Perturbative predictions for color superconductivity on the lattice

TL;DR

This paper introduces a new lattice method based on the Thouless criterion to predict color superconductivity, calculating critical parameters and pairing structures without predefined assumptions, revealing spontaneous symmetry breaking.

Contribution

A novel lattice approach using the Thouless criterion to study color superconductivity, enabling direct calculation of critical points and pairing structures without ansatz.

Findings

Critical $eta$ peaks at specific chemical potentials

Discretized energy levels influence phase transition points

Spontaneous breaking of chiral U(1) symmetry in massless case

Abstract

We develop a new method to investigate color superconductivity (CSC) on the lattice based on the Thouless criterion, which amounts to solving the linearized gap equation without imposing any ansatz on the structure of the Cooper pairs. We perform explicit calculations at the one-loop level with the staggered fermions on a $8^3 \times 128$ lattice and the Wilson fermions on a $4^3 \times 128$ lattice, which enables us to obtain the critical $\beta(=6/g^2)$ as a function of the quark chemical potential $\mu$, below which the CSC phase is expected to appear. The obtained critical $\beta$ has sharp peaks at the values of $\mu$ corresponding to the discretized energy levels of quarks similarly to what was observed in previous studies on simplified effective models. From the solution to the linearized gap equation, one can read off the flavor and spatial structures of the Cooper pairs at the critical $\beta$. In the case of massless staggered fermion, in particular, we find that the chiral $\mathrm{U}(1)$ symmetry of the staggered fermions is spontaneously broken by the condensation of the Cooper pairs.