Matter Effects on Neutrino Many Body Flavor Evolution Using the Full Hamiltonian

Neutrino flavor evolution in dense astrophysical media, such as binary neutron star mergers and core-collapse supernovae, is sensitive to neutrino-matter interactions. Dense media are theoretically predicted to exhibit appreciable neutrino-neutrino interaction effects due to the high number density of neutrinos. In this project, we perform a numerical simulation that incorporates both neutrino-neutrino and matter-neutrino interaction Hamiltonian terms, derived from the Standard Model effective Lagrangian; as far as we are aware, this study is the first to account for both interaction terms. Until recently, simulations of neutrino many-body systems have exclusively used a truncated Hamiltonian that neglects terms that mediate momentum changing scattering processes. We combine these self interaction Hamiltonian terms with the terms that mediate scattering off electrons and nucleons, treating these matter particles as a classical background field. With this Hamiltonian, we study neutrino many-body evolution in a finite, isotropic, inhomogeneous medium in equilibrium. This framework aims to capture effects such as the Mikheyev-Smirnov-Wolfenstein (MSW) resonance in a many-body context, opening the door to future investigations of flavor evolution in extreme astrophysical conditions.