HVP contribution to Running Coupling and Electroweak Precision Science

We investigate the impact of the latest Mainz/CLS collaboration’s result for the hadronic vacuum polarization (HVP) on the electroweak (EW) precision science. The subject is closely related to the muon g-2 via the HVP. Both precision tests come under scrutiny with respect to physics Beyond the Standard Model. Our HVP calculation is used for the running electromagnetic coupling at low energy and linked at various matching energies to the higher energy running evaluated by phenomenological approaches. We predict the electromagnetic coupling at the Z-pole (alpha(Mz^2)), providing a lattice-driven input to EW-global fits. Our preliminary alpha(Mz^2) is stable for a wide range of matching energies and comes with various systematics taken into account and consistent with phenomenological estimates.