Chiral susceptibility in ( 2+1 )-flavor QCD

Jens Braun,Daniel Rosenblüh,Wei-Jie Fu,Fabian Rennecke,Shi Yin,Jan M Pawlowski

doi:10.1103/physrevd.102.056010

Abstract

We calculate chiral susceptibilities in ($2+1$)-flavor QCD for different masses of the light quarks using the functional renormalization group (fRG) approach to first principles QCD. We follow the evolution of the chiral susceptibilities with decreasing masses as obtained from both the light-quark and the reduced quark condensate. The latter compares very well with recent results from the HotQCD Collaboration for pion masses ${m}_{\ensuremath{\pi}}\ensuremath{\gtrsim}100\text{ }\text{ }\mathrm{MeV}$. For smaller pion masses, fRG and lattice results are still consistent. In particular, the estimates for the chiral critical temperature are in very good agreement. We close by discussing different extrapolations to the chiral limit.

Highlights

The phase structure of QCD probed with heavy-ion collisions is well described by (2 þ 1)-flavor QCD
Assuming that the chiral phase transition is of second order in the limit of massless up and down quarks, it follows from universal scaling arguments [38] that the pion-mass scaling of the pseudocritical temperature defined as the position of the peak of the chiral susceptibility is controlled by the critical exponents of the underlying universality class
As already discussed in the previous section, the renormalized condensate only differs from the light-quark condensate by a temperature-independent shift

Summary

INTRODUCTION

The phase structure of QCD probed with heavy-ion collisions is well described by (2 þ 1)-flavor QCD. For sufficiently small masses of the three quarks, one expects a finite mass range with a first-order chiral transition [22] This first-order regime may even extend to the limit of infinitely heavy strange quarks; see, e.g., Refs. Within a very recent lattice QCD study investigating pion masses in the range of 50 ≲ mπ ≲ 160 MeV with a physical strange quark mass, the scaling properties of the chiral susceptibility are found to be compatible with the 3D Oð4Þ universality class [33]. Assuming that the chiral phase transition is of second order in the limit of massless up and down quarks, it follows from universal scaling arguments [38] that the pion-mass scaling of the pseudocritical temperature defined as the position of the peak of the chiral susceptibility is controlled by the critical exponents of the underlying universality class.

CONDENSATES AND FUNCTIONAL QCD

Chiral condensates

NR ðΔlðTÞ

Functional renormalization group approach

RESULTS

CONCLUSIONS