Thermodynamics in quenched QCD: energy–momentum tensor with two-loop order coefficients in the gradient-flow formalism

Abstract

Recently, Harlander et al. [Eur. Phys. J. C 78, 944 (2018)] have computed the twoloop order (i.e., NNLO) coefficients in the gradient-flow representation of the energymomentum tensor (EMT) in vector-like gauge theories. In this paper, we study the effect of the two-loop order corrections (and the three-loop order correction for the trace part of the EMT, which is available through the trace anomaly) on the lattice computation of thermodynamic quantities in quenched QCD. The use of the two-loop order coefficients generally reduces the t dependence of the expectation values of the EMT in the gradient-flow representation, where t is the flow time. With the use of the two-loop order coefficients, therefore, the t → 0 extrapolation becomes less sensitive to the fit function, the fit range, and the choice of the renormalization scale; the systematic error associated with these factors is considerably reduced.

Results and techniques for higher order calculations within the gradient-flow formalism

“…This was corroborated by the behavior of the t → 0 extrapolation for thermodynamical quantities evaluated in Ref. [21] using the two-loop result of Ref. [20].…”

Anisotropic pressure induced by finite-size effects in SU(3) Yang-Mills theory

“…First, unlike the analysis in Refs. [13,16], the results in the present study are not the continuum extrapolated one. However, the numerical results in this analysis are expected to be close to these after the continuum extrapolation because of the following reasons.…”

“…For guides of these results, we also show the continuum extrapolated values of P/T 4 , ε/T 4 , and (ε − 3P )/T 4 in the isotropic case obtained in Ref. [16] by the horizontal dashed lines for T /T c = 1.12, 1.40, 1.68, with the errors shown by the shaded region. From Fig.…”

“…First, when the lattice spacing becomes finer, our analysis converges to the continuum extrapolated analysis in Refs. [13,16], as the difference is proportional to a 2 for sufficiently small a. Second, the discretization effect is expected to be well suppressed already at N τ = 12.…”

Supersymmetric gradient flow in the Wess-Zumino model

“…From the construction presented above, it is obvious that the superfield action (14) is invariant under the off-shell SUSY transformation (6).…”