The Forward Neutrino Flux and its Secondaries at a 10 TeV Muon Collider

Muon decays in a muon collider ring would produce TeV neutrino and antineutrino beams of electron and muon flavor. We study this flux in the forward $\mu^+$ and $\mu^-$ beam directions at a 10 TeV muon collider, introducing MINT, a dedicated Monte Carlo simulation to model neutrino fluxes including the muon beam dynamics. We find that a benchmark detector at 5 km from the interaction point would see about $\mathcal{O}(10^{9})$ neutrino interactions per year in a $\sim3$ tonne fiducial volume with a beam spot size of $\mathcal{O}(1)$ meter. We calculate the number of secondary muons and neutrinos generated by neutrino interactions in the rock upstream of the forward detectors and find that about two secondary high-energy and highly polarized muons from the rock would cross each detector per bunch crossing. Neutrino productions of charmed mesons and taus in the rock generate a small $\nu_\tau+\bar\nu_\tau$ secondary flux, with $\mathcal{O}(0.2)$ events per year in the detectors, likely too small to be observed. Wrong-sign neutrinos from similar processes, such as $\nu_e+\bar\nu_\mu$ in the $\mu^-$ beam, are more numerous but still of $\mathcal{O}(10^{-9})$ of the number of TeV neutrino interactions. Finally, we outline how the large forward neutrino exposure can be used to search for beyond-the-Standard-Model particles produced in neutrino interactions, with examples of heavy neutral leptons coupled to electron and muon flavors through mixing or electromagnetic dipole operators.