$t\to 0$ extrapolation function in SF$t$X method for the energy-momentum tensor

Abstract

We theoretically clarify the functional form to be used in $t\to 0$ extrapolation in the small flow time expansion (SF$t$X) method for the energy-momentum tensor (EMT), which facilitates lattice simulation of the EMT based on the gradient flow. We argue that in the $t\to 0$ extrapolation analysis, lattice data should be fitted by a power function in $g(\mu (t))$, the flow time dependent running coupling, where the power is determined by the perturbation order we consider. From actual lattice data, we confirm the validity of the extrapolation function. Using the new extrapolation function, we present updated lattice results for thermodynamics quantities in quenched QCD; our results are consistent with the previous study [arXiv:1812.06444] but we obtain smaller errors due to reduction of systematic errors.

46 pages, 8 figures, version to appear in PTEP

References in corpus (12)

• The equation of state in (2+1)-flavor QCD
• Perturbative analysis of the gradient flow in non-abelian gauge theories
• Infinite N phase transitions in continuum Wilson loop operators
• Equation of State for SU(3) Gauge Theory via the Energy-Momentum Tensor under Gradient Flow
• Anisotropic pressure induced by finite-size effects in SU(3) Yang-Mills theory
• Correlations of Energy-Momentum Tensor via Gradient Flow in SU(3) Yang-Mills Theory at Finite Temperature
• Equation of state of a relativistic theory from a moving frame
• Latent heat and pressure gap at the first-order deconfining phase transition of SU(3) Yang-Mills theory using the small flow-time expansion method
• Distribution of Energy-Momentum Tensor around a Static Quark in the Deconfined Phase of SU(3) Yang-Mills Theory
• Study of energy-momentum tensor correlation function in $N_f=2+1$ full QCD for QGP viscosities
• Equation of state in (2+1)-flavor QCD at physical point with improved Wilson fermion action using gradient flow
• Latent heat and pressure gap at the first-order deconfining phase transition of SU(3) Yang-Mills theory using the small flow-time expansion method