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.

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

References in corpus (3)

• Large-N expansion for unitary superfluid Fermi gases
• Pion and Kaon Condensation at Finite Temperature and Density
• The linear sigma model at a finite isospin chemical potential

Cited by in corpus (14)

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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
• Rotation induced charged pion condensation in a strong magnetic field: A Nambu--Jona-Lasino model study
• Influence of chiral asymmetry on phase structure of the two-color quark matter
• Renormalization of O(N) model in 1/N expansion in auxiliary field formalism
• Critical point and Bose-Einstein condensation in pion matter
• Phase diagram of interacting pion matter and isospin charge fluctuations
• Bose-Einstein condensation in dense quark matter
• Non-perturbative construction of counterterms for 2PI-approximation
• 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