Three-loop hard-thermal-loop perturbation theory thermodynamics at finite temperature and finite baryonic and isospin chemical potential

In a previous paper (JHEP {\bf 05} (2014) 27), we calculated the three-loop thermodynamic potential of QCD at finite temperature $T$ and quark chemical potentials $μ_q$ using the hard-thermal-loop perturbation theory (HTLpt) reorganization of finite temperature and density QCD. The result allows us to study the thermodynamics of QCD at finite temperature and isospin chemical potential $μ_I$. We calculate the pressure, energy density, and entropy density, the trace anomaly, and the speed of sound at zero and nonzero $μ_I$. The second, fourth, and sixth-order isospin susceptibilities are calculated at zero $μ_I$. Our results can be directly compared to lattice QCD without Taylor expansions around $μ_q=0$ since QCD has no sign problem at finite isospin chemical potential.

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