The QCD crossover at finite chemical potential from lattice simulations

We provide the most accurate results for the QCD transition line so far. We optimize the definition of the crossover temperature $T_c$, allowing for its very precise determination, and extrapolate from imaginary chemical potential up to real $mu_B approx 300$ MeV. The definition of $T_c$ adopted in this work is based on the observation that the chiral susceptibility as a function of the condensate is an almost universal curve at zero and imaganiary $mu_B$. We obtain the parameters $kappa_2=0.0153(18)$ and $kappa_4=0.00032(67)$ as a continuum extrapolation based on $N_t=10,12$ and $16$ lattices with physical quark masses. We also extrapolate the peak value of the chiral susceptibility and the width of the chiral transition along the crossover line. In fact, both of these are consistent with a constant function of $mu_B$. We see no sign of criticality in the explored range.