hep-ph/9512285 12 Dec 1995 astronomers the most imp ortant problems in the astrophysics of of what resp onsible for interior of a main sequence star and observe the nuclear fusion reactions that are ultimately have calculations of in January combined standard for Physics and the American Astronomical So ciety stellar evolution and Originally presented as the Dannie Heineman Prize for Astrophysics lecture at the annual AAS meeting Astronomers This we are the most imp ortant solvable problems in the physics of learned talk solar answers neutrino starlight via the general reaction The in Institute for study neutrino the mo del solar Heinemann Prize Solar a rst of nuclear energy generation uxes solar series observations thirty Advanced Study School of Where Neutrinos neutrinos robust Why of plus electroweak predict for solar questions years for Astrophysics Princeton NJ John Study What We Abstract of for o er N Bahcall solar di erent Why To b e published in the Astrophysical Journal Solar are Are an Where neutrino the three solar is jointly administred by the opp ortunity study Neutrinos Going solar neutrinos With reasons solar Natural Sciences We research neutrinos one to than neutrinos Are neutrino solar neutrinos test neutrinos physicists For directly the the problems can What American Institute next lo ok Why are the For do es What are decade theories into the What the
H He e
e
The optical depth of the sun for a typical neutrino pro duced by nuclear fusion is
ab out orders of magnitude smaller than the optical depth for a typical optical photon
As we shall see solar neutrino exp eriments constitute quantitative well de ned tests of
the theory of stellar evolution Since stellar evolution theory is used widely in interpreting
astronomical observations direct tests of this theory are of imp ortance to astronomers
Table shows the principal nuclear reactions that accomplish Eq via the
proton proton chain of reactions In what follows we shall refer often to the reactions listed
in this table
Table The Principal Reactions of the pp Chain
Reaction Reaction Neutrino Energy
Number MeV
p p H e to
e
p e p H
e
H p He
He He He p
or
He He Be
then
e Be Li
e
Li p He He
or
p Be B
B Be e to
e
Solar neutrinos are of interest to physicists b ecause they can b e used to p erform unique
particle physics exp eriments For some of the theoretically most interesting ranges of
masses and mixing angles solar neutrino exp eriments are more sensitive tests for neutrino
transformations in ight than exp eriments that can b e carried out with lab oratory sources
The reasons for this exquisite sensitivity are the great distance b etween the accelerator
the solar interior and the detector on earth the relatively low energy MeV of solar
neutrinos and the enormous path length of matter gm cm that neutrinos
must pass through on their way out of the sun
One can quantify the sensitivity of solar neutrinos relative to lab oratory exp eriments
by considering the prop er time that would elapse for a nite mass neutrino in ight b etween
the p oint of pro duction and the p oint of detection The elapsed prop er time is a measure of
the opp ortunity that a neutrino has to transform its state and is prop ortional to the ratio
R of path length divided by energy
Path Length
Prop er Time R
Energy
Future accelerator exp eriments with multi GeV neutrinos may reach a sensitivity
of R Km GeV Reactor exp eriments have already almost reached a level of
sensitivity of R Km GeV for neutrinos with MeV energies Solar neutrino
exp eriments b ecause of the enormous distance b etween the source the center of the sun
and the detector on earth and the relatively low energies MeV to MeV of solar
neutrinos involve much larger values of neutrino prop er time
Km Km
R solar
GeV GeV
Because of the long prop er time that is available to a neutrino to transform its state
solar neutrino exp eriments are sensitive to very small neutrino masses and transition matrix
elements which can cause neutrino oscillations in vacuum Quantitatively
m solar level of sensitivity eV to eV vacuum oscillations
provided the electron neutrino that is created by b eta decay contains appreciable p ortions
of at least two di erent neutrino mass eigenstates i e the neutrino mixing angle is
relatively large Lab oratory exp eriments have achieved a sensitivity to electron neutrino
masses of order one eV Over the next several years the sensitivity of the lab oratory
exp eriments should b e improved by an order of magnitude or more
Resonant neutrino oscillations which may b e induced by neutrino interactions with
electrons in the sun the famous MSW e ect can o ccur even if the electron neutrino is
almost entirely comp osed of one neutrino mass eigenstate i e even if the mixing angles
b etween e and e neutrinos are tiny Standard solar mo dels indicate that the sun
has a high central density central gm cm which at least in principle
allows even very low energy MeV electron type neutrinos to b e resonantly converted
to the more di cult to detect or neutrinos by the MSW e ect Also the column
R
density of matter that neutrinos must pass through is large dr gm cm The
corresp onding parameters for terrestrial long baseline exp eriments are a typical density of
gm cm and an obtainable column density of ab out gm cm
Given the ab ove solar parameters the planned and op erating solar neutrino exp eriments
are sensitive to neutrino masses in the range
eV m eV
via matter induced resonant oscillations MSW e ect
The range of neutrino masses given by Eq and Eq is included in the range
of neutrino masses that are suggested by attractive particle physics generalizations of
the standard electroweak mo del including left right symmetry grand uni cation and sup ersymmetry
Both vacuum neutrino oscillations and matter enhanced neutrino oscillations can
change electron type neutrinos to the more di cult to detect muon or tau neutrinos In
addition the likelihoo d that a neutrino will have its type changed may dep end up on its
energy a ecting the shap e of the energy sp ectrum of the surviving electron type neutrinos
Future solar neutrino exp eriments will measure the ratio of the number of electron type
neutrinos to the total number of solar neutrinos via neutral current reactions and will also
measure the shap e of the electron type energy sp ectrum via charged current absorption
and by neutrino electron scattering These measurements will test the simplest version
of the standard electroweak mo del in which neutrinos are massless and do not oscillate
these tests are indep endent of solar mo del physics
What Do es the Combined Standard Mo del Tell Us Ab out Solar Neutrinos
In this section I will describ e the combined standard mo del standard solar mo del
and standard electroweak theory that is used to decide if solar neutrino exp eriments have
revealed something unexp ected Then I will present the calculated solar neutrino sp ectrum
as predicted by the standard mo del
The Combined Standard Mo del
In order to interpret solar neutrino exp eriments one must have a quantitative
theoretical mo del Unlike many other asp ects of astronomy in which one can make
imp ortant discoveries by identifying new classes of ob jects such as quasars or x ray
sources or ray sources solar neutrino research requires a reliable theoretical mo del for
comparison with the observations in order to determine whether one has found something
surprising Our physical intuition is not yet su ciently advanced to know if we should b e
:
surprised by by or by neutrino induced events p er day in a chlorine tank
the size of an Olympic swimming p o ol
I will use the most conservative mo del for comparison with exp eriments the combined
standard mo del unless explicitly stated otherwise The combined standard mo del is the
standard mo del of solar structure and evolution and the standard electroweak mo del of
particle physics
A solar mo del is required in order to predict the number of neutrinos created in a given
energy range p er unit of time On a fundamental level a solar mo del is required in order to
predict the rate of nuclear fusion by the pp chain shown in Table and discussed b elow
and the rate of fusion by the CNO reactions originally favored by H Bethe in his ep o chal
study of nuclear fusion reactions
In our discussion I will assume a result common to all mo dern solar mo dels namely
that the CNO reactions contribute only a very small fraction of the luminosity of the sun
Although the dominance of the pp chain is often taken for granted in theoretical analyses
of solar neutrino exp eriments it is not an a priori obvious result We shall come back to
this fundamental prediction of solar mo dels in the discussion given in x where we review
what has b een learned ab out astronomy from solar neutrino exp eriments
A precise solar mo del is required to calculate accurately which nuclear reaction o ccurs
more often at the two principal branching p oints of the pp fusion chain Referring to
Table the branching p oints o ccur b etween reactions and and b etween reactions and
If the pp chain is terminated by reaction only low energy MeV pp neutrinos
are pro duced whereas if the termination o ccurs via reaction higher energy Be and B
neutrinos are created The ratio of the rates for reaction and reaction determines how
often Be neutrinos two lines MeV and MeV are pro duced rather than the rare
but more easily detected B neutrinos maximum energy MeV are pro duced
The comp etition b etween reactions and and b etween reactions and determines
the energies of the emitted solar neutrinos The predicted rates in solar neutrino exp eriments
dep end sensitively up on the relative frequencies of these crucial reactions Fortunately
the theoretical uncertainties in the predicted neutrino uxes are not very large they vary
b etween ab out to ab out dep ending up on the neutrino source in question The
rates for individual detectors are determined by the energy sp ectrum by the neutrino type
of the incoming solar neutrinos and by the energy dep endence of the interaction cross
sections of the di erent detectors As we shall see in the later discussion cf x one can
largely avoid the dep endence of the predictions up on solar mo dels by comparing the results
of exp eriments that have di erent energy sensitivities These intercomparisons b etween
exp eriments primarily test standard electroweak theory
A particle physics mo del is required to predict what happ ens to the neutrinos after they
are created I will use the simplest version of the standard electroweak mo del according
to which nothing happ ens to the neutrinos after they are created in the interior of the
sun In this theory neutrinos are massless and neutrino avor electron type is conserved
The standard electroweak mo del has had many successes in precision lab oratory tests
mo di cations of this theory will b e accepted only if incontrovertible exp erimental evidence
forces a change
The Solar Neutrino Sp ectrum
Figure shows the calculated neutrino sp ectrum for the most imp ortant neutrino
sources from the sun I will discuss brie y the pp and pep neutrinos the Be neutrinos
and the B neutrinos I will concentrate on the reliability of the predictions and will indicate
the role of each of these neutrinos in the ongoing exp eriments
The dominant source of solar neutrinos is pro duced by the rst reaction listed in
Table the basic pp reaction p p D e which creates neutrinos with
e
energies less than MeV Most of the nuclear energy that emerges as sunlight b egins with
this reaction The theoretical uncertainty in the pp neutrino ux is less than Of the
planned and op erating solar neutrino exp eriments only the GALLEX and SAGE gallium
exp eriments have energy thresholds low enough to detect the pp neutrinos Ab out of
the pp fusions are b elieved to o ccur via the pep reaction the second reaction in Table
This reaction pro duces a neutrino line that contributes a small part of the calculated event
rate in the chlorine and gallium exp eriments
The next most imp ortant source of neutrinos is from the Be neutrino line at
MeV which is pro duced by reaction of Table Ab out of the solar luminosity is
pro duced by reactions which go through this channel the uncertainty in the neutrino ux
is ab out The Be neutrinos contribute signi cantly according to standard mo del
calculations to the chlorine and the gallium exp eriments but are to o low in energy to
b e detected in the Kamiokande exp eriment In an exp eriment under development called
BOREXINO Be neutrinos will b e detected by the unique signature they pro duce in
scintillation light caused by neutrino electron scattering
The B neutrino ux pro duced by reaction of Table is tiny ab out of the
ux of pp neutrinos However the B neutrinos are crucial for solar neutrino physics
and astronomy Because of their high energy MeV which takes advantage of a
sup erallowed transition from the ground state of chlorine to an excited state of argon B
neutrinos dominate the predicted capture rate for the chlorine exp eriment They are also
the only signi cant source of neutrinos ab ove the energy threshold in the water Cherenkov
exp eriment Kamiokande The SNO and Sup erkamiokande exp eriments b oth of which are
under development and which should b egin pro ducing results in also observe only B
neutrinos Unfortunately the theoretical uncertainty in the predicted B neutrino ux is
relatively large ab out
Why Are the Predicted Neutrino Fluxes Robust
The predicted event rates in the di erent solar neutrino exp eriments have b een
remarkable stable over the past years The published estimate in which
accompanied the rst rep ort by Davis and his collab orators of measurements with the
chlorine exp eriment was SNU the most recent and detailed calculation gives in
a predicted rate of SNU The theoretical errors are intended to b e as close
as p ossible to e ective errors they are obtained by carrying out detailed calculations
using uncertainties on all the measured input data and for the less imp ortant theoretical
errors by taking the extreme range of theoretical calculations to b e uncertainties
There are three reasons that the theoretical calculations of the neutrino uxes are
robust the availability of precision measurements and precision calculations of input
data the connection b etween neutrino uxes and the measured solar luminosity and
the measurement of the helioseismological frequencies of the solar pressure mo de p mo de
eigenfrequencies
Over the past three decades many hundreds of researchers have p erformed precision
measurements of crucial input data including nuclear reaction cross sections and the
abundances of the chemical elements on the solar surface Many other researchers have
calculated accurate opacities equations of state and weak interaction cross sections By
now these input data are relatively precise and their uncertainties are quanti able
The solar neutrino uxes and the solar luminosity b oth dep end up on the rates of
the nuclear fusion reactions in the solar interior Since we know exp erimentally the solar
luminosity to an accuracy of ab out the calculated neutrino uxes are strongly
constrained by the fact that the standard solar mo dels must yield precisely the measured
solar luminosity
Thousands of p mo de helioseismological frequencies have b een measured to an accuracy
of part in The b est standard solar mo dels are required to repro duce all of these
p mo de frequencies to an accuracy of b etter than one part in a thousand In fact standard
solar mo dels are in agreement with the measured helioseismological frequencies to a high
level of precision without any sp ecial adjustments of the parameters
The calculated solar neutrino uxes are after thirty years of intense study known to
relatively high accuracy b ecause of the many precise measurements and calculations of
input data b ecause of the strong constraint imp osed on the mo dels by the measured total
solar luminosity and b ecause of the imp ortant tests of solar structure that are provided by
helioseismological measurements
What Are the Three Solar Neutrino Problems
I will compare in this section the predictions of the combined standard mo del with the
results of the op erating solar neutrino exp eriments We will see that this comparison leads
to three di erent discrepancies b etween the calculations and the observations which I will
refer to as the three solar neutrino problems
Figure shows the measured and the calculated event rates in the four ongoing solar
neutrino exp eriments This gure reveals three discrepancies b etween the exp erimental
results and the exp ectations that are based up on the combined standard mo del As we
shall see only the rst of these discrepancies dep ends sensitively up on predictions of the
standard solar mo del
Calculated Versus Observed Chlorine Rate
The rst solar neutrino exp eriment to b e p erformed was the chlorine radio chemical
exp eriment which detects electron type neutrinos more energetic than MeV After
more than twenty ve years of the op eration of this exp eriment the measured event rate is
SNU which is a factor of ab out less than is predicted by the most detailed
:
theoretical calculations SNU A SNU is a convenient unit to describ e the measured
:
rates of solar neutrino exp eriments interactions p er target atom p er sec Most of
the predicted rate in the chlorine exp eriment is from the rare high energy B neutrinos
although the Be neutrinos are also exp ected to contribute signi cantly According to
standard mo del calculations the pep neutrinos and the CNO neutrinos for simplicity not
discussed here are exp ected to contribute less than a SNU to the total event rate
This discrepancy b etween the calculations and the observations for the chlorine
exp eriment was for more than two decades the only solar neutrino problem I shall refer
to the chlorine disagreement as the rst solar neutrino problem
Incompatibility of Chlorine and Water Kamiokande Exp eriments
The second solar neutrino problem results from a comparison of the measured event
rates in the chlorine exp eriment and in the Japanese pure water exp eriment Kamiokande
The water exp eriment detects higher energy neutrinos those with energies ab ove MeV
0 0
by neutrino electron scattering e e According to the standard solar
mo del see also Table B b eta decay is the only imp ortant source of these higher energy
neutrinos
The Kamiokande exp eriment shows that the observed neutrinos come from the sun
The electrons that are scattered by the incoming neutrinos recoil predominantly in the
direction of the sun earth vector the relativistic electrons are observed by the Cherenkov
radiation they pro duce in the water detector
In addition the Kamiokande exp eriment measures the energies of individual scattered
electrons and therefore provides information ab out the energy sp ectrum of the incident solar
neutrinos The observed sp ectrum of electron recoil energies is consistent with that exp ected
from B neutrinos However small angle scattering of the recoil electrons in the water
prevents the angular distribution from b eing determined well on an event by event basis
which limits the constraints the exp eriment places on the incoming neutrino sp ectrum
The event rate in the Kamiokande exp eriment is determined by the same high energy
B neutrinos that are exp ected on the basis of the combined standard mo del to dominate
the event rate in the chlorine exp eriment I have shown that solar physics changes the
shap e of the B neutrino sp ectrum by less than part in Therefore we can calculate
the rate in the chlorine exp eriment that is pro duced by the B neutrinos observed in the
Kamiokande exp eriment MeV threshold energy This partial B rate in the chlorine
exp eriment is SNU which exceeds the total observed chlorine rate of
SNU This problem is analogous to the familiar astronomical problem with the Hubble
constant in which the age of the oldest stars app ears to exceed the age of the universe at
least when the most p opular current values are used
Comparing the rates of the Kamiokande and the chlorine exp eriments one nds that
the net contribution to the chlorine exp eriment from the pep Be and CNO neutrino
sources is negative SNU The calculated rate from pep Be and CNO
neutrinos is SNU The apparent incompatibility of the chlorine and the Kamiokande
exp eriments is the second solar neutrino problem
Gallium Exp eriments No Ro om for Be Neutrinos
The results of the gallium exp eriments GALLEX and SAGE constitute the third
solar neutrino problem The average observed rate in these two exp eriments is SNU
which is essentially fully accounted for in the standard mo del by the theoretical rate of
SNU that is calculated to come from the basic pp and pep neutrinos with only a
uncertainty in the standard solar mo del pp ux The B neutrinos which are observed
ab ove MeV in the Kamiokande exp eriment must also contribute to the gallium event
rate Using the standard mo del shap e for the sp ectrum of B neutrinos and normalizing to
the rate observed in Kamiokande B contributes another SNU unless something happ ens
to the lower energy neutrinos after they are created in the sun The predicted contribution
is SNU on the basis of the standard mo del Given the measured rates in the gallium
exp eriments there is no ro om for the additional SNU that is exp ected from Be
neutrinos on the basis of standard solar mo dels calculated by di erent groups using
di erent input data and di erent stellar evolution co des
The seeming exclusion of everything but pp neutrinos in the gallium exp eriments
is the third solar neutrino problem This problem is essentially indep endent of the
previously discussed solar neutrino problems since it dep ends up on the pp neutrinos that
are not observed in the other exp eriments and whose calculated ux is approximately
mo del indep endent if the general scheme of the pp chain shown in Table is correct
The missing Be neutrinos cannot b e explained away by any change in solar physics
The B neutrinos that are observed in the Kamiokande exp eriment are pro duced in
comp etition with the missing Be neutrinos the comp etition is b etween reaction and
reaction in Table Solar mo del explanations that reduce the predicted Be ux reduce
much more to o much the predictions for the observed B ux
The ux of Be neutrinos Be is indep endent of measurement uncertainties in the
cross section for the nuclear reaction Be p B the cross section for this proton capture
reaction is the most uncertain quantity that enters in an imp ortant way in the solar mo del
calculations The ux of Be neutrinos dep ends up on the proton capture reaction only
through the ratio
R e
Be
R e R p
where R e is the rate of electron capture by Be nuclei and R p is the rate of proton
capture by Be With standard parameters solar mo dels give R p R e
Therefore one would have to increase the value of the Be p B cross section by more
than two orders of magnitude over the current b est estimate which has an estimated
uncertainty of ab out in order to a ect signi cantly the calculated B solar neutrino
ux The required change in the nuclear physics cross section would also increase the
predicted neutrino event rate by more than a hundred in the Kamiokande exp eriment
making that prediction completely inconsistent with what is observed From time to time
pap ers have b een published claiming to solve the solar neutrino problem by arti cally
changing the rate of the Be electron capture reaction Equation Eq shows that the
ux of Be neutrinos is actually indep endent of the rate of the electron capture reaction to
an accuracy of b etter than
I conclude that either at least three of the four op erating solar neutrino exp eriments
the two gallium exp eriments plus either Chlorine or Kamiokande give misleading results
or physics b eyond the standard electroweak mo del is required to change the neutrino
sp ectrum or avor content after the neutrinos are pro duced in the center of the sun
What Have We Learned
No solar mo del solution has b een found that explains the results of the four existing
solar neutrino exp eriments Many particle physics solutions have b een prop osed that can
explain the existing data
In this section I will summarize the main lessons that have b een learned from the rst
thirty years of solar neutrino research I will rst review the progress in astrophysics and
then outline brie y the developments in physics
Learned Ab out Astronomy
The chlorine solar neutrino exp eriment was prop osed in as a practical test of solar
mo del calculations in a pair of back to back Physical Review Letters Bahcall and Davis
pap ers The only motivation presented in those two pap ers for p erforming the chlorine
exp eriment was to see into the interior of a star and thus verify directly the hypothesis
of nuclear energy generation in stars
What have we learned by direct exp eriments ab out nuclear energy generation in
stars How do es our understanding compare with the results of the solar neutrino
exp eriments Table summarizes the six principal predictions that were made or which
were implicit in the theory in and compares those predictions with the results of the
four ongoing solar neutrino exp eriments
The neutrinos were predicted to originate in the solar interior the direction of origin
Table Nuclear energy generation Predictions vs
observations
Predicted Observed
Direction the Sun o k
Rates expts Predicted Rates
within factor of a few
MeV MeV
Constant in time o k
except seasonal
Cl SNU SNU
If CNO
Ga SNU SNU
H O Standard Mo del
T r K T B T
mo del mo del
of the neutrinos has b een veri ed by detecting neutrino electron scattering as was also
suggested in a futuristic pap er in in the Kamiokande exp eriment The rates of the
four op erating exp eriments are in semi quantitative agreement with the predictions the
ratios of the observed to the predicted rates are chlorine water Kamiokande
and gallium average This agreement is b etter than any of us dared hop e for in
esp ecially since the dominant neutrino ux from B b eta decay for the rst two
exp eriments dep ends up on the central temp erature of the sun as approximately the th
p ower of the central temp erature The energy range of the dominant neutrinos was
predicted to b e from MeV to MeV which is consistent with the observations from
the Kamiokande exp eriment These observations do not give detailed information on the
incoming solar neutrino energy sp ectrum but they do show that neutrinos exist in the
exp ected energy range at least ab ove MeV and that no events have b een observed
at energies b eyond the maximum energy resulting from B b eta decay Standard mo dels
predict that the neutrino uxes are constant in time except for a small seasonal variation
The Kelvin Helmholtz co oling time for the solar interior is ab out years The consensus
but not unanimous view of the exp erimentalists based up on the available data from the
pioneering four solar neutrino exp eriments all of which have rather low counting rates is
that the neutrino uxes are indeed constant in time Standard solar mo dels predict that the
sun shines almost entirely via the pp chain of nuclear fusion reactions rather than the CNO
reactions originally emphasized by Bethe If the CNO reactions were dominant the event
rates in solar neutrino exp eriments could b e calculated precisely and these rates as shown
in Table di er from the observed rates by more than an order of magnitude Finally if
we crudely characterize the rate of the B neutrino emission by its approximate dep endence
up on the central temp erature of the solar mo del then the central temp erature of the solar
mo del agrees with the value obtained from the exp erimental rates to an accuracy of ab out
or b etter
The four ongoing solar neutrino exp eriments have shown directly that the sun shines
by nuclear fusion reactions achieving the original goal Quantitative improvements in the
tests shown in Table will o ccur with the next generation of exp eriments But the most
imp ortant qualitative result has b een established neutrinos have b een observed from the
interior of the sun in approximately the number and with the energies exp ected
In the three decade long struggle to improve solar mo dels in order to calculate more
accurate solar neutrino uxes we have obtained a greater understanding of solar structure
The theoretical mo dels have gradually b een re ned as improved input data more accurate
physical descriptions and more precise numerical techniques have b een employed Perhaps
most imp ortantly the complimentary eld of helioseismology has b een developed and now
provides precise data that determine the sound velocity over most of the solar interior
these b eautiful measurements are used to test and to re ne the standard solar mo del
Further improvements in the solar mo del are desirable and imp ortant but the quantitative
agreement typically b etter than a part in b etween the calculated eigenfrequencies of
pressure mo des and the measured helioseismological frequencies provides strong evidence
for the basic correctness of the standard solar mo del
Learned Ab out Physics
To p erform more precise tests of the astrophysical predictions we will have to learn
what happ ens to neutrinos after they are pro duced in the interior of the sun Theoretical
physicists have fertile imaginations they have provided us with a rich smorgasb ord of
explanations based up on new particle physics including vauum neutrino oscillations
resonant oscillations in matter the MSW e ect resonant magnetic moment transitions
sterile neutrinos neutrino decay and violation by neutrinos of the equivalence principle
Most of these explanations can account for the existing exp erimental data if either two or
three neutrinos are involved in the new physics b eyond the standard electroweak mo del
All of these explanations and others that I have not listed can account for the existing
data on solar neutrino exp eriments without con icting with established laws of physics or
with other exp erimental constraints
The number of prop osed particle physics explanations exceeds the diagnostic p ower of
the existing solar neutrino exp eriments I think it is unlikely that the next generation of
solar neutrinos exp eriments will b e able to eleminate all but one p ossible particle physics
explanation But I hop e that the p owerful new exp eriments SNO Sup erkamiokande and
BOREXINO will together with the four op erating exp eriments p oint us in the direction
of one of the previously prop osed explanations
So what have we learned ab out particle physics We have learned that a number
of particle physics explanations are consistent with the data obtained from the rst four
solar neutrino exp eriments Perhaps most imp ortantly we have learned that an elegant
conservative extension of the standard electroweak theory the MSW e ect can describ e all
of the existing exp erimental information on solar neutrinos if the electron neutrino is mixed
with another neutrino that has a nite mass
m eV
The MSW theory is not proven but it is a b eautiful idea I think it would b e a disgrace if
Nature failed to make use of this marvelous p ossibility
What Next
In this section I will summarize the problems rst in physics and then in astronomy
that are likely to b e solved in the next decade or two
Solvable Problems in Physics
The fundamental goal of physics research on solar neutrinos is to measure the energy
sp ectrum and avor content as a function of time of the solar neutrino ux We want to
know how many neutrinos reach the earth with a given energy and with a given avor i e
neutrino type electron muon or tau all as a function of time Because of some exotic
particle physics p ossibilities we also want to know if the solar neutrino ux contains any
anti neutrinos
The standard mo del predicts that the energy sp ectrum of neutrinos from any given
neutrino source e g from B b eta decay will b e the same to high accuracy as the energy
sp ectrum inferred from terrestrial lab oratory measurements In the standard electroweak
theory only massless electron type neutrinos are created in nuclear b eta decay or nuclear
fusion reactions Standard electroweak theory predicts that the solar neutrinos pro duced by
nuclear fusion reactions are all not or According to MSW and vacuum oscillation
e
theories neutrinos created in nuclear b eta decay or nuclear fusion reactions are linear
combinations of di erent neutrino types and at least one neutrino mass is non zero Finally
the total amount of thermal energy in the solar interior implies that the neutrino uxes will
b e constant in time for time scales less than years except for the seasonal dep endences
caused by the earth s orbital eccentricity Any departure from these exp ectations will b e a
signal for physics b eyond the standard electroweak mo del
I will now list six sp eci c problems in the physics of solar neutrino research that we
can exp ect to b e solved in the next decade or so
The ratio of to The electron type neutrinos that are created in the
e total e
interior of the sun will all remain if the simplest version of the standard electroweak
e
theory is correct If neutrino oscillations o ccur vacuum or matter induced MSW e ect
oscillations then the total number of solar neutrinos observed at earth will exceed the
number that are present as electron type neutrinos only
The ratio of to can b e determined by measuring the ratio of the cross sections
e total
for two di erent reactions one that o ccurs only with electron type neutrinos and one that
will o ccur with equal probability indep endent of the type of neutrino This ratio will
b e measured for the rst time in the SNO solar neutrino exp eriment which utilizes a
kiloton of heavy water via the two reactions H p p e only and
e e
If non interacting sterile neutrinos exist in nature they will not b e detected in this exp eriment
sterile
In principle the solution of the solar neutrino problems could involve !
e sterile
H p n
total total
Shap e of the B neutrino energy sp ectrum The shap e of this sp ectrum is
indep endent of any asp ect of solar mo del physics to an accuracy of part in The shap e
is determined empirically from lab oratory nuclear physics measurements
The shap e of the B neutrino energy sp ectrum can b e determined by measuring the
energy sp ectrum of electrons created in the reaction H p p e which will b e
e
done in the SNO exp eriment Imp ortant information ab out the energy sp ectrum will also
b e obtained by the Sup erkamiokande electron scattering exp eriment Sup erkamiokande will
measure accurately the energy sp ectrum of recoiling electrons pro duced by neutrino electron
scattering in pure water
Flux of Be neutrinos The simplest particle physics interpretation of the four
op erating solar neutrino exp eriments implies that the ux of Be neutrinos is greatly
reduced with resp ect to the value predicted by the standard solar mo del I do not know
of any prop osed mo di cation of solar physics that could explain a greatly reduced Be
neutrino ux and at the same time b e consistent with only a factor of two reduction in the
B neutrino ux as observed by the Kamiokande exp eriment Therefore a much reduced
Be neutrino ux would b e a strong signal for new weak interaction physics
A measurement of the Be neutrino ux is also required to interpret the measured
event rates in the existing chlorine and gallium exp eriments Since the chlorine and gallium
exp eriments are radio chemical they do not give any indication of the energy ab ove
threshold of the neutrino that initiates the reaction
A rst measurement of the ux of Be neutrinos will b e carried out by the BOREXINO
collab oration in the Gran Sasso underground lab oratory using electron neutrino scattering
in an organic scintillator
Time Dep endence of the Neutrino Fluxes All of the prop osed exp eriments
have exp ected event rates that are one to two orders of magnitude larger than the op erating
solar neutrino exp eriments The tests for time dep endence with the existing data have
yielded only marginally suggestive results Typical event rates with existing exp eriments
are in the range of to events p er year whereas the exp ected event rates in the planned
exp eriments are typically of order a few thousand events p er year
With these future exp eriments it will b e b e p ossible to test with high precision the
standard mo del prediction that the solar neutrino event uxes are indep endent of time In
addition it will b e p ossible to measure the p eak to p eak seasonal dep endence caused by
the eccentricity of the earth s orbit One can also search with high accuracy for the strong
seasonal dep endences predicted by explanations involving vacuum neutrino oscillations for
which the oscillation wavelength is tuned to give a large e ect by b eing set approximately
equal to an integral multiple of the astronomical unit MSW theory also predicts for
certain choices of the parameters that there will b e a strong day night e ect This e ect
o ccurs b ecause muon or tau neutrinos are reconverted to electron neutrinos as they pass
through the earth at night on their way to neutrino detectors on the far side from the sun
Proton proton Neutrino Flux and Energy Sp ectrum The dominant neutrino
ux that is created in the sun is the low energy ux of neutrinos from the basic pp reaction
Because of their low energy MeV these neutrinos are unobservable in the chlorine
Kamiokande Sup erkamiokande SNO BOREXINO and Indium exp eriments Among the
planned or op erating exp eriments only the gallium exp eriments GALLEX and SAGE
have a su ciently low threshold energy to detect pp neutrinos The gallium exp eriments
detect neutrinos radio chemically they do not measure the energy of the neutrinos that
cause the conversion of Ga to Ge Therefore we have no exp erimental way at present of
determining how much of the observed event rate in the gallium exp eriments is due to pp
neutrinos and how much is due to Be CNO or B neutrinos
Two exp eriments have b een prop osed recently that are p otentially capable of detecting
and measuring the energies of individual events caused by pp neutrinos These exp eriments
b oth would use cold helium The HERON detector uses ballistic phonon propagation in
liquid helium maintained in the sup er uid state The HELLAZ detector uses a high pressure
helium gas in a time pro jection chamber
The development of a practical detector that can measure the rate and the energy
sp ectrum of the pp neutrinos is an exciting technical challenge and of fundamental
imp ortance to b oth physics and astronomy All of the prop osed physics solutions make
de nitive predictions ab out what happ ens to the low energy pp neutrinos
Re ne Nuclear physics Parameters Over the past three decades many precise
di cult and b eautiful nuclear physics exp eriments have b een p erformed in order to
determine the rates of solar fusion reactions with the accuracy required for solar mo del
calculations of neutrino uxes It is imp ortant to check these measurements with the
improved exp erimental techniques that are now available
The most imp ortant nuclear physics exp eriment to p erform in connection with solar
neutrino research is a measurement of the Be p B cross section reaction
of Table The predicted rates in the Kamiokande Sup erkamiokande and SNO
solar neutrino exp eriments are prop ortional to the low energy rate of this reaction and
the dominant contribution in the standard mo del prediction of the rate of the chlorine
exp eriment is also prop ortional to the rate of this reaction There are a number of very
b eautiful exp eriments in which the rate of the p Be B reaction has b een measured
using a radioactive target of Be and a b eam of protons It would b e most informative to
reverse the usual exp erimental situation and to use a gaseous target of protons and a b eam
of Be this reversal would involve di erent systematic uncertainties which are often most
imp ortant source of errors in di cult exp eriments Measuring the cross section for the
Be p B reaction with a Be b eam is in my view the most imp ortant exp eriment to b e
p erformed in nuclear astrophysics
The fundamental goal of physics exp eriments with solar neutrinos is to measure or
set stringent limits on the elementary prop erties of neutrinos esp ecially their masses and
mixing angles It seems likely that we will make imp ortant progress towards this goal in the
next decade
Solvable Problems in Astronomy
The fundamental goal of solar neutrino astronomy is to determine the rates of di erent
nuclear fusion reactions in the solar interior Neutrino uxes created by the di erent nuclear
sources are the signatures of the fusion reactions We must know what happ ens to the
neutrinos after they are created in order to infer the created neutrino energy sp ectrum from
the measured neutrino energy sp ectrum
With one exception progress in solar neutrino astronomy is held hostage to progress
in particle physics As discussed in the previous subsection it seems likely that we will
learn enough ab out the particle physics in the next decade to p ermit accurate inferences
ab out the rates of neutrino creation in the sun from the observed rates of neutrino arrival
at the earth The discussion in this subsection will presume that the required progress in
understanding the prop erties of the neutrino is achieved
Completing Hydrogen Fusion
Table shows that the two principal ways for completing nuclear fusion in the sun are
reactions and the so called He He and He He reactions Because of the slightly
smaller reduced mass that exists for the He He reaction Coulomb barrier p enetration
favors this reaction over the He He reaction at lower temp eratures According to the
standard solar mo del the He He reaction is dominant in the innermost region of the
sun where it is times faster than the He He reaction but overall o ccurs in only
ab out of the fusion terminations that are describ ed by Eq That is in the most
detailed solar mo dels the He He reaction is on the average more than ve times faster in
completing the nuclear fusion of protons into alpha particles than the comp eting He He
reaction
Is this prediction of the standard solar mo del correct A determination of the pp and
Be neutrino uxes corrected for what non standard particle physics has done to them
after they were created in the sun can answer this imp ortant question The average ratio
of the total number of He He reactions p er unit time in the sun to the total number of
He He reactions p er unit time in the sun is
He He Be
He He pp Be
where pp and Be are resp ectively the uxes from the pp and Be neutrinos
Eq is the most precisely testable prediction that I know of from the theory of
stellar energy generation The known theoretical uncertainties in the calculation of the
average solar ratio of He He to He He reactions is
The B Neutrino Flux
The ux of neutrinos from B b eta decay in the sun see reaction of Table is
in principle the simplest solar neutrino ux to measure The higher energies of the B
neutrinos make them easiest to detect For this reason the Kamiokande Sup erkamiokande
and SNO neutrino exp eriments will all concentrate on the B neutrinos
However one must determine the total ux of B neutrinos including the more di cult
to detect muon or tau neutrinos that may have b een pro duced from the originally created
electron type neutrinos The total number of neutrinos of all types will b e measured directly
in the SNO exp eriment via the neutral current disintegration of deuterium and less directly
via electron neutrino scattering in Sup erkamiokande This statement presumes there are
no sterile neutrinos see fo otnote in x In addition one must determine precisely the
low energy cross section for the nuclear fusion reaction p Be B as discussed in x
The magnitude of the B ux all neutrino avors which is a sensitive prob e of
Therefore it is the temp erature of the solar interior varies approximately as T
central
imp ortant to determine exp erimentally the total B solar neutrino ux
The Temperature Pro le of the Solar Interior
An accurate test of the theory of stellar structure and stellar evolution can b e p erformed
by measuring the average di erence in energy b etween the neutrino line pro duced by Be
electron capture in the solar interior and the corresp onding neutrino line pro duced in a
terrestrial lab oratory This energy shift is calculated to b e keV The energy shift is
approximately equal to the average temp erature of the solar core computed by integrating
the temp erature over the interior of the solar mo del with a weighting factor equal to the
lo cally pro duced Be neutrino emission The total range of values for the shift calculated
for a number of mo dern solar mo dels going back to is keV
A measurement of the energy shift is equivalent to a measurement of the central
temp erature distribution of the sun
The calculated energy pro le of the Be line contains analogous to line broadening in
classical photon astronomy a description of the distribution of solar interior temp eratures
The shap e of the Be neutrino line is asymmetric on the low energy side the line shap e is
Gaussian with a half width at half maximum of keV and on the high energy side the
line shap e is exp onential with a half width at half maximum of keV
The calculated shap e of the Be neutrino line is not a ected signi cantly by vacuum
neutrino oscillations by the MSW e ect or by other frequently discussed weak interaction
solutions to the solar neutrino problems This is a key result it implies that the
astronomical information contained in the line shift and in the line pro le is not held
hostage to further progress in neutrino physics
Detectors are available that have the resolution to measure the line shift Unfortunately
their current sizes are to o small to p ermit a full scale solar neutrino exp eriment However
prop osals have b een made in the literature for developing detectors that are su ciently
large to b e able to measure well the average shift in energy of the solar neutrino line
Ruling out Non Standard Solar Mo dels
In the rst decade and a half following the initial rep ort that the measured solar
neutrino ux in the chlorine exp eriment was less than the calculated value a number of
authors invented imaginative non standard solar mo dels that were designed to solve the
solar neutrino problem The situation now lo oks di erent As describ ed in x there are
now three solar neutrino problems and it do es not app ear p ossible to reconcile the four
op erating exp eriments with any mo di cation of stellar physics
I think that the neutrino uxes from the nuclear fusion reactions in the sun are known
as well as the neutrino uxes from many of the b est terrestrial lab oratory exp eriments In
the solar context we use di erent constraints on the theoretical calculations than we do
with lab oratory accelerators However the solar constraints esp ecially the measured solar
luminosity and the helioseismological frequencies provide p owerful limits on the allowed
values of the neutrino uxes These constraints are discussed in x
Nevertheless many physicists are unfamiliar with stellar physics They do not feel
comfortable judging the plausibility of di erent solar mo dels even fanciful ones in which
the solar mo del contains for example a central black hole or a non Maxwellian energy
sp ectrum for the nuclei Some physicists are willing to consider solar mo dels that nearly all
astrophysicists would dismiss as unworthy of discussion
It would b e instructive to calculate precise solar mo dels based up on some of the more
frequently discussed non standard mo dels e g a low central heavy element abundance
iron precipitation a very strong internal magnetic eld nearly complete element mixing
turbulent di usion massive mass loss or energy transp ort by WIMPs For each
non standard hypothesis a solar mo del could b e evolved using the b est available physics
opacities equation of state di usion rates and measured input data while also imp osing
the ad hoc stellar structure hypothesis The non standard mo dels computed in this way
could b e compared with the thousands of accurately measured p mo de helioseismological
frequencies
I am con dent that the non standard mo dels which have b een suggested as p ossible
solutions of the solar neutrino problem would b e ruled out by accurate and detailed
comparisons with helioseismological data Most of the suggested mo dels would fail I
susp ect on a grosser level predicting for example the wrong depth of the convective zone
or the wrong dep endence of sound velocity on depth within the sun But it would b e an
imp ortant contribution to test the conjecture that the previously suggested non standard
solar mo dels that were conco cted to solve the solar neutrino problem when it was just one
problem all fail to account for well established results of helioseismology
Discover the g Mo des
The most imp ortant discovery that one can anticipate b eing made in optical solar
astronomy is the detection of the oscillations from gravity mo des Unlike the many
pressure mo de p mo de oscillations that have b een studied so far the largest amplitudes
of the g mo des o ccur in the solar interior they are exp ected to b e damp ed heavily in the
outer regions of the sun This concentration toward the center is particularly desirable if
one wants to learn ab out solar interior prop erties that are relevant to neutrino astrophysics
However the interior concentration also makes the detection of gravity mo des very di cult
The amplitudes of the g mo de oscillations are exp ected to b e very small on the surface
of the sun where they might b e measured There is no well understoo d mechanism that
predicts g mo des will carry enough energy to b e observable They have not yet b een
detected convincingly in the sun
New exp eriments are underway to attempt to detect the g mo des from space with the
SOHO satellite and from an international network of ground based telescop es GONG
The results of these new exp eriments will b e of great interest for solar physics even if they
do not lead to the detection of g mo des since they will provide re ned observations of the
p mo des If the g mo des are detected it will b e of ep o chal imp ortance
More Complete Mo dels of the Sun
The accuracy of the physical description that is currently achieved with one dimensional
spherically symmetric mo dels of the sun that include di usion is su cient to p ermit
excellent quantitative agreement with the measured p mo de oscillation frequencies
Numerical exp eriments and theoretical arguments also suggest that further improvements
are unlikely to a ect very signi cantly the calculated neutrino uxes
Nevertheless current mo dels of the sun are incomplete They do not take account of
the two dimensional or three dimensional nature of solar structure they do not contain
a self consistent dynamical treatment of the e ects of rotation of magnetic elds of mass
loss and of other p ossible e ects that may violate the currently used approximations of
spherical symmetry and quasi static evolution We know observationally that the sun at
least near its surface contains magnetic elds that it is lo osing mass and that it departs
from spherical symmetry by ab out part in
There are b oth analytic and calculational challenges in including these complicated
pro cesses in a more complete physical description in the next generation of solar mo dels
New self consistent metho ds of calculating solar mo dels or stellar mo dels must b e
developed and then the appropriate numerical techniques must b e worked out tested and
applied
The goal of developing a more complete solar mo del is a challenge for the next decade
and b eyond Fortunately it is a challenge that could lead to imp ortant progress since
computing p ower is much greater than it was in the past and there is an abundance of
precision data with which to make detailed comparisons
Solar astrophysics has a bright future
Summary
The rst thirty years of solar neutrino research have veri ed exp erimentally the
fundamental predictions of nuclear energy generation in stars The next ten or twenty years
of research will I think concentrate on using solar neutrinos to learn more ab out weak
interaction physics As the weak interaction questions are b eing resolved it will b e p ossible
to carry out progressively more accurate tests of the theory of nuclear energy generation
and of stellar structure
In retrosp ect the history of solar neutrino research seems ironic It b egan with an
e ort to use neutrinos whose prop erties were assumed well known to study the interior
of the nearest star The pro ject was an unconventional application of microscopic physics
which was designed to carry out a unique investigation of a massive macroscopic b o dy
the sun It now app ears that a large community of physicists chemists astrophysicists
astronomers and engineers working together may have stumbled across the rst observed
manifestation of physics b eyond the standard electroweak mo del
We may have b een incredibly lucky
Will the next generation of exp eriments show that physics b eyond the electroweak
mo del is de nitely required to understand the solar neutrino exp erimental results I do not
know But I am sure that we have already learned imp ortant things ab out neutrino physics
from the existing solar neutrino exp eriments and that we will learn additional things from
the future exp eriments This research may or may not lead to a consensus view that
physics b eyond the electroweak mo del is implied by solar neutrino exp eriments To me
the marvelous lesson of solar neutrino physics is that work on the forefront of one eld of
science can lead to imp ortant and completely unanticipated developments in a di erent
eld of science This seems to me b oth humbling and b eautiful
Bibliographic Notes
Recent descriptions of the ongoing solar neutrino exp eriments are contained in the
following pap ers
Davis R in Frontiers of Neutrino Astrophysics eds Y Suzuki K Nakamura
Tokyo Universal Academy Press p Davis R Prog Part Nucl Phys
Suzuki Y Nucl Phys B Pro c Suppl Pro c of the th Int Workshop
Neutrino Telescopes Venice February ed M Baldo Ceolin p
Ab durashitov J N et al Phys Lett B Nico G et al in
Pro ceedings of the XXVI I International Conference on High Energy Physics July
Glasgow eds P J Bussey and I G Knowles Philadelphia Institute of
Physics p
Anselmann P et al Phys Lett B ibid
The standard mo del predictions used in this talk are taken from Bahcall J N
Pinsonneault M Rev Mo d Phys Octob er issue The formulation of the
neutrino problems is adapted from Bahcall J N Phys Lett B
For a general review of solar neutrino physics and astrophysics the reader can consult
two b o oks devoted to the sub ject Neutrino Astrophysics is a monograph by J N
Bahcall that is published by Cambridge University Press Solar Neutrinos
The First Thirty Years contains reprints of of the key pap ers in the development
of the sub ject plus brief introductions and summaries of recent developments in
the ma jor sub ject areas standard mo del exp ectations solar neutrino exp eriments
nuclear fusion reactions physics b eyond the standard mo del and helioseismology
This reprint volume is published by Addison Wesley Reading Massachusetts
and is edited by J N Bahcall R Davis Jr P Parker A Smirnov R Ulrich
Water Chlorine | Gallium |
|
Fig Solar Neutrino Sp ectrum This gure shows the energy sp ectrum of neutrinos
from the pp chain that is predicted by the standard solar mo del The neutrino uxes from
continuum sources pp and B are given in the units of number p er cm p er second p er MeV
at one astronomical unit The line uxes p ep and Be are given in number p er cm p er
second The arrows at the top of the gure indicate the energy thresholds for the ongoing
neutrino exp eriments The higher energy Be line is just ab ove threshold in the chlorine exp eriment
Fig Comparison of measured rates and standard mo del predictions for four solar neutrino exp eriments