A new 4D lattice QCD equation of state: extended density coverage from a generalized $T^\prime$-expansion

We present a new equation of state for QCD in which the temperature $T$ and the three chemical potentials for baryon number $\mu_B$, electric charge $\mu_Q$ and strangeness $\mu_S$ can be varied independently. This result is based on a generalization of the $T'$-expansion scheme, thanks to which the diagonal $\mu_B$ extrapolation was pushed up to a baryo-chemical potential $\mu_B/T \sim 3.5$ for the first time. This considerably extended the coverage of the Taylor expansion, limited to $\mu_B/T < 2.5-3$. As a consequence, we are able to offer a substantially larger coverage of the four-dimensional QCD phase diagram as well, compared to previously available Taylor expansion results. Our results are based on new continuum estimated lattice results on the full set of second and fourth order fluctuations.