arXiv:physics/0411190 v1 19 Nov 2004SOLAR NEUTRINOS 1Solar NeutrinosJohn N. BahcallHow does the Sun shine? How well do we unders tand the evolution and ages ofstars? Does the neutrino have a mass? Can a neutrino change its lepton numberin flight? Are there weak interactions beyond those described by the standardmodel of particle physics? These are some of the questions that motivate thestudy of solar neutrinos.A neutrino is a weakly interacting particle that travels at essentially the speedof lig ht and has an intrinsic angular momentum of12unit (~/2). Neutrinos areproduced on Earth by natural radioactivity, by nuclear re actors, and by high-energy accelerators. In the Sun, neutrinos are produced by weak interactionsthat occur during nuclear fusion. There a re three known types of neutrinos,each associated with a massive lepton that exp e riences weak, electromagnetic,and gravitational forces, but not strong interactions. The known leptons areelectrons, muons, and taus (in incre asing order of their rest masses).Neutrino astronomy is difficult for the same reason it is interesting. Becauseneutrinos only interact weakly w ith matter, they can reach us from other wiseinaccessible regions where photons, the traditional messengers of astronomy, ar etrapped. Hence, with neutrinos we can look inside stars and examine directlyenergetic physical processes that occur only in stellar interiors. We can studythe interior of the Sun or the core of a c ollapsing star as it produces a supernova.Large detectors, typically hundreds or thousa nds of tons of material, arerequired to observe astronomical neutrinos. These detectors must be placeddeep underground to avoid confusing the rare astronomical neutrino events withthe background interactions caused by cosmic rays and their secondary particles,which are relatively common near the surface of the Earth.The nearest star, our Sun, supplies the largest known flux of neutrinos a t theEarth’s surface. Every second approximately a hundred billion solar neutrinoscross every square centimeter on Earth. Quite natur ally, the first attempt todetect astronomical neutrinos began with an expe riment to obs e rve neutrinosproduced in the deep interior of the Sun.For two decades, from 1968 to 1988, the only operating solar neutrino exper-iment (carried out by Raymond Davis Jr. and his colleagues and using37Cl asa detector) yielded results in conflict with the most accurate theoretical calcu-lations of how many neutrinos are produced in the Sun. This conflict betweentheory and obser vation became known as the ’solar neutrino problem.’Both the theoretical and the observational results for the chlorine experimentare expressed in terms of the solar neutrino unit, SNU, which is the product of acharacteristic calculated solar neutrino flux (units: cm−2s−1) times a theoreticalcross section for neutrino absorption (unit: cm2). A SNU has, therefore, theunits of events per target atom p er second and is chosen fo r convenience equalto 10−36s−1.After two decades of critical examination of both the theory and the experi-ment, both results were determined robustly. The predicted rate for capturing2solar neutrinos in a37Cl target is (Bahcall and Ulr ich, 1988; Bahcall, 1989)Predicted rate = (7.9 ± 0.9) SNU . (1)The rate observed by R. Davis, Jr. (1986) and his associates in their chlorineradiochemical detector isObserved rate = (2.1 ± 0.3) SNU . (2)Both the theoretical and the experimental uncertainties are quoted as 1σ errors.The pr e dictio ns used in Eqs. (1) and (2 ) are valid for the combined standardmodel, that is, the standard model of electroweak theory (of Glas how, Weinberg,and Salam) and the standard solar model.Similar results to those shown in Eq. (1) and Eq. (2) were obtained in 1968.The most recent theoretical result is 8.5 ± 1.8 SNU (Bahcall and Pinsonneault2004) and the final experiment value is 2.6 ± 0.2 SNU (Cleveland, Da ily, Davis,et al. 1998). The robustness of the discrepancy between theory and obs e rvationstimulated the development two generations of increasingly more powerful andsophisticated detectors designed to find the reason why theory and obser vationdiffer.More is known about the Sun than about any other star and the calculatio nsof neutrino emission from the solar interior can be done with relatively highprecision. Solar neutrino experiments test in a direct and rigorous way thetheories of nuclear energy generation in stellar interiors and of stellar evolution.These tests are independent of many of the uncertainties that complicate thecomparison of the theory with observations of stellar surfaces. For example,convection and turbulence are importa nt near stellar surfaces but unimportantin the solar interior. Hence, the solar neutrino discrepancy puzzled (and worried)astronomers who want to use neutrino observations to understand better howthe Sun and other stars shine. Prior to June 2001 (see disc us s ion of SNOexp eriment below), the solar neutrino problem seemed to most (but not all)physicists to indicate that astronomers did not understand the details of thesolar nuclear fusion reactions that produce neutrinos.Neutrinos from the Sun provide particle beams for probing the weak inter-actions on distance scale s that cannot be achieved with traditional laboratoryexp eriments. Since neutrinos from the Sun travel astronomical distances beforethey reach the Earth, experiments performed with these particle beams are se n-sitive to weak-interaction phenomena that require long path lengths in orderfor slow weak-interaction effects to have time to occur. The effects of tiny neu-trino masses (≥ 1 0−6eV), unmeasurable in the laboratory, can be studied withsolar neutrinos. Moreover, neutrinos traverse an enormous amount of matter,1011gm cm−2, as they travel from the center of the Sun to detectors on Earth.The huge column density of matter that solar neutrinos traverse can give rise to’matter effects’ on neutrino propagation that have not yet been observed withterrestrial neutrinos.The Sun shines by converting protons into α particles. The overall reactionSOLAR NEUTRINOS 3Table 1: The pp chain in the Sun. The average number of pp neutr inos producedper termination in the Sun is 1.85. For all other neutrino sources, the averagenumber of neutrinos pro duced per termination is equal to the termination per-centage/100.Terminationaν energyReaction Number (%) (MeV)p + p →2H + e++ νe1a 100 ≤0.42orp + e−+ p →2H +