Searching for the BCS phase at nonzero isospin asymmetry

TL;DR

This paper investigates the existence of a superfluid BCS phase in QCD matter at high density and nonzero isospin chemical potential, using lattice computations and spectral analysis to test the connection to the BEC phase.

Contribution

It provides the first spectral analysis-based evidence to identify the BCS phase and its connection to the BEC phase in QCD at nonzero isospin chemical potential.

Findings

Spectral signatures consistent with the BCS phase were identified.

Results support a smooth crossover between BEC and BCS phases.

Lattice results suggest a continuous connection between deconfinement and superfluid phases.

Abstract

According to perturbation theory predictions, QCD matter in the zero-temperature, high-density limits of QCD at nonzero isospin chemical potential is expected to be in a superfluid Bardeen-Cooper-Schrieffer (BCS) phase of $u$ and $\bar{d}$ Cooper pairs. It is also expected, on symmetry grounds, that such phase connects via an analytical crossover to the phase with Bose-Einstein condensation (BEC) of charged pions at $\mu_\text{I}\geq m_\pi/2$. With lattice results, showing some indications that the deconfinement crossover also smoothly penetrates the BEC phase, the conjecture was made that the former connects continuously to the BEC-BCS crossover. We compute the spectrum of the Dirac operator, and use generalized Banks-Casher relations, to test this conjecture and identify signatures of the superfluid BCS phase.