The physics case for neutrino-neutrino collisions

Addressing the mass origin and properties of neutrinos is of strong interest to particle physics, baryogenesis and cosmology. Popular explanations involve physics beyond the standard model, for example, the dimension-5 Weinberg operator or heavy Majorana neutrinos arising from ``seesaw'' models. The current best direct limits on the electron neutrino mass, derived from nuclei beta decay or neutrinoless double beta decay processes, are at the sub-electronvolt level. Here we propose a novel neutrino neutrino collider where the neutrino beam is generated from TeV scale muon decays. Such collisions can happen between either neutrinos and anti-neutrinos, or neutrinos and neutrinos. We find that with a tiny integrated luminosity of about $10^{-5}$/fb we can already expect to observe direct neutrino anti-neutrino annihilation, $\nu\bar{\nu}\rightarrow {\rm Z}$, which also opens the door to explore neutrino related resonances $\nu\bar{\nu}\rightarrow {\rm X}$. The low luminosity requirement can accommodate a relatively large emittance muon beam. Such a device would also allow for probing heavy Majorana neutrino and effective Majorana neutrino mass through $\nu\nu\rightarrow {\rm H H}$ to a competitive level, for both electron and muon types.