Study of chiral symmetry restoration in linear and nonlinear O(N) models using the auxiliary field method

Abstract

We consider the O(N) linear σ model and introduce an auxiliary field to eliminate the scalar self-interaction. Using a suitable limiting process this model can be continuously transformed into the nonlinear version of the O(N) model. We demonstrate that, up to two-loop order in the CJT formalism, the effective potential of the model with auxiliary field is identical to the one of the standard O(N) linear σ model, if the auxiliary field is eliminated using the stationary values for the corresponding one- and two-point functions. We numerically compute the chiral condensate and the σ- and π-meson masses at nonzero temperature in the one-loop approximation of the CJT formalism. The order of the chiral phase transition depends sensitively on the choice of the renormalization scheme. In the linear version of the model and for explicitly broken chiral symmetry, it turns from crossover to first order as the mass of the σ particle increases. In the nonlinear case, the order of the phase transition turns out to be of first order. In the region where the parameter space of the model allows for physical solutions, Goldstone's theorem is always fulfilled.

25 pages, 9 figures, 1 table, improved version

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• Implications of the fermion vacuum term in the extended SU(3) Quark Meson model on compact stars properties
• Effects of Renormalizing the chiral SU(2) Quark-Meson-Model
• Role reversal in first and second sound in a relativistic superfluid
• On the symmetry improved CJT formalism in the $O(4)$ linear sigma model
• The O(2) model in polar coordinates at nonzero temperature
• Chiral Symmetry Restoration for the large-$N$ pion gas
• Addressing energy density functionals in the language of path-integrals I: Comparative study of diagrammatic techniques applied to the (0+0)-D $O(N)$-symmetric ${\phi }^4$-theory
• Degeneracy patterns of chiral companions at finite temperature
• Thermodynamics of the O(4) linear and nonlinear models within the auxiliary field method