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<p>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 <i>N</i><sub>F</sub>-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.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月21日

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  • R. V. Harlander,
  • R. H. Mason

摘要

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 NF-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.