Finite density lattice QCD without extrapolation: Bulk thermodynamics with physical quark masses from the canonical ensemble

Quantum Chromodynamics (QCD) at finite density is most often formulated on the lattice as a grand canonical ensemble. Since lattice QCD has a complex action problem at finite baryo-chemical potential ($\mu_B$), its results at finite density are indirect: e.g. in the form of a set of expansion coefficients. In contrast, the canonical formulation offers direct results for integer-valued net-baryon number. In this work we present for the first time results in the canonical formulation with physical quark masses. To this end we use a high statistics finite-volume lattice ($16^3\times8$) data set that we generated at $\mu_B=0$ with our 4HEX staggered action. We extend the canonical ensemble to non-integer net-baryon number and connect the results back to the grand canonical ensemble. Unlike reweighing to real $\mu_B$, this method can also be used with rooted staggered quarks. For densities where the sign problem can be overcome by brute force computing power, this scheme provides lattice QCD results (e.g. for pressure, baryon density) directly, without relying on any extrapolation in the baryo-chemical potential. In this work we chart the phase diagram by studying bulk thermodynamic observables, which we show to be feasible up to $\mu_B\approx500$~MeV.