Rocks, Water and Noble Liquids: Unfolding the Flavor Contents of Supernova Neutrinos

Measuring core-collapse supernova neutrinos, both from individual supernovae within the Milky Way and from past core collapses throughout the Universe (the diffuse supernova neutrino background, or DSNB), is one of the main goals of current and next generation neutrino experiments. Detecting the heavy-lepton flavor (muon and tau types, collectively $\nu_x$) component of the flux is particularly challenging due to small statistics and large backgrounds. While the next galactic neutrino burst will be observed in a plethora of neutrino channels, allowing to measure a small number of $\nu_x$ events, only upper limits are anticipated for the diffuse $\nu_x$ flux even after decades of data taking with conventional detectors. However, paleo-detectors could measure the time-integrated flux of neutrinos from galactic core-collapse supernovae via flavor-blind neutral current interactions. In this work, we show how combining a measurement of the average galactic core-collapse supernova flux with paleo detectors and measurements of the DSNB electron-type neutrino fluxes with the next-generation water Cherenkov detector Hyper-Kamiokande and the liquid noble gas detector DUNE will allow to determine the mean supernova $\nu_x$ flux parameters with precision of order ten percent.