Characterize non-perturbative effects for large flow times

Determine the non-perturbative contributions to the vacuum expectation values of the flowed quark bilinear operators S(t) = ⟨\bar{χ}(t,x) χ(t,x)⟩ and R(t) = ⟨\bar{χ}(t,x) \overleftrightarrow{\slashed{\mathcal{D}}} χ(t,x)⟩ in Quantum Chromodynamics in the regime m^2 t ≫ 1, and assess their impact on quark mass determination using the gradient-flow framework.

Background

The paper proposes determining quark masses by matching lattice and perturbative results for ratios of vacuum expectation values of flowed quark bilinears within the gradient-flow formalism. For small m^2 t, non-perturbative effects can be analyzed via the small-flow-time expansion, and suitable observables can suppress the leading non-perturbative terms for light quarks.

For heavy quarks and in the opposite regime m^2 t ≫ 1, the authors note that the available understanding of non-perturbative effects is insufficient. Since the accuracy of mass extraction depends on controlling such effects across flow-time regimes, characterizing non-perturbative contributions at large m^2 t is necessary to validate the method and quantify systematic uncertainties.