Susceptibilities and Taylor coefficients of magnetic QCD from perturbation theory

Abstract

We compute the coefficients $c_2(T,B)$ and $c_4(T,B)$ of the Taylor expansion for the pressure in powers of $\mu_B/T$ in the presence of a large magnetic field within perturbative QCD at finite temperature and baryon density up to two-loops for $N_f=3$ flavors with physical quark masses. We also present results for the excess of pressure, baryon density and baryon number susceptibility as functions of $\mu_B$, as well as susceptibilities as functions of the temperature in the $\{ \mu_B,\mu_Q,\mu_S \}$ basis. Our results can be directly compared to recent lattice QCD data. Even though current lattice results do not overlap with its region of validity, perturbative results seem to be compatible with those obtained on the lattice for large temperatures.