Stars as Laboratories for Fundamental Physics - MPP Theory Group

Neutrino Oscillations 293
Apparently, the anomaly observed at the Kamiokande water Cherenkov
detector (Hirata et al. 1992; Fukuda et al. 1994) can be explained
in terms of oscillations for neutrino parameters in the shaded
area in Fig. 8.6; the best-fit value is indicated by a star. These results
are a combined fit for the sub-GeV and multi-GeV data as published
by the Kamiokande collaboration (Fukuda et al. 1994). The oscillation
hypothesis appears to be buttressed by a zenith-angle variation of
the effect observed in Kamiokande’s multi-GeV data sample although
the claimed significance of this effect has been critiqued, e.g. by Fogli
and Lisi (1995) and by Saltzberg (1995).
The required large mixing angle as well as the exclusion regions
of the other experiments make it appear dubious that the anomaly is
caused by oscillations. Still, it is a serious effect that cannot be blamed
easily on problems with the Kamiokande detector. Also, the reliability
of some of the exclusion areas in Fig. 8.6 may be called into question,
notably because of their dependence on absolute flux normalizations.
The intuition against a large ν µ -ν τ mixing angle may be misguided.
In the future, it will be possible to test the relevant regime of mixing
parameters in long-baseline laboratory experiments (e.g. Schneps 1995).
At the time of this writing, the possibility that the atmospheric neutrino
anomaly may be revealing neutrino oscillations remains a lively-debated
possibility.
8.3 Oscillations in Media
8.3.1 Dispersion Relation for Mixed Neutrinos
The neutrino refractive index of a normal medium is extremely small
and so its only potentially observable effect occurs in neutrino oscillations.
The refractive index is different for different flavors—the medium
is “flavor birefringent”—and so neutrinos from different families which
propagate with the same energy through the same medium acquire different
phases. If in addition these flavors mix, the medium-induced
phase shift between them shows up in the interference between the
mixed states. Without a medium the phase difference between mixed
states arises from their mass difference. Hence, medium effects will
be noticable only if the induced “effective mass” is of the same order
as the vacuum masses. Therefore, medium refraction is important for
neutrino oscillations in certain situations because the vacuum masses
are very small.