Neutrino mass from bremsstrahlung endpoint in coherent scattering on nuclei

Abstract

We calculate the coherent bremsstrahlung process $\nu+{\cal N} \to {\cal N}+\nu+\gamma$ off a nucleus ${\cal N}$ with the aim of revealing the neutrino mass via the photon endpoint spectrum. Unfortunately, the large required power of a monochromatic neutrino source and/or large detector mass make it difficult to compete with traditional electron-spectrum endpoint measurements in nuclear $\beta$ decay. Our neutral-current process distinguishes between Dirac and Majorana neutrinos, but the change of the photon spectrum is of the order of $m_\nu/E_\nu$ and thus very small, despite the final-state neutrino coming to rest at the photon endpoint. So the "Dirac-Majorana confusion theorem" remains intact even if $E_\nu\gg m_\nu$ applies only for the initial state.