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

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

1999-01-18

arxiv.org/abs/nucl-th/9901049v2

J.Phys.G26:431-450,2000

Physics

Nuclear Physics

Nuclear Theory

21 pages, 6 figures, typos corrected and refs. added, accepted in Journal of Physics G

Scientific paper

10.1088/0954-3899/26/4/309

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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