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 $g(μ(t))$, 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.
Large-Momentum Effective Theory's Asymptotic Extrapolation vs the Inverse Problem
National Taiwan University（国立台湾大学）；National Center for Theoretical Sciences（国家理论科学中心）；Brookhaven National Laboratory（布鲁海文国家实验室）；University of Maryland, College Park（马里兰大学帕克分校）；Argonne National Laboratory（阿贡国家实验室）；South China Normal University（华南师范大学）；Universität Regensburg（雷根斯堡大学）；Shanghai Jiao Tong University（上海交通大学）
Baryon Light-Cone Distribution Amplitudes from Lattice QCD: Formalism, Renormalization, Extrapolation, and Matching
Shanghai Jiao Tong University（上海交通大学）；Institute of High Energy Physics, CAS（中国科学院高能物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Adam Mickiewicz University（亚当·密茨凯维奇大学）；South China Normal University（华南师范大学）
