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Solar Neutrinos: Where We Are, Where We Are Going1 Solar Neutrinos Where We Are Where We Are Going John N Bahcall Institute for Advanced Study School of Natural Sciences Princeton NJ Abstract This talk answers a series of questions Why study solar neutrinos What do es the combined standard mo del solar plus electroweak predict for solar neutrinos Why are the calculations of neutrino uxes robust What are the three solar neutrino problems What have we learned in the rst thirty years of solar neutrino research For the next decade what are the most imp ortant solvable problems in the physics of solar neutrinos What are the most imp ortant problems in the astrophysics of solar neutrinos Why Study Solar Neutrinos hep-ph/9512285 12 Dec 1995 Astronomers study solar neutrinos for dierent reasons than physicists For astronomers solar neutrino observations oer an opp ortunity to test directly the theories of stellar evolution and of nuclear energy generation With neutrinos one can lo ok into the interior of a main sequence star and observe the nuclear fusion reactions that are ultimately resp onsible for starlight via the general reaction Originally presented as the Dannie Heineman Prize for Astrophysics lecture at the annual AAS meeting in January The Heinemann Prize for Astrophysics is jointly administred by the American Institute for Physics and the American Astronomical So ciety To b e published in the Astrophysical Journal 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 welldened 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 protonproton 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 nitemass 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 multiGeV 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 Rsolar 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 electronneutrino that is created by b etadecay contains appreciable p ortions of at least two dierent 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 eect 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 electrontype neutrinos to b e resonantly converted to the more dicult to detect or neutrinos by the MSW eect Also the column R density of matter that neutrinos must pass through is large dr gm cm The corresp onding parameters for terrestrial longbaseline 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 matterinduced resonant oscillations MSW eect The range of neutrino masses given by Eq and Eq is included in the range of neutrino masses that are suggested by attractive particlephysics generalizations of the standard electroweak mo del including leftright symmetry grandunication and sup ersymmetry Both vacuum neutrino oscillations and matterenhanced neutrino oscillations can change electrontype neutrinos to the more dicult 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 aecting the shap e of the energy sp ectrum of the surviving electrontype neutrinos Future solar neutrino exp eriments will measure the ratio of the number of electrontype neutrinos to the total number of solar neutrinos via neutral current reactions and will also measure the shap e of the electrontype energy sp ectrum via charged current absorption and by neutrinoelectron 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 xray 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 suciently advanced to know if we should b e : surprised by by or by neutrinoinduced 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 lowenergy MeV pp neutrinos are pro duced whereas if the termination o ccurs via reaction higherenergy 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
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