Probing Anomalous Higgs Coupling through mu+ mu- --> H gamma

The process mu+ mu- --> H gamma, though small compared to the resonance process, could be observable at proposed muon colliders, given expected integrated luminosities. The apparently leading diagrams occur at tree-level, and are proportional to the Higgs-muon coupling. We show, however, that the one-loop contribution is comparable to the tree-level amplitude. Furthermore, the one-loop diagrams, unlike those at tree-level, could be greatly enhanced by possible anomalous Higgs-top quark or Higgs-gauge boson couplings. For a 500 GeV unpolarized muon collider, the total cross section for H-gamma associated production approaches 0.1 fb.