Probing the muon g-2 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 g-2 through the study of high-energy processes such as mu+ mu- -> h gamma. This high-energy test would be of the utmost importance to shed light on the long-standing muon g-2 anomaly as it is not affected by the hadronic and experimental uncertainties entering the current low-energy determination of the muon g-2. Furthermore, we show that the current bound on the muon electric dipole moment can be improved by three orders of magnitude, down to few x 10^-22 e cm.