Universal scaling properties of QCD close to the chiral limit

TL;DR

This study uses lattice QCD to precisely determine the chiral phase transition temperature in QCD with light quarks, introducing novel estimators and analyzing universal scaling near the chiral limit.

Contribution

It proposes and calculates new estimators for the chiral transition temperature and applies universal scaling relations to extrapolate to the chiral limit.

Findings

Chiral transition temperature estimated at 132^{+3}_{-6} MeV.

New estimators provide consistent results with conventional methods.

Ratio of order parameter to susceptibility can distinguish universality classes.

Abstract

We present a lattice QCD based determination of the chiral phase transition temperature in QCD with two massless (up and down) and one strange quark having its physical mass. We propose and calculate two novel estimators for the chiral transition temperature for several values of the light quark masses, corresponding to Goldstone pion masses in the range of $58~{\rm MeV}\lesssim m_\pi\lesssim 163~{\rm MeV}$. The chiral phase transition temperature is determined by extrapolating to vanishing pion mass using universal scaling relations. After thermodynamic, continuum and chiral extrapolations we find the chiral phase transition temperature $T_c^0=132^{+3}_{-6}$ MeV. We also show some preliminary calculations that use the conventional estimator for the pseudo-critical temperature and compare with the new estimators for $T_c^0$. Furthermore, we show results for the ratio of the chiral order parameter and its susceptibility and argue that this ratio can be used to differentiate between $O(N)$ and $Z_2$ universality classes in a non-parametric manner.