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Title: Mesons and diquarks in neutral color superconducting quark matter with {beta} equilibrium

Abstract

The spectrum of meson and diquark excitations in cold color superconducting (2SC) quark matter is investigated under local color and electric neutrality constraints with {beta} equilibrium. A two-flavored Nambu-Jona-Lasinio-type model including baryon {mu}{sub B}, color {mu}{sub 8}, and electric {mu}{sub Q} chemical potentials is used. The contribution from free electrons to the free energy is added to take into account the {beta} equilibrium. The sensitivity of the model to the tuning of the interaction constants in the diquark (H) and quark-antiquark (G) channels is examined for two different parametrization schemes by choosing the ratio H/G to be 3/4 and 1, respectively. The gapless neutral color superconductivity is realized at H=3G/4, and the gapped neutral color superconductivity at H=G. It is shown that color and electrical neutrality together with {beta} equilibrium lead to a strong mass splitting within the pion isotriplet in the 2SC phase (both gapped and gapless), in contrast with non-neutral matter. The {pi}- and {sigma}-meson masses are evaluated to be {approx}300 MeV. It is also shown that the properties of the physical SU(2){sub c}-singlet diquark excitation in the 2SC ground state vary for different parametrization schemes. Thus, for H=3G/4 one finds a heavy resonance with mass {approx}1100 MeVmore » in the non-neutral (gapped) case, whereas, if neutrality is imposed, a stable diquark with mass {approx}|{mu}{sub Q}|{approx}200 MeV appears in the gapless 2SC environment. For a stronger attraction in the diquark channel (H=G), there is again a resonance (with the mass {approx}300 MeV) in the neutral gapped 2SC phase. Hence, the existence of the stable massive SU(2){sub c}-singlet diquark excitation is a new peculiarity of the gapless 2SC. In addition, the behavior of the diquark mass in vacuum, i.e., at {mu}{sub B}=0, as a function of H has been investigated.« less

Authors:
 [1];  [2];  [3]
  1. Institut fuer Physik, Humboldt-Universitaet zu Berlin, 10115 Berlin (Germany)
  2. Institute of High Energy Physics, 142281, Protvino, Moscow Region (Russian Federation)
  3. Joint Institute for Nuclear Research, 141980, Dubna, Moscow Region (Russian Federation)
Publication Date:
OSTI Identifier:
21010937
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevD.75.025024; (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; BARYONS; COLOR MODEL; ELECTRONS; EXCITATION; FREE ENERGY; GROUND STATES; MEV RANGE; PIONS; POTENTIALS; QUARK MATTER; QUARK-ANTIQUARK INTERACTIONS; REST MASS; SU-2 GROUPS; SUPERCONDUCTIVITY

Citation Formats

Ebert, D., Klimenko, K. G., and Yudichev, V. L.. Mesons and diquarks in neutral color superconducting quark matter with {beta} equilibrium. United States: N. p., 2007. Web. doi:10.1103/PHYSREVD.75.025024.
Ebert, D., Klimenko, K. G., & Yudichev, V. L.. Mesons and diquarks in neutral color superconducting quark matter with {beta} equilibrium. United States. doi:10.1103/PHYSREVD.75.025024.
Ebert, D., Klimenko, K. G., and Yudichev, V. L.. Mon . "Mesons and diquarks in neutral color superconducting quark matter with {beta} equilibrium". United States. doi:10.1103/PHYSREVD.75.025024.
@article{osti_21010937,
title = {Mesons and diquarks in neutral color superconducting quark matter with {beta} equilibrium},
author = {Ebert, D. and Klimenko, K. G. and Yudichev, V. L.},
abstractNote = {The spectrum of meson and diquark excitations in cold color superconducting (2SC) quark matter is investigated under local color and electric neutrality constraints with {beta} equilibrium. A two-flavored Nambu-Jona-Lasinio-type model including baryon {mu}{sub B}, color {mu}{sub 8}, and electric {mu}{sub Q} chemical potentials is used. The contribution from free electrons to the free energy is added to take into account the {beta} equilibrium. The sensitivity of the model to the tuning of the interaction constants in the diquark (H) and quark-antiquark (G) channels is examined for two different parametrization schemes by choosing the ratio H/G to be 3/4 and 1, respectively. The gapless neutral color superconductivity is realized at H=3G/4, and the gapped neutral color superconductivity at H=G. It is shown that color and electrical neutrality together with {beta} equilibrium lead to a strong mass splitting within the pion isotriplet in the 2SC phase (both gapped and gapless), in contrast with non-neutral matter. The {pi}- and {sigma}-meson masses are evaluated to be {approx}300 MeV. It is also shown that the properties of the physical SU(2){sub c}-singlet diquark excitation in the 2SC ground state vary for different parametrization schemes. Thus, for H=3G/4 one finds a heavy resonance with mass {approx}1100 MeV in the non-neutral (gapped) case, whereas, if neutrality is imposed, a stable diquark with mass {approx}|{mu}{sub Q}|{approx}200 MeV appears in the gapless 2SC environment. For a stronger attraction in the diquark channel (H=G), there is again a resonance (with the mass {approx}300 MeV) in the neutral gapped 2SC phase. Hence, the existence of the stable massive SU(2){sub c}-singlet diquark excitation is a new peculiarity of the gapless 2SC. In addition, the behavior of the diquark mass in vacuum, i.e., at {mu}{sub B}=0, as a function of H has been investigated.},
doi = {10.1103/PHYSREVD.75.025024},
journal = {Physical Review. D, Particles Fields},
number = 2,
volume = 75,
place = {United States},
year = {Mon Jan 15 00:00:00 EST 2007},
month = {Mon Jan 15 00:00:00 EST 2007}
}
  • The spectrum of meson and diquark excitations of dense color neutral cold quark matter is investigated in the framework of a two-flavored Nambu-Jona-Lasinio-type model, including a quark {mu}- and color {mu}{sub 8}-chemical potential. It was found that, in the color superconducting (2SC) phase, i.e. at {mu}>{mu}{sub c}=342 MeV, {mu}{sub 8} acquires rather small values {approx}10 MeV in order to ensure the color neutrality. In this phase the {pi} and {sigma} meson masses are evaluated around {approx}330 MeV. The spectrum of scalar diquarks in the color neutral 2SC phase consists of a heavy [SU{sub c}(2)-singlet] resonance with mass {approx}1100 MeV, fourmore » light diquarks with mass 3|{mu}{sub 8}|, and one Nambu-Goldstone boson, which is in accordance with the Goldstone theorem. Moreover, in the 2SC phase there are five light stable particles as well as a heavy resonance in the spectrum of pseudoscalar diquarks. In the color symmetric phase, i.e. for {mu}<{mu}{sub c}, a mass splitting of scalar diquarks and antidiquarks is shown to arise if {mu}{ne}0, contrary to the case of {mu}=0, where the masses of scalar antidiquarks and diquarks are degenerate at the value {approx}700 MeV. If the coupling strength in the pseudoscalar diquark channel is the same as in the scalar diquark one (as for QCD-inspired Nambu-Jona-Lasinio models), then in the color symmetric phase pseudoscalar diquarks are not allowed to exist as stable particles.« less
  • The spectrum of meson and diquark excitations of dense cold quark matter is investigated within the framework of a Nambu-Jona-Lasinio-type model for light quarks of two flavors. It was found that a first-order phase transition occurs when the chemical potential {mu} exceeds the critical value {mu}{sub c}=350 MeV. Above {mu}{sub c}, the diquark condensate <qq> forms, breaking the color symmetry of strong interaction. The masses of {pi} and {sigma} mesons are shown to grow with the chemical potential {mu} in the color-superconducting phase, but the mesons themselves become almost stable particles. Moreover, we have found in this phase an abnormalmore » number of three, instead of five, Nambu-Goldstone bosons, together with a color doublet of light stable diquark modes and a color-singlet heavy diquark resonance with mass {approx}1100 MeV. In the color-symmetric phase, i.e., for {mu}<{mu}{sub c}, a mass splitting of diquarks and antidiquarks is shown to arise if {mu}{ne}0, contrary to the case of a vanishing chemical potential, in which the masses of antidiquarks and diquarks are degenerate at the value {approx}700 MeV.« less
  • Diquark excitations of dense quark matter are considered in the framework of the Nambu-Jona-Lasinio model with three types of massless quarks in the presence of a quark number chemical potential {mu}. We investigate the effective action of meson and diquark fields at sufficiently high values of {mu}, where the color-flavor locked (CFL) phase is realized, and prove the existence of NG bosons in the sector of pseudoscalar diquarks. In the sector of scalar diquarks an additional NG boson is found, corresponding to the spontaneous breaking of the U(1){sub B} baryon symmetry in the CFL phase. Finally, the existence of massivemore » scalar and pseudoscalar diquark excitations is demonstrated.« less
  • An important first step in the program of hadronization of chiral quark models is the bosonization in meson and diquark channels. This procedure is presented at finite temperatures and chemical potentials for the SU(2) flavor case of the NJL model with special emphasis on the mixing between scalar meson and scalar diquark modes which occurs in the 2SC color superconducting phase. The thermodynamic potential is obtained in the Gaussian approximation for the meson and diquark fields and it is given in the Beth–Uhlenbeck form. This allows a detailed discussion of bound state dissociation in hot, dense matter (Mott effect) inmore » terms of the in-medium scattering phase shift of two-particle correlations. It is shown for the case without meson–diquark mixing that the phase shift can be separated into a continuum and a resonance part. In the latter, the Mott transition manifests itself by a change of the phase shift at threshold by π in accordance with Levinson’s theorem, when a bound state transforms to a resonance in the scattering continuum. The consequences for the contribution of pionic correlations to the pressure are discussed by evaluating the Beth–Uhlenbeck equation of state in different approximations. A similar discussion is performed for the scalar diquark channel in the normal phase. Further developments and applications of the developed approach are outlined.« less
  • The color neutral two-flavor superconducting phase of cold and dense quark matter is studied in the presence of constant magnetic fields and at moderate baryon densities. In the first part of the paper, a two-flavor effective Nambu-Jona-Lasinio model consisting of a chiral symmetry breaking ({chi}SB) mass gap {sigma}{sub B}, a color superconducting (CSC) mass gap {Delta}{sub B} and a color chemical potential {mu}{sub 8} is introduced in the presence of a rotated U(1) magnetic field B-tilde. To study the phenomenon of magnetic catalysis in the presence of strong magnetic fields, the gap equations corresponding to {sigma}{sub B} and {Delta}{sub B},more » as well as {mu}{sub 8} are solved in the lowest Landau level approximation. In the second part of the paper, a detailed numerical analysis is performed to explore the effect of any arbitrary magnetic field on the above mass gaps and the color chemical potential. The structure of the {chi}SB and CSC phases is also presented in the {mu}{sub c}-e-tildeB plane, and the effect of {mu}{sub 8} on the phase structure of the model is explored. As it turns out, whereas the transition from the {chi}SB to CSC phase is of first order, nonvanishing {mu}{sub 8} affects essentially the second order phase transition from CSC to the normal phase.« less