When the transition temperature in color superconductors is not like in BCS theory

Schmitt, Andreas; Wang, Qun; Rischke, Dirk H.

doi:10.1103/physrevd.66.114010

Cited by 91 publications

(153 citation statements)

References 31 publications

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“…Such self-consistency equations predict a second-order phase transition from the CFL phase to unpaired quark matter at T c = 18.15 MeV. This value of T c is larger than the BCS value of ≃ 0.57∆ due to the two-gap structure of the quark excitations (−∆ and 2∆ for octet and singlet quarks, respectively) [28]. We note, however, that in a situation in which CFL quark matter behaves as a type-I color superconductor, thermal fluctuations in the gauge fields could play a role in changing the phase transition from second to first order and in lowering the transition temperature [14].…”

Section: A Self-consistency Equationsmentioning

confidence: 95%

Collective excitations in a superfluid of color-flavor locked quark matter

Fukushima

Iida

2005

Phys. Rev. D

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We investigate collective excitations coupled with baryon density in a system of massless threeflavor quarks in the collisionless regime. By using the Nambu-Jona-Lasinio (NJL) model in the mean-field approximation, we field-theoretically derive the spectra both for the normal and colorflavor locked (CFL) superfluid phases at zero temperature. In the normal phase, we obtain usual zero sound as a low-lying collective mode in the particle-hole (vector) channel. In the CFL phase, the nature of collective excitations varies in a way dependent on whether the excitation energy, ω, is larger or smaller than the threshold given by twice the pairing gap ∆, at which pair excitations with nonzero total momentum become allowed to break up into two quasiparticles. For ω ≪ 2∆, a phonon corresponding to fluctuations in the U (1) phase of ∆ appears as a sharp peak in the particle-particle ("H") channel. We reproduce the property known from low energy effective theories that this mode propagates at a velocity of vH = 1/ √ 3 in the low momentum regime; the decay constant fH obtained in the NJL model is identical with the QCD result obtained in the mean-field approximation. We also find that as the momentum of the phonon increases, the excitation energy goes up and asymptotically approaches ω = 2∆. Above the threshold for pair excitations (ω > 2∆), zero sound manifests itself in the vector channel. By locating the zero sound pole of the vector propagator in the complex energy plane we investigate the attenuation and energy dispersion relation of zero sound. In the long wavelength limit, the phonon mode, the only low-lying excitation, has its spectral weight in the H channel alone, while the spectral function vanishes in the vector channel. This is due to nontrivial mixing between the H and vector channels in the superfluid medium. We finally extend our study to the case of nonzero temperature. We demonstrate how Landau damping smears the phonon peak in the finite temperature spectral function. We find a pure imaginary pole of the H propagator in the complex energy plane, which can be identified as a diffusive mode responsible for the Landau damping. From the pole position we derive the thermal diffusion constant.

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Section: A Self-consistency Equationsmentioning

confidence: 95%

Collective excitations in a superfluid of color-flavor locked quark matter

Fukushima

Iida

2005

Phys. Rev. D

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“…We insert the form of the volume oscillation (38) and Eqs. (43) into these differential equations and find the solution Im δµ q = δV 0 V 0 ω λ( ∂nq ∂µq n − ∂n ∂µq n q ) (detJ) 2 ω 2 + ( ∂nq ∂µq λ) 2 ∂n q ∂µ ,…”

Section: Appendix B: Bulk Viscosity With Quark Number Effectsmentioning

confidence: 99%

“…It is currently not known whether, going down in density, the CFL phase is superseded by nuclear matter or by a different, more exotic, color-superconducting phase. Candidate colorsuperconducting phases have Cooper pairs with nonzero angular momentum [36,37,38,39] or nonzero momentum [40,41,42]. In this paper, we shall only consider the CFL and CFL-K 0 phases.…”

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confidence: 99%

Bulk viscosity in kaon-condensed color–flavor-locked quark matter

Alford¹,

Braby²,

Schmitt³

2008

J. Phys. G: Nucl. Part. Phys.

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Color-flavor locked (CFL) quark matter at high densities is a color superconductor, which spontaneously breaks baryon number and chiral symmetry. Its low-energy thermodynamic and transport properties are therefore dominated by the H (superfluid) boson, and the octet of pseudoscalar pseudo-Goldstone bosons of which the neutral kaon is the lightest. We study the CFL-K 0 phase, in which the stress induced by the strange quark mass causes the kaons to condense, and there is an additional ultra-light "K 0 " Goldstone boson arising from the spontaneous breaking of isospin. We compute the bulk viscosity of matter in the CFL-K 0 phase, which arises from the beta-equilibration processes K 0 ↔ H + H and K 0 + H ↔ H. We find that the bulk viscosity varies as T 7 , unlike the CFL phase where it is exponentially Boltzmann-suppressed by the kaon's energy gap. However, in the temperature range of relevance for r-mode damping in compact stars, the bulk viscosity in the CFL-K 0 phase turns out to be even smaller than in the uncondensed CFL phase, which already has a bulk viscosity much smaller than all other known color-superconducting quark phases.

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“…Additionally, within the "HHJ-SM with 2SC" phase we will allow for the possibility of a weak pairing channel for all the quarks which were unpaired, with typical gaps ∆ X ∼ 10 keV ÷1 MeV, as in the case of the CSL pairing channel, see [41,42]. Since we don't know yet the exact pairing pattern for this case, we call this hypothetical phase "2SC+X".…”

Section: Structure Of Hybrid Neutron Starsmentioning

confidence: 99%

Cooling Evolution of Hybrid Stars

Grigorian¹

2005

AIP Conference Proceedings

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Abstract. The cooling of compact isolated objects for different values of the gravitational mass has been simulated for two alternative assumptions. One is that the interior of the star is purely hadronic [1] and second that the star can have a rather large quark core [2]. It has been shown that within a nonlocal chiral quark model the critical density for a phase transition to color superconducting quark matter under neutron star conditions can be low enough for these phases to occur in compact star configurations with masses below 1.3 M ⊙ . For a realistic choice of parameters the equation of state (EoS) allows for 2SC quark matter with a large quark gap ∼ 100 MeV for u and d quarks of two colors that coexists with normal quark matter within a mixed phase in the hybrid star interior. We argue that, if in the hadronic phase the neutron pairing gap in 3P 2 channel is larger than few keV and the phases with unpaired quarks are allowed, the corresponding hybrid stars would cool too fast.Even in the case of the essentially suppressed 3P 2 neutron gap if free quarks occur for M < 1.3 M ⊙ , as it follows from our EoS, one could not appropriately describe the neutron star cooling data existing by today.It is suggested to discuss a "2SC+X" phase, as a possibility to have all quarks paired in two-flavor quark matter under neutron star constraints, where the X-gap is of the order of 10 keV -1 MeV. Density independent gaps do not allow to fit the cooling data. Only the presence of an X-gap that decreases with increase of the density could allow to appropriately fit the data in a similar compact star mass interval to that following from a purely hadronic model.

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When the transition temperature in color superconductors is not like in BCS theory

Cited by 91 publications

References 31 publications

Collective excitations in a superfluid of color-flavor locked quark matter

Collective excitations in a superfluid of color-flavor locked quark matter

Bulk viscosity in kaon-condensed color–flavor-locked quark matter

Cooling Evolution of Hybrid Stars

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