The basic energy source in our sun is believed to be the pp cycle, in
which four protons fuse to form 
, i.e., 
[7]. The dominant initial reactions are
The first of these results in the low energy pp neutrinos. Their number
is the firmest prediction of the solar model because it is closely tied to
the overall luminosity. However, they are very hard to detect because of
their low energy. Most of the 
is from
However, approximately 15% is believed to be produced from the sequence
which yields 
neutrinos at two discrete energies, one of which is
somewhat above the pp spectrum. Finally, a rare side reaction,
is associated with about 0.02% of the produced 
. This is
insignificant energetically, but the resulting 
neutrino spectrum
extends to much higher energy than the others, so they are easier to
detect. The predicted spectrum [7] from the pp cycle and the
rarer CNO cycle neutrinos are shown in Figure 1.
Figure: Predicted spectrum of solar neutrinos.
Table: Presently operating solar neutrino experiments.
There are currently four solar neutrino experiments, as shown in
Table 1. The Kamiokande experiment [4] is a 1 KT water
Cerenkov detector which measures the energy of the produced electrons. It
is only sensitive to the highest energy 
neutrinos, but it is a real
time experiment. It also yields some information on the direction of the
incident neutrinos, which allowed Kamiokande to show that the neutrinos are
really coming from the sun. Homestake [3] was the first solar
neutrino experiment, and it has been running for 25 years. It
consists of 
gallons of 
, and detects neutrinos via capture
on the chlorine. It has a much lower energy threshold than Kamiokande, and
is therefore sensitive to the higher 
line as well as the lower energy
parts of the 
spectrum. However, its largest sensitivity is still to
higher energies. In the last few years two gallium experiments, the SAGE
experiment in the Baksan Neutrino observatory in
the Caucasus mountains,
and the GALLEX experiment in the Gran Sasso tunnel in
Italy, have been running. They are sensitive to the low energy pp
neutrinos, as well as to the higher energy neutrinos. The predicted
contributions to the gallium and chlorine experiments in the standard solar
model are shown in Table 2.
Table: Predicted rates in SNU
(
atom
)
from the various flux components for the
chlorine and gallium experiments, from [26]. The
uncertainties are the total theoretical range, 
.
The results of the experiments are compared with the predictions of two standard solar models, that of Bahcall and Pinsonneault (BP) [26] and that of Turck-Chieze and Lopes (TCL) [27], in Table 3.
Table: Predictions of the BP and TCL standard solar models for the
Kamiokande, Homestake, and Gallium experiments compared with the
experimental rates. The Kamiokande flux is in units of 
, while
the Homestake and gallium rates are in SNU. The experimental rates
relative to the theoretical predictions are shown in the last two
columns, where the first uncertainty is experimental and the second is
theoretical. After 1986 the Homestake rate was slightly higher 
SNU, which corresponds to 
compared to BP and
compared to TCL. All uncertainties are 1 
.
It is seen that the predictions for the Kamiokande and Homestake
experiments are between 
and 
of the BP expectations; the
Kamiokande rate is still low compared to TCL, although somewhat closer; the
Gallium rates are about 60% of the predictions. This deficit of neutrinos
is shown in Figure 2, which also displays the typical neutrino
energy to which each class of experiment is sensitive.
Figure: The experimental observations relative to the predictions of the
BP and TCL standard solar models. The error bars on the points are
experimental; the (1 
)
theoretical uncertainties are displayed separately.
Each experiment is sensitive to a range of neutrino energies. The values
shown represent typical energies for each experiment.
The solar neutrino problem has two aspects. The older and less significant
is that all of the experiments are below the SSM predictions. This was
never a serious concern for the Kamiokande and Homestake
experiments individually, which
are mainly sensitive to the high energy 
neutrinos which are less
reliably predicted. However, the predictions for the gallium experiments
are harder to modify due to the constraint of the overall solar luminosity,
and the statistics on the gallium experiments are starting to be good
enough that the deficit observed there is hard to account for.
A second and more serious problem is that the Kamiokande rate indicates
less suppression than the Homestake rate. The Homestake experiment has a
lower energy threshold, and the lower observed rate suggests that there is
more suppression in the middle of the spectrum (the 
line and the
lower energy part of the 
spectrum) than at higher energies. This is
very hard to account for by astrophysical or nuclear physics mechanisms: the
is made from 
(eqn (5)), so any suppression of 
\
should be accompanied by at least as much suppression of 
. Furthermore,
all known
mechanisms for distorting the 
decay spectrum are negligible
[35].
There are several generic explanations of the solar neutrino problem. In discussing astrophysical/nuclear solutions, one must distinguish between the uncertainties in the standard solar models, and nonstandard solar models with new physics ingredients. 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 [15]. There are other possible explanations, such as the more complicated 3-flavor MSW [36], vacuum oscillations [37]--[42], neutrino decay [43], large magnetic moments [44], or violation of the equivalence principle [45]. Many of these are disfavored by the data and are, to my mind, less natural. The third possibility is that some or all of the experiments are wrong. However, this is becoming harder to accept, because the same difficulties follow from any two of the classes of experiments: one no longer has to believe all of the results to conclude that there is a problem.
