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

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.