Precursor of color superconductivity in hot quark matter

Abstract

We investigate the possible precursory phenomena of color superconductivity in quark matter at finite temperature T with use of a low-energy effective theory of QCD. It is found that the fluctuating pair field exists with a prominent strength even well above the critical temperature T c . We show that the collective pair field has a complex energy located in the second Riemann sheet, which approaches the origin as T is lowered to T c . We discuss the possible relevance of the precursor to the observables to be detected in heavy ion collisions.It is an intriguing subject to explore how the QCD vacuum changes in hot and dense hadronic matter ͓1,2͔. The recent lattice QCD simulations ͓3͔ show that the QCD vacuum undergoes a phase transition to a chirally restored and deconfined phase at low temperature ͑T͒ as T ϳ170 MeV. Although it is still a great challenge to perform a Monte Carlo simulation with a finite chemical potential on lattice QCD with an SU͑3͒ color group, we believe that a chirally restored and deconfined system is realized in dense hadronic matter with large .It is to be noticed that a system with a finite at low T can have a Fermi surface and the system may be described as a Fermi liquid composed of quarks. In accordance with the validity of the diquark-quark picture of baryons ͓4͔, the quark-quark interaction is attractive in some specific channels. Then the existence of the Fermi surface gives rise to a Cooper instability with respect to the formation of the diquark or Cooper pair in the most attractive channel, and the system is rearranged to a superconducting phase where the color-gauge symmetry is dynamically broken ͓5͔. Such color superconductivity ͑CSC͒ has recently acquired renewed interest, because the resulting gap ⌬ was shown to be as large as 100 MeV ͓6,7͔. Furthermore, the color and flavor degrees of freedom of quarks give a fantastically rich structure in dense quark matter with CSC ͓8͔: Such quark matter may be realized in the deep interior of neutron stars ͑NS͒, and characteristic phenomena observed for NS such as the glitch phenomena might be attributed to the existence of the CSC in the NS.Can CSC be relevant to experiments in the laboratory on Earth? The experiment using the available facilities, such as the BNL Relativistic Heavy Ion Collider ͑RHIC͒ using high energy heavy ion collisions seems unfortunately unfit for the problem, because the matter produced by RHIC is almost baryon-free with much higher temperatures than the critical temperature T c ϳ50-60 MeV of CSC. The purpose of the present paper is to explore possible precursory phenomena of CSC at TϾT c , i.e., in the Wigner phase and show that the fluctuation of the pair field is significant at T well above T c , which thereby might affect observables to be detected by the heavy ion collisions with large baryon stopping ͓9͔.Since we are interested in relatively the low T and region, we adopt a low-energy effective theory of QCD as was done in ͓6,10͔ where an instanton-induced interaction is employed. We remark here that a si...

BCS/BEC crossover in quark matter and evolution of its static and dynamic properties from the atomic unitary gas to color superconductivity

“…In the nonrelativistic superconductor, it is known that the fluctuating pair fields affect the electric conductivity above T c [88,89,90]. In the context of two-flavor color superconductivity, it is noted in [45] that these soft modes may affect not only transport coefficients but also the dilepton spectrum.…”

“…As the system goes towards lower density, the gauge coupling grows and some strong coupling effects beyond the mean field approximation (MFA) come to play an important role as pointed out earlier by evaluating the Cooper pair correlation length within the MFA [43,44]. Some theoretical efforts to examine the strong coupling effects beyond the MFA were then made with a particular focus on the precursory soft mode [45,46,47], where non-vanishing diquark correlation and the pseudogap above the critical temperature are reported. Along with this line, the limit temperature T * where the resonances decouple from the spectrum is evaluated both for the chiral and diquark channels in [17].…”

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

“…For simplicity we ignore the H-vector mixing and the antiparticle contribution in locating the complex pole position. This kind of pole search has been performed in the context of chiral restoration in a hot and dense medium [31] and of a phase transition from the normal to the 2SC phase [2]. Appendix B is devoted to exhibiting how to perform the analytic continuation into the second Riemann sheet where the attenuated mode would be found.…”

“…In possible physical realizations in heavy ion collisions and neutron stars, color superconducting quark matter might leave evidences for color superconductivity via precursory phenomena above the critical temperature [2], neutrino emission from proto-neutron stars [3], and neutron star cooling [4,5], etc. To obtain such possible evidences, it is indispensable to clarify the equilibrium properties of color superconductors such as the equation of state and elementary excitations.…”

Pions in the quark matter phase diagram

“…It has been pointed out [10] that this situation in hot and dense QCD matter bears similarities with strongly coupled plasmas in other systems where bound state dissociation or Mott-Anderson delocalization [11] occurs since the effective coupling strength is modified by electronic screening and/or Pauli blocking effects. It is thus a very general effect expected to occur in a wide variety of dense Fermi systems with attractive interactions [12,13,14,15,16,17,18,19,20,21]. When this Mott transition from truly bound to resonantly paired states occurs under conditions of Bose condensation one speaks of a BEC-BCS crossover [22,23,24].…”