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The O(N) Model at Finite Temperature: Renormalization of the Gap Equations in Hartree and Large-N Approximation

J. T. Lenaghan·D. H. Rischke
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Abstract

The temperature dependence of the sigma meson and pion masses is studied in the framework of the O(N) model. The Cornwall-Jackiw-Tomboulis formalism is applied to derive gap equations for the masses in the Hartree and large-N approximations. Renormalization of the gap equations is carried out within the cut-off and counter-term renormalization schemes. A consistent renormalization of the gap equations within the cut-off scheme is found to be possible only in the large-N approximation and for a finite value of the cut-off. On the other hand, the counter-term scheme allows for a consistent renormalization of both the large-N and Hartree approximations. In these approximations, the meson masses at a given nonzero temperature depend in general on the choice of the cut-off or renormalization scale. As an application, we also discuss the in-medium on-shell decay widths for sigma mesons and pions at rest.

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J. T. Lenaghan, D. H. Rischke. 2000-02-09. The O(N) Model at Finite Temperature: Renormalization of the Gap Equations in Hartree and Large-N Approximation. https://doi.org/10.1088/0954-3899%2F26%2F4%2F309

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