First neutrino mass limit with CRES: A Bayesian analysis for Project 8 Phase II

Project 8 aims to determine the absolute neutrino mass scale from the shape of the tritium beta decay spectrum near its endpoint. For this purpose, the collaboration developed a novel frequency-based technique for measuring electron energies: Cyclotron Radiation Emission Spectroscopy (CRES). This talk presents the Bayesian analysis of the first tritium spectrum obtained with CRES, which contains 3770 events and no background events above the endpoint. We develop an analytic likelihood model of the beta spectrum and detector response, suitable for Bayesian inference with the Stan computing platform. Systematic uncertainties are propagated by incorporating them into prior distributions. Monte Carlo (MC) studies validate the likelihood model, with MC inputs sampled from priors. Separate MC studies demonstrate that priors chosen for the endpoint and neutrino mass are weakly informative. We report an endpoint result of E₀=18553±17 eV (literature: 18574 eV) and an electron-weighted neutrino mass limit of m_β<169 eV/c² (90% C.L.). A parallel frequentist analysis produced consistent results.