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

Abstract

We consider two-flavor chiral perturbation theory ($\chi$PT) at finite isospin chemical potential ${\mu }_I$ and finite temperature $T$. We calculate the effective potential and the quark and pion condensates as functions of $T$ and ${\mu }_I$ to next-to-leading order in the low-energy expansion in the presence of a pionic source. We map out the phase diagram in the ${\mu }_I$--$T$ plane. Numerically, we find that the transition to the pion-condensed phase is second order in the region of validity of $\chi$PT, which is in agreement with model calculations and lattice simulations. Finally, we calculate the pressure to two-loop order in the symmetric phase for nonzero ${\mu }_I$ and find that $\chi$PT seems to be converging very well.

arXiv comment11 pages and 6 figures, LaTeX; typos corrected, references added

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• Pion crystals hosting topologically stable baryons
• QCD equation of state at finite isospin density from the linear sigma model with quarks: The cold case
• New Way to Resum the Lattice QCD Taylor Series Equation of State at Finite Chemical Potential
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• Critical point and Bose-Einstein condensation in pion matter
• Describing the speed of sound peak of isospin-asymmetric cold strongly interacting matter using effective models
• Pion stars embedded in neutrino clouds
• On the effective lagrangian at nonzero isospin chemical potential
• Isospin asymmetric matter in a nonlocal chiral quark model