Enhanced contribution of the pairing gap to the QCD equation of state at large isospin chemical potential

TL;DR

This paper investigates the superfluid state of QCD at high isospin density, revealing an enhanced pairing gap and its significant impact on the equation of state, bridging lattice and perturbative QCD results.

Contribution

It provides a detailed calculation of the pairing gap at large isospin chemical potential, showing its enhancement and impact on the QCD equation of state, which helps reconcile lattice and perturbative results.

Findings

Pairing gap is larger than in baryon chemical potential scenarios.

Condensation energy significantly influences the QCD equation of state at high isospin.

The results explain discrepancies between lattice QCD and perturbative QCD at a few GeV.

Abstract

I study QCD at large isospin density, which is known to be in the superfluid state with Cooper pairs carrying the same quantum number as pions. I solve the gap equation derived from the perturbation theory up to the next-to-leading order corrections. The pairing gap at large isospin chemical potential is found to be enhanced compared to the color-superconducting gap at large baryon chemical potential due to the $\sqrt{2}$ difference in the exponent arising from the stronger attraction in one-gluon exchange in the singlet channel. Then, using the gap function, I evaluate the contribution of the condensation energy of the superfluid state to the QCD equation of state. At isospin chemical potential of a few GeV, where the lattice QCD and the perturbative QCD can be both applied, the effect of the condensation energy becomes dominant even compared to the next-to-leading order corrections to the pressure in the perturbation theory. It resolves the discrepancy between the recent lattice QCD results and the perturbative QCD result.