Exploring Nf=2+1 QCD thermodynamics from the gradient flow

TL;DR

This study applies the gradient flow method to compute the energy-momentum tensor and chiral condensate in (2+1)-flavor QCD, providing new insights into thermodynamics and chiral symmetry restoration at finite temperature.

Contribution

First application of the gradient flow method with dynamical quarks in (2+1)-flavor QCD to evaluate thermodynamic quantities and chiral condensate.

Findings

Results agree with previous methods below 280 MeV

Discrepancies at higher temperatures likely due to lattice artifacts

Clear signal of chiral restoration crossover at T~190 MeV

Abstract

The energy-momentum tensor plays an important role in QCD thermodynamics. Its expectation value contains information of the pressure and the energy density as its diagonal part. Further properties like viscosity and specific heat can be extracted from its correlation function. Recently a new method based on the gradient flow was introduced to calculate the energy-momentum tensor on the lattice, and has been successfully applied to quenched QCD. In this paper, we apply the gradient flow method to calculate the energy-momentum tensor in (2+1)-flavor QCD. As the first application of the method with dynamical quarks, we study at a single but fine lattice spacing a=0.07 fm with heavy u and d quarks ($m_\pi/m_\rho=0.63$) and approximately physical s quark. Performing simulations on lattices with Nt=16 to 4, the temperature range of T=174-697 MeV is covered. We find that the results of the pressure and the energy density by the gradient flow method are consistent with the previous results using the T-integration method at T<280 MeV, while the results show disagreement at T>350 MeV (Nt<8), presumably due to the small-Nt lattice artifact of $O((aT)^2)=O(1/N_t^2)$. We also apply the gradient flow method to evaluate the chiral condensate taking advantage of the gradient flow method that renormalized quantities can be directly computed avoiding the difficulty of explicit chiral violation with lattice quarks. We compute the renormalized chiral condensate in the MS-bar scheme at renormalization scale $\mu=2$ GeV with a high precision to study the temperature dependence of the chiral condensate and its disconnected susceptibility. Even with the Wilson-type quark action, we obtain the chiral condensate and its disconnected susceptibility showing a clear signal of pseudocritical temperature at T~190 MeV related to the chiral restoration crossover.