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