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

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.

Comments: 8 pages and 4 figs. v2: Expanded discussion, in particular the matching between two- and three flavor couplings for large strange-quark masses. Matches published version