Realistic Earth matter effects and a method to acquire information about smallθ13in the detection of supernova neutrinos

Abstract

In this paper, we first calculate the realistic Earth matter effects in 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 θ, the neutrino mass hierarchy ∆m 2 31 , the crossing probability at the high resonance region inside the supernova, PH , the neutrino temperature, Tα, and the pinching parameter in the neutrino spectrum, ηα. We also take into account the collective effects due to neutrino-neutrino interactions inside the supernova. With the expression for the dependence of PH on the neutrino mixing angle θ13, we obtain the relations between θ13 and the event numbers for various reaction channels of supernova neutrinos. Using these relations, we propose a possible method to acquire information about θ13 smaller than 1.5• . Such a sensitivity cannot yet be achieved by the Daya Bay reactor neutrino experiment which has a sensitivity of the order of θ13 ∼ 3• . Furthermore, we apply this method to other neutrino experiments, i.e. Super-K, SNO, KamLAND, LVD, MinBooNE, Borexino, and Double-Chooz. We also study the energy spectra of the differential event numbers, dN/dE.

Acquiring information about neutrino parameters by detecting supernova neutrinos

“…4, we plot P H as a function of 13 for different values of E and t. It is found that at some values of 13 , which depends on the energy of SN neutrinos, P H begins to change very rapidly with 13 at t ¼ 4 s, and the behavior of the P H dependence on 13 is different from that given in Ref. [11]. These differences are attributable to the different SN matter effects when the shock effects are included in the consid-TABLE I.…”

“…Defining P ð " P Þ as the probability that the (anti)neutrino ð " Þ remains as ð " Þ after the collective effects, Dasgupta et al [6] introduced a much simplified picture to explain the characteristics of the collective effects which we followed in our earlier paper [11], i.e., P ¼ " P ¼ 1 in the case of normal mass hierarchy; and " P ¼ 1,…”

“…where VðxÞ is the potential e experiences due to the matter density ðxÞ inside the Earth [11,42,48] VðxÞ ¼ ffiffiffi 2…”

“…[11], we studied the Earth matter effects in the detection of SN neutrinos at the Daya Bay experiment and proposed a possible method to acquire information about the neutrino mixing angle 13 smaller than 1.5 which is difficult to access in reactor neutrino experiments. We defined the ratio R as the event number of e over that of " e .…”

“…Furthermore, in order to reduce the uncertainties of unknown parameters in SN neutrino fluxes such as luminosity, temperature, and pinching parameter, we will define the ratio of the event number of SN neutrinos for the charged-current reaction detected after 1 s over that detected before 1 s (this is different from the ratio considered in Ref. [11]). With this ratio, we may identify the mass hierarchy, Ám 2 31 > 0 vs Ám 2 31 < 0, and acquire information about 13 .…”