Mono-chromatic single photon events at the muon collider

The cross section for lepton pair annihilation into a photon and a dark photon or an axion-like particle is constant for large center-of-mass energies because some of the portal operators coupling Standard Model and dark sector are proportional to the energy. Feebly coupled though they are, these portal operators will be enhanced by the large center-of-mass energy made available by a muon collider and thus provide the ideal example of possible physics beyond the Standard Model to be studied with such a machine. We discuss the characteristic signature of the presence of these operators: mono-chromatic single photon events for the two benchmarks of having center-of-mass energies of 3 and 10 TeV and integrated luminosity of, respectively, 1 and 10 ab$^{-1}$. We find that an effective scale of the portal operator as large as $\Lambda=112$ TeV for an axion-like particle and $\Lambda=141$ TeV for a dark photon can be separated from the background with a confidence level of 95% in the first benchmark; these interaction scales can be raised to $\Lambda=375$ TeV and $\Lambda=459$ TeV in the case of the second benchmark. The signal for the pseudo scalar particle can be distinguished from that of the spin-1 with about 500 events. The response of the detector to high-energy photons is examined.