Quark-mass effects in gradient-flow observables through next-to-next-to-leading order in QCD

TL;DR

This paper computes vacuum expectation values of key QCD operators in the gradient-flow formalism at NNLO, including effects of heavy quark masses, aiding precise lattice QCD parameter extraction.

Contribution

It presents the first NNLO calculations of these operators with heavy quark mass effects in the gradient-flow formalism, applicable to charm and bottom quarks.

Findings

Numerical results for vacuum expectation values at NNLO.

Inclusion of heavy quark mass effects in the calculations.

Results are presented in a mass-independent form.

Abstract

We provide results for the vacuum expectation values of the flowed action density, the quark condensate, and the quark kinetic operator in the gradient-flow formalism. We work in $N_\text{F}$-flavor QCD, keeping the heaviest quark massive and all others massless. The vacuum expectation values of these operators are calculated numerically through next-to-next-to-leading order QCD, providing important input for the extraction of fundamental QCD parameters from lattice calculations. While the focus is on charm- and bottom-quark mass effects, we provide the results in a form that is independent of the specific quark mass.