Abstract
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 Nf=2+1+1 flavours of Wilson fermions at maximal twist. We identify an order parameter free from 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 ≲T≲300 MeV. We discuss violation of scaling at larger masses and a possible cross-over to mean field behaviour. The chiral extrapolation T0=134−4+6 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.
Highlights
The appearance of pseudo-Goldstone bosons in the spectrum signals the spontaneous breaking of chiral symmetry of strong interactions
We note the sharper decrease of ψψ 3, very understandable given that it is closer to the chiral condensate in the chiral limit, followed by the high temperature behaviour just described
We show the chiral susceptibility for all ensembles. We note that this observable has a strong regular contribution, in addition to an additive renormalization. These features are qualitatively clear in the plots: rather than the simple symmetric shape predicted by the Equation of State (EoS), the curves are skewed and have a long high temperature tail
Summary
The appearance of pseudo-Goldstone bosons in the spectrum signals the spontaneous breaking of chiral symmetry of strong interactions. If the symmetry restoring transition is continuous, the link between the genuine critical behaviour in the chiral limit and the observations at finite masses is made transparent by the universal Equation of State (EoS). This is true only within a limited region around criticality – the scaling window. A recent work [21] confirms these findings, suggesting that pion masses as light as 30 MeV are needed to reach the scaling window in QCD, with a consistent extrapolation to T0 142 MeV in the chiral limit from different prescriptions. A is a mass independent parameter, and Tc for different observables should scale with the same exponent 2/βδ, but with different zp s
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