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State-of-the-art lattice QCD studies of hot and dense strongly interactingmatter currently rely on extrapolation from zero or imaginary chemicalpotentials. The ill-posedness of numerical analytic continuation puts severelimitations on the reliability of such methods. Here we use the more directsign reweighting method to perform lattice QCD simulation of the QCD chiraltransition at finite real baryon density on phenomenologically relevantlattices. This method does not require analytic continuation and avoids theoverlap problem associated with generic reweighting schemes, so has onlystatistical but no uncontrolled systematic uncertainties for a fixed latticesetup. This opens up a new window to study hot and dense strongly interactingmatter from first principles. We perform simulations up to a baryochemicalpotential-temperature ratio of $\mu_B/T=2.5$ covering most of the RHIC BeamEnergy Scan range in the chemical potential. We also clarify the connection ofthe approach to the more traditional phase reweighting method.

Lattice simulations of the QCD chiral transition at real baryon density