A second possibility is particle physics solutions, which invoke nonstandard neutrino properties. Of these I will concentrate on what I consider the simplest and most favored explanation, the Mikheyev-Smirnov-Wolfenstein (MSW) matter enhanced conversion of one neutrino flavor into another [41]. There are other possible explanations [16], such as the more complicated 3-flavor MSW, vacuum oscillations, neutrino decay, large magnetic moments, or violation of the equivalence principle. Many of these are disfavored by the data and are, to my mind, less natural.
There are now a number of analyses of the
data assuming MSW [42]-[50],[16].
One usually assumes the
SSM predictions for the initial neutrino fluxes.
It is important to properly incorporate their theoretical uncertainties,
which can be due to the core temperature
, as well as to the production and detector cross sections. One must
also include the correlations
of those uncertainties between different flux
components and between different experiments [42], and carry out
a joint 
analysis of the data to find the allowed regions.
The Earth effect [51], i.e., the
regeneration of 
in the Earth at night, is significant for a
small but important region of the MSW parameters, and not only affects the
time-average rate but can lead to day/night asymmetries. The Kamiokande
group has looked for such asymmetries and has not observed them
[52], therefore excluding a particular region of the MSW
parameters in a way independent of astrophysical uncertainties.
Figure: Allowed regions at 95% CL from individual experiments and from
the global MSW fit. The Earth effect is included for both time-averaged and
day/night asymmetry data, full astrophysical and nuclear physics
uncertainties and their correlations are accounted for, and a joint
statistical analysis is carried out. The region excluded by the Kamiokande
absence of the day/night effect is also indicated. From
[42,40].
The allowed regions from the overall fit for normal oscillations
or 
are shown in Figure 2,
assuming the BP SSM for the initial fluxes. There
are two solutions at 95% C.L., one for small mixing angles
(non-adiabatic), and one for large angles. The former gives a much better
fit. There is a second large angle
solution with smaller 
, which only occurs at 99% C.L.
MSW fits can also be performed using other solar models as
inputs [42,40]. The allowed
regions are qualitatively similar, but differ in detail.
One can even go a step further and consider nonstandard solar
models and MSW simultaneously [27,42]. There is now
sufficient data to determine both the MSW parameters and the core
temperature in a simultaneous fit. One obtains 
, in remarkable agreement with the standard solar model
prediction 
. One can similarly allow the 
flux to
be a free parameter [27,42].
One can also consider transitions 
into
sterile neutrinos. These are different in part because the MSW formulas
contain a small contribution from the neutral current scattering from
neutrons. Much more important is the lack of the neutral current
scattering of the 
in the Kamiokande experiment. There is a
non-adiabatic solution similar to the one for active neutrinos, though the
fit is poorer. However, there is no acceptable large angle solution
because of the lack of a neutral current, which makes that case similar to
astrophysical solutions. Oscillations into a sterile neutrino in that
region are also disfavored by Big Bang nucleosynthesis [16].
The next generation of solar neutrino experiments, SNO, Superkamiokande, and Borexino, should be able to cleanly establish or refute the MSW and other particle physics and astrophysical interpretations of the solar neutrino anomaly [4]. They will have at their disposal a number of observables that are relatively free of astrophysical uncertainties, including neutral to charged current ratios, spectral distortions, and day-night and seasonal time dependence. If MSW does turn out to be correct, there should be enough data to simultaneously determine the neutrino mass and mixing parameters and the initial neutrino flux components [27].