Transition temperature to the superconducting phase of QCD at high baryon density

Abstract

Recent interest in the study of color superconductivity has focused on the regime of high baryon density where perturbative QCD may be employed. Based on the dominant one-gluon-exchange interaction, both the transition temperature and zero temperature gap have been determined to leading order in the coupling, g. While the leading non-BCS behavior, T C ∼ µg −5 e −κ/g , is easily obtained, the pre-exponential factor has proved more difficult to evaluate. Focusing on the transition temperature, we present a perturbative derivation of this factor, exact to leading order in g. This approach is first motivated by the study of a toy model and involves working to second order in the perturbative expansion. We compare this result to the zero temperature gap. Additionally, we extend the analysis to the case of higher angular momentum for longitudinal and transverse quark pairing.

Hard loops, soft loops, and high density effective field theory

“…Brown et al showed that the soft quark self energy and quark gluon vertex function satisfy BRST identities [32].…”

“…(31) we find three contributions to the polarization function, the particle-hole, particle-antiparticle, and anti-particle-anti-hole terms. The particle-hole contribution shown in Fig.1a is…”

“…This perturbative scheme is similar to the one used by Brown et al in order to compute corrections to the critical temperature [31]. We first observe that the functions ∆ n (x) form an orthogonal set of solutions of the gap equation…”

“…Brown et al observed that there are two distinct kinematic regimes for the vertex function, depending on whether (p 1 − p 2 ) 4 is bigger or smaller than (l p 1 − l p 2 ) [32]. In the limit …”

“…Vertex corrections to the gap equation were first considered in [39] but the arguments given in that work are not correct. A more detailed study can be found in [32].…”