arXiv:hep-ph/9905257 v1 6 May 1999Neutrino PhysicsWick C. HaxtonInstitute for Nuclear Theory, Box 351550,and Department of Physics, Box 3515 60,University of Washington, Seattle, WA 98195andBarry R. HolsteinInstitut f ¨ur KernphysikForschungszentrum J¨ulichD-52425 J¨ulich, GermanyandDepartment of Physics and AstronomyUniversity of Massachusetts, Amherst, MA 01003August 23, 2002AbstractThe basic concepts of neutrino physics are presented at a levelappropriate for integration into elementary cours es on quantum me-chanics and/or modern physics.01 IntroductionThe neutrino has been in the news recently, with reports that the Su-perKamiokande collaboration — which operates a 50,000 ton detector ofultrapure water isolated deep within the Japanese mine Kamiokande — hasfound evidence o f a nonzero neutrino mass [1]. The neutrino, a ghostly par-ticle which can easily pass through the entire earth without intera cting, haslong fascinated both the professional physicist and the layman, as this dittyfrom writer John Updike [2] attestsNeutrinos, they are very smallThey have no charge and have no massAnd do not interact at all.The earth is j ust a silly ballTo them, through which they simply pass,Like dustmaids down a drafty hallOr photons through a sheet of glass.They snub the most exquisite gas,Ignore the most substantial wall,Cold-shoulder steel and sounding brass,Insult the stallion in his stall,And, scorning barriers of class,Infiltrate you and me! Like tallAnd painless guillotines, they fallDown through our heads into the grass.At night, they enter a t NepalAnd pierce the lover and his lassFrom undernea t h the bed—you callIt wonderful; I call it crass.We present this pedagogical discussio n of basic neutrino physics in t he hopethat aspects of this topical and fascinating subject can be integrated intointroductory courses, providing a timely link between classroom physics andscience news in the popular press. In this way an instr uctor may be ableto build on student curiosity in order to enrich the curriculum with someunusual new physics. In this spirit we present below some of the basic physics1underlying massive neutrinos and neutrino mixing, as well as other propertiesof neutrinos relevant to both terrestrial experiments and astrophysics.2 Neutrinos: HistoryWe begin with a bit of history—an interesting and more detailed discussioncan be f ound in Laurie Brown’s article in the September 1978 issue of PhysicsToday [3]. Nuclear beta decay is a natural form of radioactivity wherein aparent nucleus decays to a daughter with the same atomic mass, but anatomic number changed by one unit, with the missing char ge carried off byan electron or positron(A, Z) → (A, Z ± 1) + e∓(1)This is quite literally nuclear transmutatio n of the type that fascinated al-chemists of an earlier age. One well-known example is the decay of a freeneutron into a proton and electron, with a half life of about 10 minutes.Another is the decay of a bound neutron in tritium to pro duce an electronand3He with a half life of 1 2.26 years: the effects of the nuclear binding inchanging the energy released in the decay is responsible for the great increasein the half life. At the end of the 1920’s the existence of such beta emitterswas well established. However, the spectrum of the emitted electrons waspuzzling. If beta decay occurs from rest into a two -body final state as givenin Eq. 1, momentum conservation would require the momenta of the emittedelectron and recoiling nucleus to be equal and o pposite. Energy conservationwould then fix the outgoing electron energy which, because the nucleus isheavy and thus r ecoils with a negligible velocity, is nearly equal to the dif-ference of the parent and daughter nuclear masses (known as the reactionenergy release or Q-value)Q ≃ M(A, Z) − M(A, Z ± 1) (2)As the Q-value in the beta decay of tritium is 18.6 keV, one would expect amonochromatic spectrum with all emitted electrons having this energy. In-stead experimentalists found a continous spectrum of electron energies rang-ing from the rest mass meto the Q -value, peaking at an energy about half wayin between, as shown in Figure 1. Various explanations were considered—Niels Bohr even propo sed the possibility that energy conservation was no2ddEeEeQmeexpectedspectrumobservedspectrumFigure 1: The β energy spectrum fo r decay into a heavy daughter nucleus,electron, and neutrino is compared t o the monoenergetic spectrum for decayinto a daughter nucleus and electron, o nly. The spectrum is idealized: dis-tortions due to the Co ulomb interaction between the electron and daughternucleus have been neglected.longer exact in such subatomic processes, and rather preserved only in a sta-tistical sense, somewhat in analogy with the second law of thermodynamics!However, in a letter dated December, 1930, Pauli sug gested an alternativeexplanation—that an unobserved light neutral particle (called by him the“neutron” or neutral one but later renamed by Fermi the “neutrino” or littleneutral one) accompanied the outgoing electron and carried off the missingenergy that was required to satisfy energy conservation. Pauli offered thisexplanation tentatively as a “desperate remedy” to solve t he energy prob-lem. Although he publicized it in various talks over the next three years, nopublication occurred until his contributio n to the Seventh Solvay Conferencein October 1933 [4]. He also proposed (correctly) that the neutrino was aparticle carrying spin 1/2 in order to satisfy angular momentum conservationand statistics.3Fermi was present at a number of Pauli’s presentations and discussedthe neutrino with him on these occasions. In 1934 he published his insight fulmodel for the beta decay process, and indeed for weak interactions in general[5]. He described beta decay in analogy with Dirac’s successful model of theelectromagnetic interaction, wherein two charg ed particles interact via theexchange of a (virtual) photon that is produced and then absorbed by theelectromagnetic currents associated with the particles (cf. Figure 2a). Fermirepresented the wea k interaction in terms of the product of weak “currents,”one connecting the initial a nd final nucleon and the other connecting thefinal state electr on/positron and Pauli’s neutrino (cf. Figure 2b). In electro-magnetism the virtual photon connects the two currents at distinct pointsin space-time: indeed the masslessness of the photon is the r