Color superconductivity on the lattice -- analytic predictions from QCD in a small box

TL;DR

This paper uses lattice QCD to analytically predict color superconductivity, identifying the critical coupling and condensate structure, and providing insights for future simulations overcoming the sign problem.

Contribution

It introduces a lattice-based analytical approach to study color superconductivity, predicting critical points and condensate properties without assuming explicit forms.

Findings

Critical coupling constant for superconductivity identified

Spatially isotropic s-wave pairing near the Fermi surface

Chiral symmetry breaking by scalar and pseudo-scalar condensates

Abstract

We investigate color superconductivity on the lattice using the gap equation for the Cooper pair condensate. The weak coupling analysis is justified by choosing the physical size of the lattice to be smaller than the QCD scale, while keeping the aspect ratio of the lattice small enough to suppress thermal excitations. In the vicinity of the critical coupling constant that separates the superconducting phase and the normal phase, the gap equation can be linearized, and by solving the corresponding eigenvalue problem, we obtain the critical point and the Cooper pair condensate without assuming its explicit form. The momentum components of the condensate suggest spatially isotropic s-wave superconductivity with Cooper pairs formed by quarks near the Fermi surface. The chiral symmetry in the massless limit is spontaneously broken by the Cooper pair condensate, which turns out to be dominated by the scalar and the pseudo-scalar components. Our results provide useful predictions, in particular, for future lattice simulations based on methods to overcome the sign problem such as the complex Langevin method.