Equation of state of a hot-and-dense quark gluon plasma: lattice simulations at real $\mu_B$ vs. extrapolations

The equation of state of the quark gluon plasma is a key ingredient of heavy ion phenomenology. In addition to the traditional Taylor method, several novel approximation schemes have been proposed with the aim of calculating it at finite baryon density. In order to gain a pragmatic understanding of the limits of these schemes, we compare them to direct results at $\mu_B>0$, using reweighting techniques free from an overlap problem. We use 2stout improved staggered fermions with 8 time-slices and cover the entire RHIC BES range in the baryochemical potential, up to $\mu_B/T=3$.