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

Iritani, Takumi (Theoretical Research Division, Nishina Center, RIKEN, Wako 351-0198, Japan) ; Kitazawa, Masakiyo (Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan) (J-PARC Branch, KEK Theory Center, Institute of Particle and Nuclear Studies, KEK, 203-1 Shirakata, Tokai, Ibaraki 319-1106, Japan) ; Suzuki, Hiroshi (Department of Physics, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan) ; Takaura, Hiromasa (Department of Physics, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan)

28 February 2019

Abstract: Recently, Harlander et al. [Eur. Phys. J. C 78 , 944 (2018)] have computed the two-loop order (i.e., NNLO) coefficients in the gradient-flow representation of the energy–momentum 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 dependence of the expectation values of the EMT in the gradient-flow representation, where is the flow time. With the use of the two-loop order coefficients, therefore, the 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.

Published in: PTEP 2019 (2019) 023B02
Published by: Oxford University Press/Physical Society of Japan
DOI: 10.1093/ptep/ptz001
arXiv: 1812.06444
License: CC-BY-3.0

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