Abnormal number of Nambu-Goldstone bosons in the color-asymmetric 2SC phase of an NJL-type model

Abstract

We consider an extended Nambu--Jona-Lasinio model including both (q \bar q)- and (qq)-interactions with two light-quark flavors in the presence of a single (quark density) chemical potential. In the color superconducting phase of the quark matter the color SU(3) symmetry is spontaneously broken down to SU(2). If the usual counting of Goldstone bosons would apply, five Nambu-Goldstone (NG) bosons corresponding to the five broken color generators should appear in the mass spectrum. Unlike that expectation, we find only three gapless diquark excitations of quark matter. One of them is an SU(2)-singlet, the remaining two form an SU(2)-(anti)doublet and have a quadratic dispersion law in the small momentum limit. These results are in agreement with the Nielsen-Chadha theorem, according to which NG-bosons in Lorentz-noninvariant systems, having a quadratic dispersion law, must be counted differently. The origin of the abnormal number of NG-bosons is shown to be related to a nonvanishing expectation value of the color charge operator Q_8 reflecting the lack of color neutrality of the ground state. Finally, by requiring color neutrality, two massive diquarks are argued to become massless, resulting in a normal number of five NG-bosons with usual linear dispersion laws.

13 pages, 4 figures, revtex4

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Cited by in corpus (46)

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• Counting Rules of Nambu-Goldstone Modes
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• Superfluidity in a Three-flavor Fermi Gas with SU(3) Symmetry
• Inhomogeneous charged pion condensation phenomenon in the NJL${}_2$ model with quark number and isospin chemical potentials
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• Pion, sigma-meson and diquarks in the 2SC phase of dense cold quark matter
• Inhomogeneous charged pion condensation in chiral asymmetric dense quark matter in the framework of NJL${}_2$ model
• Finite-size effects in pion condensation phenomena of dense baryonic matter in the NJL${}_2$ model
• Charged pion condensation and duality in dense and hot chirally and isospin asymmetric quark matter in the framework of NJL${}_2$ model
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• Pion condensation of quark matter in the static Einstein universe
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• Goldstone boson counting in linear sigma models with chemical potential
• Spontaneous symmetry breaking in the linear sigma model at finite chemical potential: One-loop corrections
• 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
• Quark-Hadron Matter at Finite Temperature and Density in a Two-Color PNJL model
• Relation Between Chiral Susceptibility and Solutions of Gap Equation in Nambu--Jona-Lasinio Model
• Quasi-Nambu-Goldstone modes in nonrelativistic systems
• Diquark Bose-Einstein Condensation and Nuclear Matter
• Manifestation of Instabilities in Nambu-Jona-Lasinio type models
• Goldstone bosons in presence of charge density
• Mass spectrum of diquarks and mesons in the color--flavor locked phase of dense quark matter
• The Quantum Yang Baxter conditions: The fundamental relations behind the Nambu-Goldstone theorem
• Pseudoscalar Goldstone bosons in the color-flavor locked phase at moderate densities
• Mesons and diquarks in neutral color superconducting quark matter with $\beta$-equilibrium
• Diquarks in the color--flavor locked phase of dense quark matter
• Dynamical stabilization of runaway potentials at finite density
• Bound States and Superconductivity in Dense Fermi Systems
• Higgs Mechanism with Type-II Nambu-Goldstone Bosons at Finite Chemical Potential
• Axial anomaly effect to the chiral-partner structure of diquarks at high temperature
• Magnetic Stability Analysis for Abelian and Non-Abelian Superconductors
• Affinity of NJL${}_2$ and NJL${}_4$ model results on duality and pion condensation in chiral asymmetric dense quark matter
• Stability and Absence of a Tower of States in Ferrimagnets
• On the Ground State of Two Flavor Color Superconductor
• How does color neutrality affect collective modes in color superconductors?
• Dynamical stabilization of runaway potentials and landscape of vacua at finite density
• Pairing fluctuation effects in a strongly coupled color superfluid/superconductor
• Dynamical Chiral Symmetry Breaking, Color Superconductivity, and Bose-Einstein Condensation in an $SU(N_c)\times U(N_f{)}_L\times U(N_f{)}_R$-invariant Supersymmetric Nambu$-$Jona-Lasinio Model
• Spontaneous symmetry breaking in strong and electroweak interactions
• Mesons and diquarks in a color superconducting regime