Inference solves a boundary-value collision problem, with relevance to neutrino flavor transformation

Abstract

Understanding neutrino flavor transformation in dense environments such as core-collapse supernovae (CCSN) is critical for inferring nucleosynthesis and interpreting a detected neutrino signal. The role of direction-changing collisions in shaping the neutrino flavor field in these environments is important and poorly understood; it has not been treated self-consistently. There has been progress, via numerical integration, to include the effects of collisions in the dynamics of the neutrino flavor field. While this has led to important insights, integration is limited by its requirement that full initial conditions must be assumed known. On the contrary, feedback from collisions to the neutrino field is a boundary value problem. Numerical integration techniques are poorly equipped to handle that formulation. This paper demonstrates that an inference formulation of the problem can solve a simple collision-only model representing a CCSN core -- without full knowledge of initial conditions. Rather, the procedure solves a two-point boundary value problem with partial information at the bounds. The model is sufficiently simple that physical reasoning may be used as a confidence check on the inference-based solution, and the procedure recovers the expected model dynamics. This result demonstrates that inference can solve a problem that is artificially hidden from integration techniques -- a problem that is an important feature of flavor evolution in dense environments. Thus, it is worthwhile to explore means of augmenting the existing powerful integration tools with inference-based approaches.