Thermodynamics of Color Superconductor in a QCD-like Effective Theory

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  • 量子色力学類似有効理論に於けるカラー超伝導体の熱力学

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Abstract

We have investigated the thermodynamics of two-flavor color superconductor (2SC) at finite temperature (T) and quark chemical potential (1) within the framework of a QCD-like effective theory, in which an asymptotically free momentum-dependent running coupling is used. Two kinds of systems have been investigated. One is with a tree-level gluon propagator (model A) and the other is with the lattice-QCD based (LQB) gluon propagator (model B). We have found that 2￠T =0 =3:43kBTc in model B (￠:energy p=pF gap, kB:Boltzmann constant, Tc:critical temperature). This value is very close to the famous BCS result, which is 2Δ = 3:52kBTc. We have found that the coherence length (´) is not affected by T in 2SC, while Δ decreases as T increases and vanishes at Tc. In addition, we have found that the Cooper pair wave function c(p) is not affected by T , apart from normalization constant. With these results, the second-order phase transition between 2SC and a normal quark matter, which is considered to be quark-gluon plasma, can be characterized by the constant spatial structure and decrease in the coherent Cooper pair number with increased T . The quark density of the 2SC has been found to be in a realistic region for compact star core. The value of η in 2SC is shorter than the averaged interquark density (d). The small size of the Cooper pair suggests that they are tightly bound and rather bosonic. Therefore, it is natural that we expect the realizability of quark Bose-Einstein condensation phase. Some of our results, the larger ￠, higher Tc, wider μ region and shorter η in model B suggest that the LQB gluon propagator induces stronger quark-quark interaction than the tree-level one.

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