Nf=2+1 QCD thermodynamics with gradient flow using two-loop matching coefficients

Abstract

We study thermodynamic properties of N f = 2 + 1 QCD on the lattice adopting a nonperturbatively O(a)-improved Wilson quark action and the renormalization group-improved Iwasaki gauge action. To cope with the problems due to explicit violation of the Poincaré and chiral symmetries, we apply the Small Flow-time eXpansion (SFtX) method based on the gradient flow, which is a general method to correctly calculate any renormalized observables on the lattice. In this method, the matching coefficients in front of operators in the small flow-time expansion are calculated by perturbation theory thanks to the asymptotic freedom around the small flow-time limit. In a previous study using one-loop matching coefficients, we found that the SFtX method works well for the equation of state extracted from diagonal components of the energy-momentum tensor and for the chiral condensates and susceptibilities. In this paper, we study the effect of two-loop matching coefficients which have been calculated by Harlander et al. recently. We also test the influence of the renormalization scale in the SFtX method. We find that, by adopting the µ 0 renormalization scale of Harlander et al. instead of the conventional µ d = 1/ √ 8t scale, the linear behavior at large flow-times is improved so that we can perform the t → 0 extrapolation of the SFtX method more confidently. In the calculation of the two-loop matching coefficients by Harlander et al., the equa-*

Properties of the QCD thermal transition with $N_f=2+1$ flavours of Wilson quark

“…As the pion mass is reduced, the pseudocritical temperature is seen to decrease, but no estimates for its value are given. The WHOT collaboration, in a series of papers [20][21][22], has studied N f = 2 + 1 QCD thermodynamics using gradient flow. They employ isotropic lattices at a single lattice spacing, with a pion heavier than in nature.…”

“…Estimates for the pion mass dependence of T ψψ pc , extracted from the inflection point of the renormalised chiral condensate, for N f = 2+1+1 twisted-mass[24] and N f = 2+1 Wilson-clover (this work) fermions. The dashed line presents the fit(22), with the diamond denoting the extrapolated value at the physical pion mass, T ψψ pc = 159(6) MeV.…”

Lattice QCD at nonzero temperature and density

“…A handful of studies for N f = 2 + 1(+1) flavours of Wilson quarks exist. The fixed-scale approach is used on isotropic lattices by the Budapest-Wuppertal collaboration [14,15], for pion masses m π = 545, 440, 285 MeV, and taking a continuum extrapolation; by the WHOT collaboration [16][17][18][19] using gradient flow at a single lattice spacing; and using twisted mass fermions (with N f = 2 + 1 + 1 flavours) [20][21][22], for multiple pion masses, including at the physical point at a single lattice spacing. All of these studies use isotropic lattices.…”

Lattice QCD at nonzero temperature and density

“…A handful of studies for N f = 2 + 1(+1) flavours of Wilson quarks exist. The fixed-scale approach is used on isotropic lattices by the Budapest-Wuppertal collaboration [14,15], for pion masses m π = 545, 440, 285 MeV, and taking a continuum extrapolation; by the WHOT collaboration [16][17][18][19] using gradient flow at a single lattice spacing; and using twisted mass fermions (with N f = 2 + 1 + 1 flavours) [20][21][22], for multiple pion masses, including at the physical point at a single lattice spacing. All of these studies use isotropic lattices.…”