Spontaneous symmetry breaking in the linear sigma model at finite chemical potential: One-loop corrections

Abstract

We investigate spontaneous symmetry breaking within the linear sigma model with the SU(2)xU(1) internal symmetry at finite chemical potential, which was suggested as a model for kaon condensation in the CFL phase of dense quark matter. One-loop corrections to the scalar field effective potential as well as its propagator are calculated. Particular attention is paid to the type-II Goldstone boson that appears in the Bose--Einstein condensed phase. Furthermore, we show that the type-I Goldstone boson -- the superfluid phonon -- is allowed to decay due to the nonlinearity of its dispersion relation at high momentum, and determine its decay width.

arXiv comment13 pages, REVTeX4, 37 eps figures; v2: substantial error in Sec. IV corrected, references added, other minor corrections; version to appear in Phys. Rev. D

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• Anomalous low-temperature thermodynamics of QCD in strong magnetic fields
• Goldstone bosons in presence of charge density
• Beliaev theory of spinor Bose-Einstein condensates
• Gluonic phases, vector condensates, and exotic hadrons in dense QCD
• Mesons and diquarks in neutral color superconducting quark matter with $\beta$-equilibrium
• Effective Field Theory for Spontaneously Broken Symmetry
• Diquarks in the color--flavor locked phase of dense quark matter
• The connection between nonzero density and spontaneous symmetry breaking for interacting scalars
• Gapped Goldstones at the cut-off scale: a non-relativistic EFT
• Scattering amplitudes of massive Nambu-Goldstone bosons
• Inhomogeneous superfluids
• Dynamical stabilization of runaway potentials and landscape of vacua at finite density
• An introduction to Goldstone boson physics and to the coset construction