We determine the curvature of the pseudo-critical line of strong interactions by means of numerical simulations at imaginary chemical potentials. We consider $N_f=2+1$ stout improved staggered fermions with physical quark masses and the tree level Symanzik gauge action, and explore two different sets of lattice spacings, corresponding to temporal extensions $N_t = 6$ and $N_t = 8$. Both the renormalized chiral condensate and the renormalized chiral susceptibility are used to locate the transition. The determinations obtained from the two quantities are in good agreement, a preliminary continuum extrapolation yields $κ= 0.013(2)(1)$. We also investigate the impact of a non-zero strange quark chemical potential and compare our results to previous determinations in the literature, discussing the possible sources of systematic errors affecting the various procedures.

16 pages, 12 figures, 11 tables. Published version