Stars as Laboratories for Fundamental Physics - MPP Theory Group

Solar Neutrinos 383
The ν e survival probability as a function of energy is shown in
Fig. 10.17 for ∆m 2 ν = 0.8×10 −10 eV 2 and sin 2 2θ = 0.8. The Sun is
treated as a point-like source because the extension of its neutrinoproducing
core is minute relative to the oscillation length of order the
Earth-Sun distance. The solid line is for the minimum, the dashed line
for the maximum annual distance to the Sun. The nearly monochromatic
beryllium neutrinos (E ν = 0.862 MeV) easily retain their phase
relationship because they are distributed in energy only over a width
of about 2 keV (Fig. 10.4). Therefore, one would expect a pronounced
annual flux variation which is not observed, thereby reducing the allowed
range of masses and mixing angles where long-wavelength oscillations
could solve the solar neutrino problem. The analysis of Barger,
Phillips, and Whisnant (1992) and more recently of Krastev and Petcov
(1994) reveals that there remain a few small parameter pockets with
sin 2 2θ around 0.8−1 and ∆m 2 ν around 0.6−0.9×10 −10 eV 2 . Krastev
and Petcov (1994) also conclude that oscillations into sterile neutrinos
are slightly disfavored.
While the spectral deformation of the 8 B neutrino spectrum is quite
dramatic, the spectrum of recoil electrons smears out most of this effect
(Fig. 10.18). Notably, above the Kamiokande detection threshold of
about 7 MeV the expected distortion is too small to be detected and
Fig. 10.18. Spectrum of 8 B neutrinos and of recoil electrons. Dotted lines:
Standard spectrum from Fig. 10.12. Solid lines: Surviving ν e spectrum after
oscillations (suppression factor from Fig. 10.17) and modified electron recoil
spectrum. For oscillations into ν µ,τ one would have to include their neutralcurrent
scattering on electrons with a cross section about 1 6 that of ν e.