Thermal QCD phase transition and its scaling window from Wilson twisted mass fermions

Abstract: We investigate the thermal QCD phase transition and its scaling properties on the lattice. The simulations are performed with $N_f=2+1+1$ Wilson twisted mass fermions at pion masses from physical up to heavy quark regime. We introduce a novel chiral order parameter, which is free from linear mass contributions and turns out to be very useful for the study of scaling behaviour. Our results are compatible with $O(4)$ universal scaling for the physical pion mass and the temperature range $[120:300]$ MeV. Violations to scaling at larger masses and other possible scenarios, including mean field behaviour and $Z(2)$ scaling scenario are also discussed. We provide an estimation for the critical temperature in the chiral limit $T_0$.