Resolve the anomalous dimension governing leading cutoff effects in the continuum extrapolation

Determine the anomalous dimension that governs the leading lattice‑spacing dependence in the Symanzik effective‑theory description of cutoff effects for hadronic vacuum polarization observables computed with non‑perturbatively O(a)‑improved Wilson quarks, so that the continuum extrapolation does not rely on an unresolved choice among candidate anomalous dimensions (e.g., 0.76 for spectral/sea contributions versus 0.395 for vector bilinears).

Background

The paper models the small‑a behaviour of lattice artifacts using Symanzik effective theory, where leading cutoff effects scale as a^n_min [α_s(1/a)]^Γ̂ with n_min=2 due to non‑perturbative O(a) improvement. For the action used, prior analyses suggest Γ̂=0.76 for spectral quantities and sea contributions, and Γ̂=0.395 for vector bilinears. These possibilities are incorporated into the fits, but the available lattice‑spacing range does not allow the authors to resolve which anomalous dimension controls the leading term.

Pinning down the relevant anomalous dimension is important because it affects the functional form of the continuum extrapolation and the interpretation of systematic uncertainties in high‑precision determinations of hadronic vacuum polarization contributions.