Quantized Nuclear Recoil in the Search for Sterile Neutrinos in Tritium Beta Decay with PTOLEMY

The search for keV-scale sterile neutrinos in tritium beta decay is made possible through the theoretically allowed small admixture of electron flavor in right-handed, singlet, massive neutrino states. A distinctive feature of keV-scale sterile-neutrino–induced threshold distortions in the tritium beta spectrum is the presence of quantized nuclear-recoil effects, as predicted for atomic tritium bound to two-dimension materials such as graphene. The sensitivities to the sterile neutrino mass and electron-flavor mixing are considered in the context of the PTOLEMY detector simulation with tritiated graphene substrates. The ability to scan the entire tritium energy spectrum with a narrow energy window, low backgrounds, and high-resolution differential energy measurements provides the opportunity to pinpoint the quantized nuclear-recoil effects. providing an additional tool for identifying the kinematics of the production of sterile neutrinos. Background suppression is achieved by transversely accelerating electrons into a high magnetic field, where semi-relativistic electron tagging can be performed with cyclotron resonance emission RF antennas followed by deceleration through the PTOLEMY filter into a high-resolution differential energy detector operating in a zero-magnetic-field region. The PTOLEMY-based approach to keV-scale searches for sterile neutrinos involves a novel precision apparatus utilizing two-dimensional materials to yield high-resolution, sub-eV mass determination for electron-flavor mixing fractions of  (Formula presented.)  and smaller.