Maximal νe→νs solution to the solar neutrino problem: just-so, MSW or energy independent?
Introduction
Five experiments have measured solar neutrino fluxes that are significantly deficient relative to standard solar model expectations 1, 3. Four out of the five experiments find overall fluxes that are roughly 50% of the theoretical predictions. (The Chlorine experiment sees a larger deficit.) Maximal mixing between the electron neutrino and a sterile flavour has been proposed as the underlying explanation for these observations [4]. This oscillation mode produces a 50% reduction in the day-time solar neutrino flux for a large range of the relevant Δm2 parameter:The upper bound arises from the lack of disappearence in the CHOOZ experiment [5]4, while the lower bound is a rough estimate of the transition region between the totally averaged oscillation regime and the “just-so” regime.
The very special feature of maximal mixing between the νe and a sterile flavour is well motivated by the Exact Parity Model (also known as the mirror matter model) 4, 7. In this theory, the sterile flavour maximally mixing with the νe is identified with the mirror electron neutrino. The characteristic maximal mixing feature occurs because of the underlying exact parity symmetry between the ordinary and mirror sectors. The potentially maximal mixing observed for atmospheric muon neutrinos is beautifully in accord with this framework [8], which sees the atmospheric neutrino problem resolved through `νμ→ mirror partner' oscillations.5 The Exact Parity Model therefore provides a unified understanding of the solar and atmospheric neutrino problems: each is due to maximal oscillations of the relevant ordinary neutrino into its mirror partner. Note that the mirror neutrino scenario is phenomenologically similar to the pseudo-Dirac scenario [9].
The chlorine result is not quantitatively consistent with this view of the origin of the solar neutrino anomaly, it being about 30% too low. We await with interest some new experiments that have the capacity to double-check this result.
The purpose of this paper is to make a more detailed analysis of the maximal νe→νs solution to the solar neutrino problem. We do so because of two recent developments: (i) the clarification from Guth et al. [10]that a day-night asymmetry generically exists even for maximal mixing (due to Earth regeneration which affects the night-time events) and (ii) the observation by SuperKamiokande of an interesting feature in the recoil electron energy spectrum for E>13 MeV [3]. We will calculate the day-night asymmetry and the recoil electron spectrum as a function of Δm2 in the range 10−3 eV2 to 10−11 eV2. We will draw the important conclusion that the maximal νe→νs scenario has a larger number of characteristic and testable features than realised hitherto. We will summarise the “smoking gun” experimental signatures for this scenario in the concluding section.
Section snippets
Day-night asymmetry
Guth et al. [10]have recently provided a very lucid account of the physics of the day-night effect for maximally mixed solar neutrinos. This is important for the maximal νe→νs scenario for two reasons. First, high statistics experiments such as SuperKamiokande have an on-going programme to measure the solar neutrino day-night asymmetry. It had been previously and erroneously thought that maximally mixed νe's would not give rise to a day-night asymmetry. We will calculate this asymmetry for the
Recoil electron spectrum
An interesting situation exists at present with regard to the recoil electron energy spectrum measured by SuperKamiokande [3]. If the hep neutrino flux predictions from standard solar models are taken at face value, then SuperKamiokande has evidence for a distortion in the boron neutrino induced recoil energy spectrum for energies greater than about 13 MeV. We will call this the “spectral anomaly”. More specifically, the spectral anomaly is an excess of events relative to what would be expected
Conclusion
Maximal νe→νs oscillations have been proposed as a solution to the solar neutrino problem 4, 9. This idea can be well-motivated by the mirror matter hypothesis [4], or by the pseudo-Dirac neutrino idea [9]. In this paper we have demonstrated the following points:
- 1.
Across the allowed Δm2 spectrum, maximal νe→νs oscillations lead to three qualitatively different behaviours for the νe survival probability; just-so, MSW or approximately energy independent. These occur in the Δm2/eV2 ranges
Acknowledgements
R.M.C. is supported by the Commonwealth of Australia and the University of Melbourne. R.F. and R.R.V. are supported by the Australian Research Council. We thank M.B. Smy for a useful communication.
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