QCD transition at the physical point, and its scaling window from twisted mass Wilson fermions

We study the scaling properties of the finite temperature QCD phase transition, for light quark masses ranging from the heavy quark regime to their physical values. The lattice results are obtained in the fixed scale approach from simulations of $N_f=2+1+1$ flavours of Wilson fermions at maximal twist. We identify an order parameter free from the the linear contributions in mass due to additive renormalization and regular terms in the Equation of State, which proves useful for the assessment of the hypothesized universal behaviour. We find compatibility with the 3D $O(4)$ universality class for the physical pion mass and temperatures $120$ MeV $ \lesssim T \lesssim 300$ MeV. We discuss violation of scaling at larger masses and a possible cross-over to mean field behaviour. The chiral extrapolation $T_0 = 134^{+6}_{-4}$ MeV of the pseudocritical temperature is robust against predictions of different universality classes and consistent with its estimate from the $O(4)$ Equation of State for the physical pion mass.