Equation of state in (2+1)-flavor QCD with gradient flow

Understand

The energy-momentum tensor and equation of state are studied in finite-temperature (2+1)-flavor QCD with improved Wilson quarks using the method proposed by Makino and Suzuki based on the gradient flow.

• We find that the results of the gradient flow are consistent with the previous results using the $T$-integration method at $T \mathrel{\rlap{\raise 0.511ex \hbox{$<$}}{\lower 0.511ex \hbox{$\sim$}}} 280$ MeV ($N_t\mathrel{\rlap{\raise 0.511ex \hbox{$>$}}{\lower 0.511ex \hbox{$\sim$}}}10$), while a disagreement is found at $T \mathrel{\rlap{\raise 0.511ex \hbox{$>$}}{\lower 0.511ex \hbox{$\sim$}}} 350$ MeV ($N_t \mathrel{\rlap{\raise 0.511ex \hbox{$<$}}{\lower 0.511ex \hbox{$\sim$}}} 8$) presumably due to the small-$N_t$ lattice artifact.
• We also report on the results on the renormalized chiral condensate and its disconnected susceptibility using the method of Hieda and Suzuki.
• The results show a clear signal of the expected chiral restoration crossover even with Wilson-type quarks which violate the chiral symmetry explicitly.