skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Ground state of gapless two flavor color superconductors

Abstract

This paper is devoted to the study of some aspects of the instability of two flavor color-superconductive quark matter. We find that, beside color condensates, the Goldstone boson related to the breaking of U(1){sub A} suffers from a velocity instability. We relate this wrong sign problem, which implies the existence of a Goldstone current in the ground state or of gluonic condensation, to the negative squared Meissner mass of the 8th gluon in the gapless two flavor color superconductor (g2SC) phase. Moreover we investigate the Meissner masses of the gluons and the squared velocity of the Goldstone in the multiple-plane-wave Larkin-Ovchinnikov-Fulde-Ferrel (LOFF) states, arguing that in such phases both the chromomagnetic instability and the velocity instability are most probably removed. We also do not expect Higgs instability in such multiple-plane-wave LOFF, at least when one considers fluctuations with small momenta. The true vacuum of gapless two flavor superconductors is thus expected to be a multiple-plane-wave LOFF state.

Authors:
;  [1];  [2]
  1. Depart. de Physique Theorique, Universite de Geneve, CH-1211 Geneva 4 (Switzerland)
  2. (Italy)
Publication Date:
OSTI Identifier:
20929543
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 11; Other Information: DOI: 10.1103/PhysRevD.75.114004; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; COLOR MODEL; FLAVOR MODEL; GLUONS; GOLDSTONE BOSONS; GROUND STATES; HIGGS MODEL; INSTABILITY; MASS; QUARK MATTER; SUPERCONDUCTORS; U-1 GROUPS; WAVE PROPAGATION

Citation Formats

Gatto, R., Ruggieri, M., and Dipartimento di Fisica, Universita di Bari, I-70126 Bari, Italy and INFN, Sezione di Bari, I-70126 Bari. Ground state of gapless two flavor color superconductors. United States: N. p., 2007. Web. doi:10.1103/PHYSREVD.75.114004.
Gatto, R., Ruggieri, M., & Dipartimento di Fisica, Universita di Bari, I-70126 Bari, Italy and INFN, Sezione di Bari, I-70126 Bari. Ground state of gapless two flavor color superconductors. United States. doi:10.1103/PHYSREVD.75.114004.
Gatto, R., Ruggieri, M., and Dipartimento di Fisica, Universita di Bari, I-70126 Bari, Italy and INFN, Sezione di Bari, I-70126 Bari. Fri . "Ground state of gapless two flavor color superconductors". United States. doi:10.1103/PHYSREVD.75.114004.
@article{osti_20929543,
title = {Ground state of gapless two flavor color superconductors},
author = {Gatto, R. and Ruggieri, M. and Dipartimento di Fisica, Universita di Bari, I-70126 Bari, Italy and INFN, Sezione di Bari, I-70126 Bari},
abstractNote = {This paper is devoted to the study of some aspects of the instability of two flavor color-superconductive quark matter. We find that, beside color condensates, the Goldstone boson related to the breaking of U(1){sub A} suffers from a velocity instability. We relate this wrong sign problem, which implies the existence of a Goldstone current in the ground state or of gluonic condensation, to the negative squared Meissner mass of the 8th gluon in the gapless two flavor color superconductor (g2SC) phase. Moreover we investigate the Meissner masses of the gluons and the squared velocity of the Goldstone in the multiple-plane-wave Larkin-Ovchinnikov-Fulde-Ferrel (LOFF) states, arguing that in such phases both the chromomagnetic instability and the velocity instability are most probably removed. We also do not expect Higgs instability in such multiple-plane-wave LOFF, at least when one considers fluctuations with small momenta. The true vacuum of gapless two flavor superconductors is thus expected to be a multiple-plane-wave LOFF state.},
doi = {10.1103/PHYSREVD.75.114004},
journal = {Physical Review. D, Particles Fields},
number = 11,
volume = 75,
place = {United States},
year = {Fri Jun 01 00:00:00 EDT 2007},
month = {Fri Jun 01 00:00:00 EDT 2007}
}
  • We explore the phase diagram of neutral quark matter at high baryon density as a function of the temperature T and the strange quark mass M{sub s}. At T=0, there is a sharp distinction between the insulating color-flavor locked (CFL) phase, which occurs where M{sub s}{sup 2}/{mu}<2{delta}, and the metallic gapless CFL phase, which occurs at larger M{sub s}{sup 2}/{mu}. Here, {mu} is the chemical potential for quark number and {delta} is the gap in the CFL phase. We find this distinction blurred at T{ne}0, as the CFL phase undergoes an insulator to metal crossover when it is heated. Wemore » present an analytic treatment of this crossover. At higher temperatures, we map out the phase transition lines at which the gap parameters {delta}{sub 1}, {delta}{sub 2}, and {delta}{sub 3} describing ds pairing, us pairing and ud pairing, respectively, go to zero in an Nambu-Jona-Lasinio (NJL) model. For small values of M{sub s}{sup 2}/{mu}, we find that {delta}{sub 2} vanishes first, then {delta}{sub 1}, then {delta}{sub 3}. We find agreement with a previous Ginzburg-Landau analysis of the form of these transitions and find quantitative agreement with results obtained in full QCD at asymptotic density for ratios of coefficients in the Ginzburg-Landau potential. At larger M{sub s}{sup 2}/{mu}, we find that {delta}{sub 1} vanishes first, then {delta}{sub 2}, then {delta}{sub 3}. Hence, we find a ''doubly critical'' point in the (M{sub s}{sup 2}/{mu},T) plane at which two lines of second order phase transitions ({delta}{sub 1}{yields}0 and {delta}{sub 2}{yields}0) cross. Because we do not make any small-M{sub s} approximation, if we choose a relatively strong coupling leading to large gap parameters, we are able to pursue the analysis of the phase diagram all the way up to such large values of M{sub s} that there are no strange quarks present.« less
  • In neutral cold quark matter that is sufficiently dense that the strange quark mass M{sub s} is unimportant, all nine quarks (three colors; three flavors) pair in a color-flavor locked (CFL) pattern, and all fermionic quasiparticles have a gap. We recently argued that the next phase down in density (as a function of decreasing quark chemical potential {mu} or increasing strange quark mass M{sub s}) is the new 'gapless CFL' (gCFL) phase in which only seven quasiparticles have a gap, while there are gapless quasiparticles described by two dispersion relations at three momenta. There is a continuous quantum phase transitionmore » from CFL to gCFL quark matter at M{sub s}{sup 2}/{mu}{approx_equal}2{delta}, with {delta} the gap parameter. Gapless CFL, like CFL, leaves unbroken a linear combination Q-tilde of electric and color charges, but it is a Q-tilde conductor with gapless Q-tilde-charged quasiparticles and a nonzero electron density. In this paper, we evaluate the gapless CFL phase, in several senses. We present the details underlying our earlier work which showed how this phase arises. We display all nine quasiparticle dispersion relations in full detail. Using a general pairing ansatz that only neglects effects that are known to be small, we perform a comparison of the free energies of the gCFL, CFL, two-flavor (2SC), gapless 2SC, and two-flavor up-strange phases. We conclude that as density drops, making the CFL phase less favored, the gCFL phase is the next spatially uniform quark matter phase to occur. A mixed phase made of colored components would have lower free energy if color were a global symmetry, but in QCD such a mixed phase is penalized severely.« less
  • The gapless color-flavor locked (gCFL) phase is a candidate for the second-densest phase of matter in the QCD phase diagram, making it a plausible constituent of the core of neutron stars. We show that even a relatively small region of gCFL matter in a star will dominate both the heat capacity C{sub V} and the heat loss by neutrino emission L{sub {nu}}. The gCFL phase is characterized by an unusual quasiparticle dispersion relation that makes both its specific heat c{sub V} and its neutrino emissivity {epsilon}{sub {nu}} parametrically larger than in any other phase of nuclear or quark matter. Duringmore » the epoch in which the cooling of the star is dominated by direct Urca neutrino emission, the presence of a gCFL region does not strongly alter the cooling history because the enhancements of C{sub V} and L{sub {nu}} cancel against each other. At late times, however, the cooling is dominated by photon emission from the surface, so L{sub {nu}} is irrelevant, and the anomalously large heat capacity of the gCFL region keeps the star warm. The temperature drops with time as T{approx}t{sup -1.4} rather than the canonical T{approx}t{sup -5}. This provides a unique and potentially observable signature of gCFL quark matter.« less
  • Electric and color neutral solutions, and the critical conditions for the formation of gapless color superconductors, are investigated in K{sup 0} condensed color-flavor locked quark matter for nonzero strange quark mass. We show that as the strange quark mass increases, gapless modes for up-strange quark pairing occur first, followed by down-strange quark pairing. The behavior of the gaps, the dispersion relations, and the thermodynamic potential are all found as functions of the strange quark mass on the basis of a Nambu-Jona-Lasinio type model. To a high degree of accuracy, they are presented as relatively simple elementary functions. This allows formore » easy computation for any reasonable range of baryon chemical potential and strange quark mass.« less
  • We investigate spin-one color superconductivity of a single quark flavor using the Ginzburg-Landau theory. First we examine the classic analysis of Bailin and Love and show that by restricting to the so-called inert states, it misses the true ground state in a part of the phase diagram. This suggests the use of the more general, noninert states, in particular, within three-flavor quark matter where the color neutrality constraint imposes stress on the spin-one pairing and may disfavor the symmetric color-spin-locked state. In the second part of the paper we show that, in analogy to some ferromagnetic materials, lack of space-inversionmore » symmetry leads to a new term in the Ginzburg-Landau functional, which favors a spatially nonuniform long-range ordering with a spiral structure. In color superconductors, this new parity-violating term is a tiny effect of weak-interaction physics. The modified phase diagram is determined and the corresponding ground states for all the phases constructed. At the end, we estimate the coefficient of the new term in the free energy functional, and discuss its relevance for the phenomenology of dense quark matter.« less