In the T2K experiment the proton beam accelerated by the J-PARC high-intensity proton synchrotron is driven on a target. The emerging pions are focussed in the forward direction and then drift in a vacuum pipe in which they decay. At the end of the decay volume all the charged and neutral particles are absorbed, with the exclusion of neutrinos. The neutrino beam is aimed to the Super-Kamiokande detector located at Kamioka at a distance L = 295 km. The neutrino flux at Kamioka, averaged over the duty cycle, will be Φ = 2 x 10¹¹ m^–2yr^–1. Super-Kamiokande is a water Cherenkov detector with a fiducial mass of 22.5 kt.Consider the detection of the ν_μs by observing the μ produced via the CC processes on protons and neutrons and similarly of the of the νes by observing the e. Assume across-section per nucleon σ = 3 x 10^-43 m^-2 in both cases.

(1) Which is the dominant neutrino flavour in the resulting neutrino beam?

(2) Considering pions of energy E_π = 5 GeV, what is the energy Eν of the neutrinos emitted at the angle θ = 2.5°? Which is the corresponding angleθ° in the pion CM frame?

(3) What is the energy E_ν of the neutrinos emitted at the angle θ = 0°?