Unless the experiments are seriously in error, there must be some problem with either our understanding of the sun or of neutrinos. Clearly, the standard solar models (SSM) cannot account for the data, but there is the possibility of a highly nonstandard solar model (NSSM). For example, some of the astrophysical parameters or nuclear cross sections could differ significantly from what is usually assumed, or there could be some new physics ingredient, such as a large magnetic field in the core, that is not included in the standard calculations.
Most of the NSSM manifest themselves for the neutrinos by leading
to a lower temperature for the core of the sun [33,34].
However, in all reasonable models the 
neutrinos should be the most
temperature sensitive, leading to the lowest counting rate (relative
to the SSM) for the Kamiokande experiment, contrary to observations.
Similarly, a lower cross section for 
production would suppress
the 
and 
equally. A lower cross section for 
production,
which has been suggested by one recent experiment [35],
would actually make matters worse: by accounting for the suppression
of the 
neutrinos, there would be less room for other mechanisms
to explain the larger 
suppression. None of these mechanisms
explain the data [36].
Though most explicitly-constructed
nonstandard models involve either the temperature or the cross sections
[34] there is always the possibility of very nonstandard
physical inputs which cannot be described in this way. It is therefore
useful to carry out a model-independent analysis [26,27,37].
All that matters for the neutrinos are
the magnitudes 
, 
, 
and 
of the
flux components. We can analyze the data making only three
minimal assumptions. One is that the solar luminosity is quasi-static and
generated by the normal nuclear fusion reactions. This implies
where the coefficients correct for the neutrino energies.
The second
assumption is that astrophysical mechanisms cannot distort the shape of the
spectrum significantly from what is given by normal weak interactions.
(All known distortion mechanisms are negligibly small
[32].) It is this assumption which differentiates
astrophysical mechanisms from MSW, which can distort the shape
significantly. Our third assumption is that the experiments are correct, as
are the detector cross section calculations.
In this (almost) most general possible solar model all one has to play with
are the four neutrino flux components
subject to the luminosity
constraint. The strategy is to fit the data to the 
and 
fluxes.
For each set of fluxes, one varies 
and 
so as to
get the best fit. The CNO and other minor fluxes play little role because
they are bounded below by zero, and larger values make the fits worse.
Figure 1 displays the allowed region from all data, updated
from [26,27]. The best fit
would occur in the unphysical region of negative 
fluxes.
Constraining the flux to be positive, the best fit requires
and 
of the
SSM [26,27]. This, however, has a
poor 
of 3.3 for 1 d.f., which is
excluded at 93% CL.
More important, the best fit it is in a region that is hard to account for by astrophysical mechanisms. Figure 1 also displays predictions of the BP and TCL standard solar models, the 1,000 Monte Carlos SSMs of Bahcall and Ulrich (dots) [38], other explicitly constructed nonstandard models [16], and the general predictions of cool sun and low cross section models. All are far from the allowed region. Similar conclusions hold even if one ignores any one of the classes of experiment [27,28,30,39], as shown in Table 2. It is unlikely that any NSSM will explain the data.
Figure: 90% CL combined fit for the 
and 
fluxes.
Also shown are
the predictions of the BP and TCL SSM's, 1000 Monte Carlo SSM's
[38], various nonstandard solar models, and the models
characterized by a low core temperature or low cross section for
production. Updated from
[26,27,40].
Table: Fluxes compared to the BP standard solar model for
various combinations of experiments. From [26,27,40].
