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We explore applications of the maximum entropy method (MEM) to determineproperties of unstable particles using the four-dimensional O(4) $\phi^4$theory as a laboratory. The spectral function of the correlation function ofthe unstable $\sigma$ particle is calculated with MEM, and shown to yieldreliable results for both the mass of $\sigma$ and the energy of the two-pionstate. Calculations are also made for the case in which $\sigma$ is stable.Distinctive differences in the volume dependence of the $\sigma$ mass andtwo-pion energy for the stable and unstable cases are analyzed in terms ofperturbation theory.Comment: 9 page

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

Analysis of an unstable particle with the maximum entropy method in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:mn>4</mml:mn><mml:mo>)</mml:mo><mml:mn /><mml:mi /><mml:mrow><mml:msup><mml:mrow><mml:mi>φ</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>theory on the lattice

Analysis of an unstable particle with the maximum entropy method inO(4)φ4theory on the lattice