Damping of supernova neutrino transitions in stochastic shock-wave density profiles

Supernova neutrino flavour transitions during shock-wave propagation are known to encode relevant information not only about the matter density profile but also about unknown neutrino properties, such as the mass hierarchy (normal or inverted) and the mixing angle θ₁₃. While previous studies have focused on 'deterministic' density profiles, we investigate the effect of possible stochastic matter density fluctuations in the wake of supernova shock-waves. In particular, we study the impact of small-scale fluctuations on the electron (anti)neutrino survival probability, and on the observable spectra of inverse beta-decay events in future water Cherenkov detectors. We find that such fluctuations, even with relatively small amplitudes, can have significant damping effects on the flavour transition pattern, and can partly erase the shock-wave imprint on the observable time spectra, especially for \sin^2 \theta_{13} \gtrsim {\mathcal

O}(10^{-3}) .