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Color superconductivity in weak coupling
| Content Provider | Semantic Scholar |
|---|---|
| Copyright Year | 1999 |
| Abstract | Cooper’s theorem [1–3] implies that if there is an attractive interaction in a cold Fermi sea, the system is unstable with respect to formation of a particle-particle condensate. In QCD, single-gluon exchange between quarks of different color generates an attractive interaction in the color-antitriplet channel [4]. Thus, it appears unavoidable that color superconductivity occurs in dense quark matter which is sufficiently cold [5–20]. How a dense quark phase matches onto hadronic matter is difficult to address [7,11]. In particular, while a quark-quark condensate may form, such condensation competes with the tendency of a quark-quark pair to bind with a third quark, to form a color-singlet hadron. One way of understanding color superconductivity is to compute at very high densities, where by asymptotic freedom, perturbation theory can be used. At nonzero temperature, but zero quark density, it is well known that perturbation theory is a particularly bad approximation [21]. If g is the coupling constant for QCD, the free energy is not an expansion in g, but only in g, with a series which is well behaved only for g ≤ 1. In contrast, at zero temperature and nonzero quark density, the free energy is an expansion in g ln(1/g), and appears to be well behaved for much larger values of the coupling constant, up to values of g ≤ 4 [22]. Similar conclusions can be reached by comparing the gluon “mass”, mg ∼ gμ or ∼ gT to the chemical potential, μ, or the temperature, T [15]. Thus for cold, dense quark matter, perturbation theory might give us information which not even lattice QCD calculations can provide. Color superconductivity is rather different from ordinary superconductivity, as in the model of Bardeen, Cooper, and Schrieffer (BCS) [1–3]. In BCS-like theories, superconductivity is determined by infrared divergences which arise in the scattering between two fermions close to the Fermi surface: the initial fermions, with momenta k and −k, scatter into a pair with momenta k′ and −k′. Summing up bubble diagrams generates an instability which is only cured by a fermion-fermion condensate. If the fermions interact through a point-like four-fermion coupling, though, there is no correlation between the initial and outgoing momenta, k and k′. In the gap equation, this implies that the gap function is constant with respect to momentum, as long as the momenta are near the Fermi surface. In QCD, however, scattering through single-gluon exchange strongly correlates the direction of the inand out-going quarks: there is a logarithmic divergence for forward-angle scattering, ∼ ∫ dθ/θ. This extra logarithm from forward-scattering implies that the gap is not an exponential in 1/g, as in BCS-like theories, but only in 1/g [7,8,13,15]. As a consequence, the gap function is no longer constant as a function of momentum, even about the Fermi surface. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://cds.cern.ch/record/404476/files/9910056.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Approximation Arabic numeral 0 Color Control theory Coupling constant Dead Sea Scrolls Diagram Femtometer Greater Instability Lattice QCD Logarithm Perturbation theory Singlet state Superconductivity Unstable Medical Device Problem density exponential free energy |
| Content Type | Text |
| Resource Type | Article |
