Realistic Earth matter effects and a method to measure small θ_{13} in the detection of supernova neutrinos

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  • 17 June 2008
Abstract
In this paper, we first calculate the realistic Earth matter effects on the detection of type II supernova neutrinos at the Daya Bay reactor neutrino experiment which is currently under construction. It is found that the Earth matter effects depend on the neutrino incident angle \theta, the neutrino mass hierarchy \Delta m_{31}^{2}, the crossing probability at the high resonance region inside the supernova, P_H, the neutrino temperature, T_{\alpha}, and the pinching parameter in the neutrino spectrum, \eta_{\alpha}. We give the expression for the dependence of P_H on the neutrino mixing angle \theta_{13}. With this we obtain the relations between \theta_{13} and the event numbers for various reaction channels of supernova neutrinos. Using these relations, we propose a possible way to measure \theta_{13} smaller than 1.5^\circ. Such a sensitivity cannot be achieved by the Daya Bay neutrino experiment (the sensitivity of the Daya Bay experiment is \theta_{13}\sim 3^\circ). Furthermore, we apply this method to other neutrino experiments, i.e., Super-K, KamLAND, SNO, LVD, MinBooNE, Borexino, and Double Chooz. We also study the energy spectra of the differential event numbers, \frac{dN}{dE}. We find that when the incident angle \theta increases the Earth matter effects become more and more obvious and that the energy spectrum may change with \theta_{13} in the range of 0^\circ\sim1.5^\circ, hence it is possible to study \theta_{13} in this value range by the energy spectrum of supernova neutrinos.

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