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

TL;DR

This paper clarifies the appropriate functional form for $t o 0$ extrapolation in the SF$t$X method for the energy-momentum tensor, improving lattice simulation accuracy and reducing systematic errors.

Contribution

It introduces a power function fit based on the flow-dependent coupling for $t o 0$ extrapolation, validated with lattice data, enhancing the precision of thermodynamics calculations in quenched QCD.

Findings

The proposed extrapolation function is validated with lattice data.

Updated lattice results show smaller errors in thermodynamics quantities.

Results are consistent with previous studies but with improved accuracy.

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.