Stars as Laboratories for Fundamental Physics - MPP Theory Group

384 Chapter 10
so the spectral shape measured at Kamiokande (Fig. 10.13) does not
further constrain the vacuum oscillation hypothesis.
Barger, Phillips, and Whisnant (1992) as well as Krastev and Petcov
(1994) gave precise confidence contours in the sin 2 2θ-∆m 2 ν-plane
where the solar neutrino problems are solved. However, some of the
input information involves large systematic uncertainties so that it is
well possible that, for example, a revised S 17 factor would shift the
allowed regions beyond their stated confidence contours—see, for example,
Berezhiani and Rossi (1995). The main message is that there remain
parameters in the quoted range where vacuum oscillations (“just
so oscillations”) could reconcile all solar flux measurements with the
standard flux predictions, except for the apparent anticorrelation of
the Homestake data with solar activity.
10.6.3 Resonant Oscillations (MSW Effect)
The solar neutrino problem has become tightly intertwined with the issue
of neutrino oscillations thanks to the work of Mikheyev and Smirnov
(1985) who showed that even for small mixing angles one can achieve
a large rate of flavor conversion because of medium-induced “resonant
oscillations.” This “MSW effect” was conceptually and quantitatively
discussed in Sect. 8.3.
For a practical application to the solar neutrino problem two main
features of the MSW effect are of great relevance. One is the bathtubshaped
suppression function of Fig. 8.10 which replaces a constant
reduction factor (short-wavelength vacuum oscillations) or the wiggly
shape of Fig. 10.17 (long-wavelength vacuum oscillations). It implies
that ν e ’s of intermediate energy can be reduced while low- and highenergy
ones are left relatively unscathed. This is what appears to be indicated
by the observations with the beryllium neutrinos more strongly
suppressed than the pp or boron ones.
Another important feature are the triangle-shaped suppression contours
in the sin 2 2θ-∆m 2 ν-plane for a fixed neutrino energy (Fig. 8.9).
Each experiment produces its own triangular band of neutrino parameters
where its measured rate is reconciled with the standard flux prediction.
As the signal in different detectors is dominated by neutrinos
of different energies, these triangles are vertically offset relative to one
another and so there remain only a few intersection points where all
experimental results are accounted for. Therefore, as experiments with
three different spectral responses are now reporting data the MSW solution
to the solar neutrino problem is very well constrained.