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We map out the QCD crossover line $\frac{T_c(\mu_B)}{T_c(0)} = 1 - \kappa_2\left( \frac{\mu_B}{T_c(0)} \right)^2 - \kappa_4 \left( \frac{\mu_B}{T_c(0)}\right)^4 + \mathcal{O}(\mu_B^6)$ for the first time up to$\mathcal{O}(\mu_B^4)$ for a strangeness neutral system by performing a Taylorexpansion of chiral observables in temperature $T$ and chemical potentials$\mu$. At vanishing chemical potential, we report a crossover temperature$T_c(0) = (156.5 \pm 1.5)\;\mathrm{MeV}$ defined by the average of severalsecond-order chiral susceptibilities. For a system with thermal conditionsappropriate for a heavy-ion collision, we determined a curvature from thesubtracted condensate as $\kappa_2 = 0.0120(20)$ and from the disconnectedsusceptibility as $\kappa_2 = 0.0123(30)$. The next order $\kappa_4$ issignificantly smaller. We also report the crossover temperature as a functionof the chemical potentials for: baryon-number, electric charge, strangeness andisospin. Additionally, we find that $T_c(\mu_B)$ is in agreement with lines ofconstant energy density and constant entropy density. Along this crossoverline, we study net baryon-number fluctuations and show that their increase issubstantially smaller compared to that obtained in HRG model calculations.Similarly, we analyze chiral susceptibility fluctuations along the crossoverline and show that these are constant. We conclude that no signs for anarrowing of the crossover region can be found for baryon chemical potential$\mu_B < 250\;\mathrm{MeV}$.

The QCD crossover at zero and non-zero baryon densities from Lattice QCD