Astroparticle Physics

92 6 Primary Cosmic Raystau production?If, however, muon neutrinos have oscillated into tau neutrinos,a deficit of muon neutrinos will be observed in thedetector because tau neutrinos would only produce taus inthe water Cherenkov counter, but not muons. Since, however,the mass of the tau is rather high (1.77 GeV/c 2 ), tauneutrinos normally would not meet the requirement to providethe necessary center-of-mass energy for tau production.Consequently, they would escape from the detector withoutinteraction. If the deficit of muon neutrinos would be interpretedby (ν µ → ν τ ) oscillations, the mixing angle and thedifference of mass squares δm 2 can be determined from theexperimental data. The measured value of the double ratioR = 0.69 leads toδm 2 ≈ 2 × 10 −3 eV 2 (6.24)neutrino mass(see also parts b,c of Problem 4 in this section). The validityof this conclusion relies on the correctly measured absolutefluxes of electron and muon neutrinos. Because of the differ-ent Cherenkov pattern of electrons and muons in the waterCherenkov detector the efficiencies for electron neutrino andmuon neutrino detections might be different. To support theoscillation hypothesis one would therefore prefer to have anadditional independent experimental result. This is providedin an impressive manner by the ratio of upward- to downward-goingmuons. Upward-coming atmospheric neutrinoshave traversed the whole Earth (≈ 12 800 km). They wouldhave a much larger probability to oscillate into tau neutrinoscompared to downward-going neutrinos which have traveledtypically only 20 km. Actually, according to the experimentalresult of the Super-Kamiokande collaboration thezenith-angle dependenceat maximal mixing (sin 2 2θ = 1, corresponding to θ =45 ◦ ). 1 If one assumes that in the neutrino sector a similarmass hierarchy as in the sector of charged leptons exists(m e ≪ m µ ≪ m τ ), then the mass of the heaviest neutrinocan be estimated from (6.24),√≈ δm 2 ≈ 0.045 eV (6.25)m ντ1 The 90% coincidence limit for δm 2 given by the Super-Kamiokande experiment is 1.3 × 10 −3 eV 2 ≤ δm 2 ≤ 3 ×10 −3 eV 2 . The accelerator experiment K2K sending muon neutrinosto the Kamioka mine gets δm 2 = 2.8 × 10 −3 eV 2 [5].K2K – from KEK to Kamioka, Long-baseline Neutrino OscillationExperiment