The recent Fermilab experimental result, combined with the previous BNL one,
confirms the ongoing four-sigma tension between the SM theory prediction of
the anomalous magnetic moment (g-2) of the muon and the experimental value.
However, some lattice QCD calculations have produced results for the
hadronic vacuum polarization (HVP) contribution to the muon g-2 that solve
the discrepancy with the experiments without the need of BSM physics. If
this is confirmed, a new tension would arise either with the hadronic
cross-section at low energies or with global electroweak fits. Lattice QCD
results for the HVP contribution to the running of the electroweak couplings
can shed light on this possible tension.