Photon Scattering in Muon Collisions

We estimate the benefit of muon colliders for photon physics. We calculate the rate at which photons are emitted from muon beams in different production mechanisms. Bremsstrahlung is reduced, beamstrahlung disappears, and laser backscattering suffers from a bad conversion of the incoming to the outgoing photon beam in addition to requiring very short wavelengths. As a consequence, the cross sections for jet photoproduction in $\mu p$ and $\mu^+\mu^-$ collisions are reduced by factors of 2.2 and 5 compared to $ep$ and $e^+e^-$ machines. However, the cross sections remain sizable and measurable giving access to the photon and proton parton densities down to $x$ values of $10^{-3}$ to $10^{-4}$.