Up - down atmospheric neutrino flux asymmetry predictions for various neutrino oscillation scenarios

We compute up-down asymmetries for atmospheric neutrino induced electron and muon events in the SuperKamiokande detector for the following neutrino oscillation models: (A) maximally mixed νμ− ντ or νμ− νs, (B) maximally mixed νμ− νe, (C) threefold maximal mixing between νe, νμ and ντ , and (D) neutrino oscillations via Equivalence Principle or Lorentz invariance violation. We emphasise the role of different momentum cuts. The solar [1] and atmospheric [2]-[7] neutrino observations and the LSND [8] experiment provide strong evidence that neutrinos have nonzero masses and oscillate. Many specific neutrino mass scenarios have been proposed as explanations for some or all of these results. These explanations will be put to stringent tests in the next few years as more data are collected. In this paper we will focus on ways to experimentally test several different proposed explanations of the atmospheric neutrino anomaly. One good way to discriminate between these possible explanations is through the up-down asymmetry, with respect to zenith angle, of the detected charged leptons in experiments such as SuperKamiokande [9][10][11]. This idea was introduced in Ref.[9] and studied in detail in Ref.[10] in the context of the Exact Parity Model solution to the atmospheric neutrino anomaly [12]. The updown asymmetry idea was independently considered by the authors of Ref.[11] in the case of six possible neutrino oscillation models. As emphasised in Ref.[11], the sign and energy dependence of the up-down asymmetry will provide a useful diagnostic tool in differentiating the various explanations of the atmospheric neutrino anomaly. Reference [11] focussed on the energy dependence of the up-down asymmetry. A complementary approach is to study the asymmetry with various cuts in momentum [10][13]. This is useful because the Kamiokande and SuperKamiokande collaborations have divided their event sample into two classes (sub-GeV and multi-GeV) on the basis of momentum cuts. In the future, improved statistics may lead to the event sample being further subdivided with respect to momentum. The purpose of this paper is to study the up-down asymmetry expected at SuperKamiokande with various cuts in momentum for a variety of neutrino oscillation models. It is a priori interesting to consider various cuts in zenith angle as well as energy when analysing the up-down asymmetries of charged lepton events in SuperKamiokande [10]. A class of measures of the up-down asymmetry can be defined by introducing the quantities y e and y η μ, where y e ≡ N e N e , y μ ≡ N μ N μ . (1) Here N e (N +η e ) is the number of charged electrons produced in the detector with zenith angle cosΘ < −η (cosΘ > η). N μ are the analogous quantities for charged muons. The zenith angle Θ is defined so that Θ = 0 corresponds to downward travelling and Θ = π to upward travelling charged leptons. Different choices for η correspond to different cuts in zenith angle. (Note that Ref.[11] considered the η = 0 case in detail for several different models, while Ref.[10] studied different choices for η for the Exact Parity Model.) Since y e,μ are ratios of fluxes, they will be approximately free of the systematic errors arising from uncertain absolute fluxes (±30%) as well as uncertain μ/e flux ratios (± a few percent). For symmetry reasons, y e,μ ≃ 1 is expected in the absence of neutrino oscillations. If neutrino oscillations are present, however, then y e,μ 6= 1 is expected.