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arXiv · 2506.09537

A new approach to quark mass determination using the gradient flow

Hiromasa Takaura·Robert V. Harlander·Fabian Lange
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Abstract

We propose a new method to determine quark masses using ratios of the vacuum-expectation values (VEVs) of flowed quark bilinear operators. They can be expressed as functions of the flow time $t$ and the ${\overline {\rm MS}}$ quark mass $\overline{m}$, which can then be determined by matching with the corresponding lattice results. Motivated by this, we evaluate these VEVs perturbatively through next-to-leading order in the strong coupling. We provide the results as expansions in the limits of small and large $\overline{m}^2 t$. To this end, we develop a new expansion technique based on the Laplace transform. Additionally, we present numerical results with the exact mass dependence over a wide range of $\overline{m}^2t$. We discuss the expected perturbative precision for the mass determination based on our next-to-leading order perturbative calculations, and possible non-perturbative corrections.

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Hiromasa Takaura, Robert V. Harlander, Fabian Lange. 2025-06-11. A new approach to quark mass determination using the gradient flow. https://arxiv.org/abs/2506.09537

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