Abstract
In this paper, we calculate the equation of state of two-flavor finite isospin chiral perturbation theory at next-to-leading order in the pion-condensed phase at zero temperature. We show that the transition from the vacuum phase to a Bose-condensed phase is of second order. While the tree-level result has been known for some time, surprisingly quantum effects have not yet been incorporated into the equation of state. We find that the corrections to the quantities we compute, namely the isospin density, pressure, and equation of state, increase with increasing isospin chemical potential. We compare our results to recent lattice simulations of 2 + 1 flavor QCD with physical quark masses. The agreement with the lattice results is generally good and improves somewhat as we go from leading order to next-to-leading order in chi PT.
Highlights
While finite baryon density is inaccessible through lattice Quantum chromodynamics (QCD), finite isospin systems in real QCD can be studied using lattice-based methods, see Refs. [6,7] for some early results
The most thorough of these studies were performed only recently [8,9,10] even though finite isospin QCD was first studied over a decade ago using chiral perturbation theory (χ PT) in a seminal paper by Son and Stephanov [11]. χ PT [12,13,14,15] is a low-energy effective field theory of QCD that describes the dynamics of the pseudo-Goldstone bosons that are the result of the spontaneous symmetry breaking of global symmetries in the QCD vacuum
We derive the Lagrangian that is needed for all next-to-leading order (NLO) calculations within χ PT at finite isospin chemical potential allowing for a charged pion condensate
Summary
While finite baryon density is inaccessible through lattice QCD, finite isospin systems in real QCD can be studied using lattice-based methods, see Refs. [6,7] for some early results. Being based only on symmetries and degrees of freedom, the predictions of χ PT are model independent It is agreed through both lattice QCD and chiral perturbation theory studies that at an isospin chemical potential equal to the physical pion mass there is a second-order phase transition at zero temperature from the vacuum phase to a pion-condensed phase. We derive the Lagrangian that is needed for all next-to-leading order (NLO) calculations within χ PT at finite isospin chemical potential allowing for a charged pion condensate. It is well known that chiral perturbation theory encodes the interactions among the Goldstone bosons (pions) that arise due to the spontaneous breaking of chiral symmetry by the QCD vacuum, i.e. Under chiral rotations, i.e. SU (2)L × SU (2)R, the lefthanded and right-handed fields transform as ψL → LψL (6).
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