Linear sigma model at finite density in the 1/N expansion to next-to-leading order

Abstract

We study relativistic Bose-Einstein condensation at finite density and temperature using the linear sigma model in the one-particle-irreducible 1/N-expansion. We derive the effective potential to next-to-leading (NLO) order and show that it can be renormalized in a temperature-independent manner. As a particular application, we study the thermodynamics of the pion gas in the chiral limit as well as with explicit symmetry breaking. At nonzero temperature we solve the NLO gap equation and show that the results describe the chiral-symmetry-restoring second-order phase transition in agreement with general universality arguments. However, due to nontrivial regularization issues, we are not able to extend the NLO analysis to nonzero chemical potential.

arXiv comment12 pages, REVTeX4, 6 eps figures; v2: added references + minor corrections throughout the text; version to appear in Phys. Rev. D

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• Lattice QCD at finite isospin density at zero and finite temperature
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• Finite-size effects in pion condensation phenomena of dense baryonic matter in the NJL${}_2$ model
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• Duality between chiral symmetry breaking and charged pion condensation at large $N_c$: Consideration of an NJL${}_2$ model with baryon-, isospin- and chiral isospin chemical potentials
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• Affinity of NJL${}_2$ and NJL${}_4$ model results on duality and pion condensation in chiral asymmetric dense quark matter
• Scaling violation and the magnetic equation of state in chiral models
• Bose-Einstein condensation in dense quark matter
• Large-$N$ properties of a non-ideal Bose gas
• Non-perturbative construction of counterterms for 2PI-approximation
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• Axial Vector Coupling and Chiral Anomaly in the Spectral Quark Model
• Renormalized O(N) model at next-to-leading order of the 1/N expansion: Effects of the Landau pole
• Renormalization and resummation in the O(N) model