Probing the g-2 muon anomaly with the Higgs boson at a muon collider

We point out that heavy new physics contributions in leptonic dipole moments and high-energy cross sections of lepton pairs into Higgs bosons and photons are connected model-independently. In particular, we demonstrate that a muon collider, running at center-of-mass energies of several TeV, can provide a unique test of new physics in the muon through the study of high-energy processes such as . This high-energy test would be of the utmost importance to shed light on the longstanding muon anomaly as it is not affected by the hadronic and experimental uncertainties entering the current low-energy determination of the muon . Furthermore, we show that the current bound on the muon electric dipole moment can be improved by three orders of magnitude, down to .