Towards a parameter-free determination of critical exponents and chiral phase transition temperature in QCD

TL;DR

This paper introduces a parameter-free method to accurately determine the critical exponents and transition temperature in QCD's chiral phase transition using an improved order parameter, reducing divergences and enabling precise analysis.

Contribution

It presents a novel, divergence-free order parameter and a ratio-based approach to determine critical properties in QCD without dependence on parameters.

Findings

Successful determination of the chiral transition temperature T_c

Extraction of the critical exponent δ from lattice QCD data

First numerical results using staggered fermions on N_tau=8 lattices

Abstract

In order to quantify the universal properties of the chiral phase transition in (2+1)-flavor QCD, we make use of an improved, renormalized order parameter for chiral symmetry breaking which is obtained as a suitable difference of the $2$-flavor light quark chiral condensate and its corresponding light quark susceptibility. Having no additive ultraviolet as well as multiplicative logarithmic divergences, we use ratios of this order parameter constructed from its values for two different light quark masses. We show that this facilitates determining in a parameter-independent manner, the chiral phase transition temperature $T_c$ and the associated critical exponent $\delta$ which, for sufficiently small values of the light quark masses, controls the quark mass dependence of the order parameter at $T_c$. We present first results of these calculations from our numerical analysis performed with staggered fermions on $N_\tau=8$ lattices.