Speaker
Description
A detailed understanding of the time kernels entering the time-momentum representation of hadronic vacuum polarization (HVP) observables is a prerequisite for precision lattice determinations of a broad class of quantities. Building on recent analytical developments, we discuss the properties of these kernels and their role in controlling the time integral relevant to HVP observables.
As a first application, we present our complete results for the first high-precision determination of the next-to-leading order HVP contribution to the anomalous magnetic moment of the muon. Using more than 30 independent CLS gauge ensembles with $\mathrm{O}(a)$-improved Wilson fermions, together with window observables and dedicated treatments of several sources of systematic uncertainty, including short-distance cutoff effects and finite-volume corrections, we achieve a final precision better than $0.6\%$.
Finally, we report on ongoing efforts to extend this framework to other low-energy hadronic vacuum polarization observables, including the anomalous magnetic moment of the electron and related quantities, such as the slope of the vacuum polarization function at vanishing momentum. These studies include observables sensitive to the low-momentum structure of the vacuum polarization function, where lattice determinations become increasingly challenging due to long-distance noise.