  Most lattice studies of hot and dense QCD matter rely on extrapolation from
zero or imaginary chemical potentials. The ill-posedness of numerical analytic
continuation puts severe limitations on the reliability of such methods. We
studied the QCD chiral transition at finite real baryon density with the more
direct sign reweighting approach. We simulate up to a baryochemical
potential-temperature ratio of $\mu_B/T=2.7$, covering the RHIC Beam Energy
Scan range, and penetrating the region where methods based on analytic
continuation are unpredictive.This opens up a new window to study QCD matter at
finite $\mu_B$ from first principles.
