to analyze unstable particles, specifically the $g$-particle, by extracting its resonance parameters from finite-volume energy spectra.

Contribution

It applies L"uscher's finite-volume method to a non-perturbative lattice simulation of the broken phase of the 4D $O(4)$ sigma model, including the analysis of unstable particles.

Findings

Successfully observed the $g$-resonance.

Extracted the mass and width of the $g$-particle.

Validated the applicability of L"uscher's method for unstable particles.

Abstract

According to a proposal of L\"uscher it is possible to determine elastic scattering phases in infinite volume from the energy spectrum of two-particle states in a periodic box. We demonstrate the applicability of this method in the broken phase of the 4-dimensional $O(4)$ non-linear $\sigma$-model in a Monte-Carlo study on finite lattices. This non-perturbative approach also permits the study of unstable particles, the $\sg$-particle in our case. We observe the $\sg$-resonance and extract its mass and its width.