Study of 2 + 1 flavor finite-temperature QCD using improved Wilson quarks at the physical point with the gradient flow

We study thermodynamic properties of 2+1 flavor QCD applying the Small Flow-time eXpansion (SFtX) method based on the gradient flow. The method provides us with a general way to compute correctly renormalized observables irrespective of explicit violation of symmetries due to the regularization, such as the Poincare and chiral symmetries on the lattice. We report on the status of our on-going project to compute the energy-momentum tensor and the chiral condensate at the physical point with improved Wilson quarks, extending our previous study with slightly heavy u and d quarks. We also report on our test of two-loop matching coefficients recently calculated by Harlander et al., revisiting the case of QCD with slightly heavy u and d quarks. Our results suggest that the SFtX method is powerful in extracting physical observables on the lattice.