Color superconductivity and chiral symmetry restoration at non-zero baryon density and temperature

Abstract

We explore the phase diagram of strongly interacting matter as a function of temperature and baryon number density, using a class of models for two-flavor QCD in which the interaction between quarks is modelled by that induced by instantons. Our treatment allows us to investigate the possible simultaneous formation of condensates in the conventional quark-anti-quark channel (breaking chiral symmetry) and in a quark-quark channel leading to color superconductivity: the spontaneous breaking of color symmetry via the formation of quark Cooper pairs. At low temperatures, chiral symmetry restoration occurs via a first order transition between a phase with low (or zero) baryon density and a high density color superconducting phase. We find color superconductivity in the high density phase for temperatures less than of order tens to 100 MeV, and find coexisting qq and qq condensates in this phase in the presence of a current quark mass. At high temperatures, the chiral phase transition is second order in the chiral limit and is a smooth crossover for nonzero current quark mass. A tricritical point separates the first order transition at high densities from the second order transition at high temperatures. In the presence of a current quark mass this tricritical point becomes a second order phase transition with Ising model exponents, suggesting that a long correlation length may develop in heavy ion collisions in which the phase transition is traversed at the appropriate density. †

Inhomogeneous chiral condensates

“…On the other hand it is known that at very high densities the ground state of QCD is a color superconductor, whereas particle-hole pairing is suppressed in this regime [38]. Moreover, NJL-model calculations for homogeneous matter typically find that the chiral phase transition at low temperature goes directly from the chirally broken phase into a color superconducting phase, at least for isospin symmetric matter [172,89,68]. It is therefore natural to ask how the chiral phase transition looks like if both possibilities, particle-hole and particle-particle pairing, are taken into account.…”

Evidence for BCS diquark condensation in the 3+1d lattice NJL model

“…The basic idea is that diquark pairs at the Fermi surface in quark matter become bound and condense in a relativistic analogue of the BCS mechanism for electronic superconductivity [2]. Because of the strong attractive qq force in QCD, however, estimates of the energy gap ∆, which opens up at the Fermi surface, can be as large as 100MeV [3], with potentially important consequences for the physics of compact stars. For instance, one intriguing possibility is that pairing between quarks with differing Fermi momenta may lead to a crystalline phase in which translational invariance of the ground state is spontaneously broken [4].…”

Colour-SU(3)-Ginzburg Landau effective potential for order parameter with 3 3 symmetry

“…(10) and (11), can be rewritten with the normal coordinates (d i , |φ i |, θ i ) defined in eq. (9). For simplification, we introduce the variables …”

“…A lot of studies have been done for physical properties of color superconductors on the basis of the QCD-inspired models [5][6][7][8][9].…”