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Title: Stress-free BCS pairing in color superconductors is impossible

Abstract

Cold, asymptotically dense three-flavor quark matter is in the color-flavor locked (CFL) phase, in which all quarks pair in a particularly symmetric fashion. At smaller densities, taking into account a nonzero strange quark mass and electric and color neutrality, the CFL phase requires pairing of quarks with mismatched Fermi momenta. We present a classification of all other possible, less symmetric, pairing patterns and prove that none of them can avoid this mismatch. This result suggests unconventional, e.g., spatially inhomogeneous, superconducting phases for moderate densities.

Authors:
 [1];  [2]
  1. Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States)
  2. Department of Physics, Washington University St Louis, MO 63130 (United States)
Publication Date:
OSTI Identifier:
21056893
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 892; Journal Issue: 1; Conference: QCHS7: 7. conference on quark confinement and the hadron spectrum, Ponta Delgada, Acores (Portugal), 2-7 Sep 2006; Other Information: DOI: 10.1063/1.2714453; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BCS THEORY; COLOR MODEL; FLAVOR MODEL; PAIRING INTERACTIONS; QUANTUM CHROMODYNAMICS; QUARK MATTER; REST MASS; S QUARKS; STRESSES; SUPERCONDUCTIVITY; SUPERCONDUCTORS

Citation Formats

Rajagopal, Krishna, and Schmitt, Andreas. Stress-free BCS pairing in color superconductors is impossible. United States: N. p., 2007. Web. doi:10.1063/1.2714453.
Rajagopal, Krishna, & Schmitt, Andreas. Stress-free BCS pairing in color superconductors is impossible. United States. doi:10.1063/1.2714453.
Rajagopal, Krishna, and Schmitt, Andreas. Tue . "Stress-free BCS pairing in color superconductors is impossible". United States. doi:10.1063/1.2714453.
@article{osti_21056893,
title = {Stress-free BCS pairing in color superconductors is impossible},
author = {Rajagopal, Krishna and Schmitt, Andreas},
abstractNote = {Cold, asymptotically dense three-flavor quark matter is in the color-flavor locked (CFL) phase, in which all quarks pair in a particularly symmetric fashion. At smaller densities, taking into account a nonzero strange quark mass and electric and color neutrality, the CFL phase requires pairing of quarks with mismatched Fermi momenta. We present a classification of all other possible, less symmetric, pairing patterns and prove that none of them can avoid this mismatch. This result suggests unconventional, e.g., spatially inhomogeneous, superconducting phases for moderate densities.},
doi = {10.1063/1.2714453},
journal = {AIP Conference Proceedings},
number = 1,
volume = 892,
place = {United States},
year = {Tue Feb 27 00:00:00 EST 2007},
month = {Tue Feb 27 00:00:00 EST 2007}
}
  • We examine the role that the gap dependence of the pairing interaction plays in the gap equation for a weakly coupled uniform superfluid of three-flavor massless quarks near the transition temperature T{sub c}. We find that the feedback effects on Landau-damped transverse gluons mediating the pairing interaction alter the gap magnitude in a way dependent on the color structure of the gap. We estimate corrections by these effects to the parameters characterizing the fourth order terms in the Ginzburg-Landau free energy and ensure the stability of a color-flavor locked state near T{sub c}.
  • At sufficiently high densities, cold dense three-flavor quark matter is in the color-flavor locked (CFL) phase, in which all nine quarks pair in a particularly symmetric fashion. Once the heaviness of the strange quark (mass m{sub s}) and the requirements of electric and color neutrality are taken into account, the CFL pattern of color superconductivity requires the pairing of quarks that would, in the absence of pairing, have Fermi momenta that differ by of order m{sub s}{sup 2}/{mu}, with {mu} the quark number chemical potential. This means that at sufficiently small {mu}, the 'stress' on the pairing is large enoughmore » that the system can lower its energy by breaking pairs, resulting in some unconventional color superconductor which includes gapless excitations, spatial inhomogeneity, counter-propagating currents, or all three. In this paper we ask whether there is some less symmetric but still conventional pattern of pairing that can evade the stress. In other words, is there a pattern of pairing in which, once electric and color neutrality are imposed by suitable chemical potentials, pairing only occurs among those quarks whose Fermi momenta would be equal in the absence of pairing? We use graph-theoretical methods to classify 511 patterns of conventional color-superconducting pairing, and show that none of them meet this requirement. All feel a stress, and all can be expected to become unstable to gapless modes at a density comparable to that at which the CFL phase becomes unstable.« less
  • A theoretical study of BCS pairing in an extended Hubbard model with on-site repulsion ([ital U]) and a BCS pairing field ([ital V]) is presented. Treating the effect of [ital U] in the Gutzwiller approximation, we study the effect of increasing [ital U] in the Fermi-liquid phase, on the BCS pairing due to [ital V]. It is found that the superconducting energy gap ([Delta]) is strongly enhanced in the correlated metallic phase near half-filling of the band due to the localization effects of [ital U]. Further, the ground state is found to be superconducting even when [vert bar][ital V][vert bar][lt][italmore » U], contrary to the prediction in a Hartree-Fock treatment.« less
  • We investigate the BCS treatment of neutron-proton pairing involving time-reversed orbits. We conclude that an isospin-symmetric Hamiltonian, treated with the help of the generalized Bogolyubov transformation, fails to describe the ground state pairing properties correctly. In order for the np isovector pairs to coexist with the like-particle pairs, one has to break the isospin symmetry of the Hamiltonian by artificially increasing the strength of the np pairing interaction above its isospin-symmetric value. We briefly discuss the prescription how to choose the coupling constant of this auxiliary isospin-breaking pairing force. {copyright} {ital 1997} {ital The American Physical Society}