In the pursuit of direct detection of new physics, there is an in- creasing number of experiments making more accurate determinations of cer- tain key observables. One of the prime examples at the moment is the E989 project at Fermilab, which recently published its first results for the anomalous magnetic moment of the muon, confirming the BNL E821 experiment and the long-standing tension with the Standard Model determination.
This discrepancy poses fascinating questions about the fundamental reasons behind it and can affect other sectors of the Standard Model too. In particular, the link between the electromagnetic coupling and the anomalous magnetic moment may affect the indirect determination of the Higgs-boson mass provided by the electroweak global fits, where the electromagnetic coupling enters.
However, the current studies of the muon are not the only avenue to look for new physics. For example, the new experiments P2 in Mainz and Moller and Solid in JLab strive for a more accurate value of the weak mixing angle, which is essential in studying parity violation and neutrino scattering.
The primary hurdle for an accurate theoretical determination of the anoma- lous magnetic moment and the running of the electromagnetic coupling and weak mixing angle is the non-perturbative or hadronic contributions of QCD at low energies. In this talk, the Mainz group approach to compute these hadronic effects from first principles using lattice QCD simulations is presented. The re- sults are compared with other data-driven determinations, and the consequences to the electroweak global fits are explained.