Equation of state of imbalanced cold matter from chiral perturbation theory

Abstract

We study the thermodynamic properties of matter at vanishing temperature for non-extreme values of the isospin chemical potential and of the strange quark chemical potential. From the leading order pressure obtained by maximizing the static chiral Lagrangian density we derive a simple expression for the equation of state in the pion condensed phase and in the kaon condensed phase. We find an analytical expression for the maximum of the ratio between the energy density and the Stefan-Boltzmann energy density as well as for the isospin chemical potential at the peak both in good agreement with lattice simulations of quantum chromodynamics. We speculate on the location of the crossover from the Bose-Einstein condensate state to the Bardeen-Cooper-Schrieffer state by a simple analysis of the thermodynamic properties of the system. For ${\mu }_I\gtrsim 2m_{\pi }$ the leading order chiral perturbation theory breaks down; as an example it underestimates the energy density of the system and leads to a wrong asymptotic behavior.

arXiv comment5 pages, 3 figures, minor changes. Accepted version as Rapid Communication on PRD

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Cited by in corpus (17)

• Boson Stars and Oscillatons: A Review
• Meson condensation
• Scrutinizing the pion condensed phase
• Two-flavor chiral perturbation theory at nonzero isospin: Pion condensation at zero temperature
• QCD at finite isospin density: chiral perturbation theory confronts lattice data
• Isospin asymmetry in holographic baryonic matter
• Pion crystals hosting topologically stable baryons
• Thermodynamics and susceptibilities of isospin imbalanced QCD matter
• Condensates and pressure of two-flavor chiral perturbation theory at nonzero isospin and temperature
• Pion and kaon condensation at zero temperature in three-flavor $\chi$PT at nonzero isospin and strange chemical potentials at next-to-leading order
• Multicomponent meson superfluids in chiral perturbation theory
• QCD topology and axion properties in an isotropic hot and dense medium
• Metastable pions in dense media
• Quarkyonic picture of isospin QCD
• Meson Physics in Asymmetric Matter
• Isospin asymmetric matter in a nonlocal chiral quark model
• Existence of a supersymmetric extension of the gauged non-linear $\Sigma$-model and the transition from integrability to chaos