Identification of neutrino bursts associated to supernovae with Real-time Test Statistic (RTS$^2$) method

This paper proposes a new approach for the selection of low-energy neutrino bursts, such as the ones detected after a supernova. It exploits the temporal structure of the expected signal with respect to the more diffuse background by defining a "Real-time Test Statistic" (RTS) that would allow identifying very weak signals, hard to select using standard clustering methods. For a given background rate, the new method (RTS$^2$: RTS for Supernovae) increases signal efficiency while keeping the same false alarm rate for Poisson-distributed background. By adding a spatial penalty term to the definition of RTS, one can also reject spatially-correlated backgrounds such as the ones due to spallation events. Furthermore, the method is easy to implement in a real-time monitoring system as RTS can be computed recursively for successive events, and it can be easily adapted for detectors of all scales that may want to send prompt alerts e.g. through SNEWS 2.0 network.