# Electrons and X-rays to Muon Pairs (EXMP)
###### Abstract  
One of the challenges of future muon colliders involves the production of muon beams carrying high phase space densities. In particular, the muon beam normalised transverse emittance is a relevant figure of merit used to meet luminosity requests. A typical issue impacting the achieved transverse emittance in muon collider schemes, thus far considered, is the phase space dilution caused by the Coulomb interaction of primary particles propagating into the target where muons were generated. In this study, we present a new scheme(named electrons and X-rays to muon pairs) for muon beam generation occurring in a vacuum via interactions of electron and photon beams. Setting the center of mass energy at about twice the threshold (i.e., around 350 MeV), the normalised emittance of the muon beam generated via muon pair production reaction (\(e^{-}+\gamma\to e^{-}+\mu^{+}+\mu^{-}\)) is largely independent on the emittance of the colliding electron beam and is set basically by the excess of transverse momentum in the muon pair creation. In absence of any other mechanism for emittance dilution, the resulting muon beam, with energy in the range of a few tens of GeV, is characterised by an ultra-low normalised transverse RMS emittance of a few nm rad, corresponding to a geometrical emittance below 10 \(\pi\) pm rad. This opens up the way to a new muon collider paradigm based on muon sources conceived with primary colliding beams delivered by 100 GeV-class energy recovery LINACs interacting with hard-X ray free electron lasers. The challenge is to achieve the requested luminosity of the muon collider adopting a strategy of low muon fluxes/currents combined to ultra-low emittances, to largely reduce the levels of muon beam-induced backgrounds. muon collider; high efficiency XFEL; FELs for colliders; low emittance muon beam photoproduction 20222123149  
study, implementing the idea of muon photo-production in a different environment, that of electron-photon collisions, with the scheme electrons and X-rays to muon pairs (EXMP). The reason why pertains not really to the larger cross section of the \(e\), \(\gamma\) reaction, with respect to \(p,\ \gamma\) (the increase is quite modest), but in the possibility of running an electron-photon collider at a much larger luminosity than a proton-photon collider, such as in the HPC scheme. The focal spot size of a 100-GeV-class electron beam colliding in-vacuum with a counterpropagating photon beam can be much smaller than that of a TeV proton beam stored in a machine, such as LHC, as well as that of an electron-positron collider final focus. The former is actually limited by the minimum beta achievable in a proton storage ring due to cm-long proton bunches, the latter is actually limited by the beam-beam interaction, originated by the presence of colliding charged particles, focused into a tight focal region. In cases of electron-photon collisions, none of these effects are actually present since electrons and photons interact through two-particle QED reactions without a significant collective e.m. field effect impacting the beam propagation through the interaction region. Thus, the maximum focus achievable in the collision region is dictated by the final focus beam optics, electron and photon bunch lengths, and transverse emittances of the two colliding beams. In order to reach center of mass (CM) energies in excess of 300 MeV to which the muon pair production total cross section exceeds a few hundred nano barns, we were forced to consider electrons with energies higher than 200 GeV and photons with energy in the 60-150 keV range.