Pairing Correlation in Quark Matter

The superconductivity in quark matter is investigated by a generalized mean field approximation. If we assume that two quarks interact each other via the one·gluon exchange potential, attractive force appears in the color·triplet and spin-parallel state. Applying a BCS-like theory to the system, it is shown that we obtain a new superconducting state which is more stable than the normal (Fermi gas) state. We also give the explicit expression of the superconducting state. Recently the possibility of strange quark matter1> has been studied by many authors by using various effective models for QCD. In these approaches2> they have supposed that the ground state of the quark matter is a degenerate Fermi gas state where each quark occupies a single-particle state with definite momentum under the Fermi momentum. We think that this assumption is not so evident. If the interac­ tion between two quarks is attractive and strong enough, the ground state would become a correlated state just like the BCS state in the superconductors rather than the normal state (the Fermi gas state). We will investigate this possibility in this paper. There are several approaches3>.4> to take into account such pairing correlations. They are restricted to the SU(2) quark matter because any two-quark system has color necessarily. In the SU(3), we note that there are three kinds of quark pairs which bear the same color as three kinds of anti-quarks. If such three quark pairs condense in the same way, there may exist a new boson condensate which is a color-singlet state. It is the purpose of this note to discuss such possibility, the color SU(3) superconductivity in the quark matter, by using a mean field approximation. § 2. Attractive force between two quarks First let us consider possibility of appearance of the attractive force between two quarks. We assume the one-gluon exchange potential,5>