Factorization vs. Non-Factorization: S-Matrix Corrections for Precision Neutrino Physics

The standard treatment of neutrino oscillations usually relies on factorization which assumes neutrino production, propagation, and detection are independent processes. As a consequence, the total probability is given by the product of production, oscillation and detection probabilities. As next-generation experiments are bringing neutrino physics to a high level of precision, the validity of this assumption must be checked. We present an S matrix treatment of the entire experimental chain, pion decay, neutrino propagation, and nucleon interaction, as a single, coherent quantum process. Our results reveal non-factorizable terms arising from spin and angular correlations between production and detection final states.In the $\Delta L=0$ channel, these corrections introduce a $\sim 1\%$ systematic shift in the energy spectrum and a non-vanishing azimuthal asymmetry, important to be taken into account for precision measurements of $\delta_{CP}$. For the $\Delta L=2$ Majorana channel, we demonstrate that the S-matrix formalism is generating an azimuthal modulation that provides a direct way to access to the Majorana CP phases, which remain hidden in standard factorized effective mass approximations.