Study of unstable particle through the spectral function in O(4) $ϕ^4$ theory

Abstract

We test application of the maximum entropy method to decompose the states contributing to the unstable $σ$ correlation function through the spectral function in the four dimensional O(4) $ϕ^4$ theory. Reliable results are obtained for the $σ$ mass and two-particle $ππ$ state energy using only the $σ$ correlation function. We also find that the property of the $σ$ particle is different between the unstable ($m_σ/m_π>2$) and stable ($m_σ/m_π<2$) cases.