Se p 20 04 Klein – Gordon Equation for Quark Pairs in Color Superconductor

The wave equation is derived for quark pairs in color superconductor in the regime of low density/strong coupling. During the last five years color superconductivity became a compelling topic in QCD – see the review papers [1]. Grossly speaking, we have a fair understanding of color superconductivity physics in the high den-sity/weak coupling regime. In the low density/strong coupling region the situation is different. Here, the theory faces the well-known difficulties of the nonperturbative QCD and use is made of the models, like NJL, or instanton gas. By low density we mean the quark densities 3–4 times larger than that in the normal nuclear matter. Model calculations show (see [2] and references in [1]) that at such densities the gap equation acquires a nontrivial solution. This was interpreted [1] as the onset of the Bardeen–Cooper–Schrieffer (BCS) regime, i.e., the formation of the condensate of Cooper pairs made of u-and d-quarks. It is known, however , that nonzero value of the gap is only a signal of the presence of the fermion pairs. Depending on the dynamics of the system, on the fermion density, and on the temperature, such pairs may be either stable, or fluctuating in time, may form a BCS condensate, or the dilute Bose gas, or undergo a Bose condensation. The continuous evolution from the BCS regime to the regime of the Bose–Einstein condensation (BEC) is called the BCS–BEC crossover. Such a transition takes place either by increasing the strength of the interaction, or by decreasing the carrier density. The fact that the BCS wave function may undergo a smooth evolution and describe the tightly bound fermion pairs was first noticed long ago 1