Unbinned test of time-dependent signals in real-time neutrino oscillation experiments

Real-time neutrino oscillation experiments such as Super-Kamiokande (SK), the Sudbury Neutrino Observatory (SNO), the Kamioka Liquid scintillator Anti-Neutrino Detector (KamLAND), and Borexino, can detect time variations of the neutrino signal, provided that the statistics is sufficiently high. We quantify this statement by means of a simple unbinned test, whose sensitivity depends on the variance of the signal in the time domain, as well as on the total number of signal and background events. The test allows a unified discussion of the statistical uncertainties affecting current or future measurements of eccentricity-induced variations and of day–night asymmetries (in SK, SNO, and Borexino), as well as of reactor power variations (in KamLAND).