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

In a previous paper [N. Haque et al., J. High Energy Phys. 05 (2014) 27], we calculated the three-loop thermodynamic potential of QCD at finite temperature T and quark chemical potentials mu(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 finite baryon, strangeness, and isospin chemical potentials mu(B), mu(S), and mu(I). We calculate the pressure at nonzero mu(B) and mu(I) with mu(S) = 0, and the energy density, the entropy density, the trace anomaly, and the speed of sound at nonzero mu(I) with mu(B) = mu(S) = 0. The second- and fourth-order isospin susceptibilities are calculated at mu(B) = mu(S) = mu(I) = 0. Our results can be directly compared to lattice QCD without Taylor expansions around mu(q) = 0 since QCD has no sign problem at mu(B) = mu(S) = 0 and finite isospin chemical potential mu(I).