QCD at finite isospin density: chiral perturbation theory confronts lattice data

TL;DR

This paper uses chiral perturbation theory to analyze the thermodynamics of three-flavor QCD at finite isospin density, comparing predictions with lattice data and exploring the transition to a pion-condensed superfluid phase.

Contribution

It provides a detailed next-to-leading order calculation of thermodynamic quantities in three-flavor QCD at nonzero isospin chemical potential and compares these with lattice results, extending previous two-flavor analyses.

Findings

Good agreement between three-flavor chiral perturbation theory and lattice data for $<200$ MeV.

Surprisingly good agreement between lattice data and two-flavor predictions for larger $$, better than three-flavor results.

In the limit of large strange quark mass, three-flavor observables reduce to two-flavor results with renormalized parameters.

Abstract

We consider the thermodynamics of three-flavor QCD in the pion-condensed phase at nonzero isospin chemical potential ($\mu_I$) and vanishing temperature using chiral perturbation theory in the isospin limit. The transition from the vacuum phase to a superfluid phase with a Bose-Einstein condensate of charged pions is shown to be second order and takes place at $\mu_I=m_{\pi}$. We calculate the pressure, isospin density, and energy density to next-to-leading order in the low-energy expansion. Our results are compared with recent high-precision lattice simulations as well as previously obtained results in two-flavor chiral perturbation theory. The agreement between the lattice results and the predictions from three-flavor chiral perturbation theory is very good for $\mu_I<200$ MeV. For larger values of $\mu_I$, the agreement between lattice data and the two-flavor predictions is surprisingly good and better than with the three-flavor predictions. Finally, in the limit $m_{s}\gg m_{u}=m_{d}$, we show that the three-flavor observables reduce to the two-flavor observables with renormalized parameters. The disagreement between the results for two-flavor and three-flavor $\chi$PT can largely be explained by the differences in the measured low-energy constants.