Stars as Laboratories for Fundamental Physics - MPP Theory Group

Solar Neutrinos 381
deficits in all detectors may give us the first indication for neutrino
oscillations and thus for nonvanishing neutrino masses and mixings.
Because of the statistically high significance of the anticorrelations
with solar activity of the Homestake results it is not entirely obvious
how to proceed with a quantitative test of the oscillation hypothesis
which can cause only a day-night or semiannual time variation. In the
present section a possible long-term variability of the solar neutrino
flux or its detection methods is ignored, i.e. the apparent anticorrelation
with solar activity at Homestake is considered to be a statistical
fluctuation. In Sect. 10.7 a possible explanation in terms of neutrino
interactions with the solar magnetic field is considered.
One may take the opposite point of view that the variability at
Homestake is a real effect, and that it is not related to neutrino magnetic
moments because that hypothesis requires fairly extreme values
for the dipole moments and solar magnetic fields (Sect. 10.7). An interpretation
of the data in terms of neutrino oscillations then becomes
difficult because one admits from the start that unknown physical effects
are either operating in the Sun, in the intervening space, or in
the detectors. One could argue perhaps that the apparent variability
of the Homestake data in itself was evidence that something was wrong
with this experiment. In this case one could still test the hypothesis
of neutrino oscillations under the assumption that the signal recorded
at Homestake was spurious in which case one must discard the entire
data set, not only parts of it as has sometimes been done. Ignoring
the Homestake data does not solve the solar neutrino problem, but its
significance is reduced.
Still, as no one has put forth a plausible hypothesis for a specific
problem with the Homestake experiment it is arbitrary to discard the
data. Admittedly, it is also arbitrary to consider the time variation
spurious even though standard statistical methods seem to reveal a
highly significant anticorrelation with solar activity.
10.6.2 Vacuum Oscillations
A formal treatment of vacuum neutrino oscillations was presented in
Sect. 8.3. If the observer is many oscillation lengths away from the
source, and if the neutrinos are produced with a broad spectrum of energies
from an extended source, one will observe an incoherent mixture
of the mass eigenstates. If one considers two-flavor oscillations ν e ↔ ν a
with ν a = ν µ , ν τ , or some hypothetical sterile flavor, the ν e flux is reduced
by a factor 1 − 1 2 sin2 2θ (vacuum mixing angle θ). Therefore,