QCD equation of state at finite isospin density from the linear sigma model with quarks: The cold case

Abstract

We use the two-flavor linear sigma model with quarks to study the phase structure of isospin asymmetric matter at zero temperature. The meson degrees of freedom provide the mean field chiral- and isospin-condensates on top of which we compute the effective potential accounting for constituent quark fluctuations at one-loop order. Using the renormalizability of the model, we absorb the ultraviolet divergences into suitable counter-terms that are added respecting the original structure of the theory. These counter-terms are determined from the stability conditions which require the effective potential to have minima in the condensates directions at the classical values, as well as the transition from the non-condensed to the condensed phase to be smooth as a function of the isospin chemical potential. We use the model to study the evolution of the condensates as well as the pressure, energy and isospin densities and the sound velocity as functions of the isospin chemical potential. The approach does a good average description up to isospin chemical potentials values not too large as compared to the vacuum pion mass.

11 pages and 7 figures. Expanded discussion, references and graphs added, conclusions unchanged

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• Absence of inhomogeneous chiral phases in 2+1-dimensional four-fermion and Yukawa models
• Spatially oscillating correlation functions in $\left(2+1\right)$-dimensional four-fermion models: The mixing of scalar and vector modes at finite density
• Describing the speed of sound peak of isospin-asymmetric cold strongly interacting matter using effective models
• On the origin of the peak of the sound velocity for isospin imbalanced strongly interacting matter
• Pion stars embedded in neutrino clouds
• Chiral restoration temperature at finite spin density in QCD