Analysis of unstable particle with the maximum entropy method in O(4) $\phi^4$ theory on the lattice

TL;DR

This paper applies the maximum entropy method to analyze unstable particles in lattice O(4) $\,\phi^4$ theory, successfully extracting spectral functions and particle properties, and comparing stable and unstable cases.

Contribution

It demonstrates the effectiveness of MEM in determining spectral functions and particle properties in lattice field theory, specifically for unstable particles in O(4) $\,\phi^4$ theory.

Findings

Reliable extraction of $\,\sigma$ particle mass and two-pion energy using MEM.

Distinct volume dependence observed between stable and unstable $\,\sigma$ cases.

Perturbation theory explains differences in volume dependence.

Abstract

We explore applications of the maximum entropy method (MEM) to determine properties of unstable particles using the four-dimensional O(4) $\phi^4$ theory as a laboratory. The spectral function of the correlation function of the unstable $\sigma$ particle is calculated with MEM, and shown to yield reliable results for both the mass of $\sigma$ and the energy of the two-pion state. Calculations are also made for the case in which $\sigma$ is stable. Distinctive differences in the volume dependence of the $\sigma$ mass and two-pion energy for the stable and unstable cases are analyzed in terms of perturbation theory.