Quark and pion condensates at finite isospin density in chiral perturbation theory

Abstract

In this paper, we consider two-flavor QCD at zero temperature and finite isospin chemical potential $$\mu _I$$ μ I using a model-independent analysis within chiral perturbation theory at next-to-leading order. We calculate the effective potential, the chiral condensate and the pion condensate in the pion-condensed phase at both zero and nonzero pionic source. We compare our finite pionic source results for the chiral condensate and the pion condensate with recent (2+1)-flavor lattice QCD results. Agreement with lattice results generally improves as one goes from leading order to next-to-leading order.

Condensates and pressure of two-flavor chiral perturbation theory at nonzero isospin and temperature

“…1 The temperatureindependent terms agree with the result first obtained in Ref. [51] for the full vacuum energy to order O( p 6 ) in χ PT.…”

“…At O( p 6 ), there are 53 terms and four contact terms in the SU (2) chiral Lagrangian [8,50]. However, only two terms contribute to the static Lagrangian L static 6 [51]. Denoting the bare couplings by c i , only the sum 16(c 10 + 2c 11 )(2B 0 m) 3 contributes, where…”

“…Integrating this equation and defining the constantsc 10 and c 11 as the renormalized couplings c r 10 and c r 11 at the scale Λ = M up to the prefactor − 3l 3 64(4π) 4 [51], we can write…”

Quark, pion and axial condensates in three-flavor finite isospin chiral perturbation theory

“…This condensate becomes inhomogeneous in the presence of an external magnetic field due to the spontaneous symmetry breaking of the U (1) gauge symmetry [9,10]. Furthermore, the condensate increases monotonically as has been observed in lattice QCD and NLO twoflavor calculations [11] for values of the isospin chemical potential up to approximately 2m π . This behavior is analogous to that observed in the context of nuclear matter [12] in that there is a simultaneous weakening of the chiral condensate with increasing nuclear density or in our case isospin density.…”

“…It has been studied in lattice QCD with the added benefit that unlike the pion and chiral condensates, the zero-source limit results have been extracted [13]. We have previously compared finite source results for the pion and chiral condensates with two-flavor QCD [11] with results in very good agreement.…”