A neutrino group at Rutherford Lab starts a collaboration with the Kamioka Experiment in Japan which is operating a water Cerenkov detector. Neutrinos will be produced at Rutherford Lab and sent to Kamioka where they will be detected. The collaboration wants to observe neutrino oscillations. The distance between Rutherford Lab and Kamioka is 9500km. a) The following proposal is submitted: The neutrino beam will be produced at Rutherford Lab by colliding high-energetic protons at a fixed target. The emerging charged Kaons decay mainly into electron neutrinos. The neutrinos will be bent by a magnetic field and pointed towards Kamioka. They will then travel unhindered through the earth's upper layer. Once they enter the Kamioka water-Cerenkov detector, they will emit Cerenkov radiation. The condition for a particle to produce Cerenkov radiation is that its velocity is larger than the velocity of light in vacuum. Neutrinos of different flavour can be distinguished by the flavour of the particle they produce in the interaction. Electrons and muons can be distinguished, as muons produce larger cerenkov cones than electrons, if both have the same velocity. Find six flaws in the proposal, explain why they are flawed and correct them. b) The team wants to measure neutrino oscillations due to the small squared mass difference Am² 7.4 x 10-5 eV2. Calculate the neutrino beam energy needed to observe a maximum disappearance of muon neutrinos produced at Rutherford Lab on their way to Kamioka. Explain the difficulties the team would face if they wanted to measure the large mass differ- ence Am² 2.5 x 10-3 eV2 with the same experiment. (Hint: Use approximate calculations and results from the exercises.) c) Draw two Feynman diagrams describing interactions of electron and muon neutrinos which produce the corresponding charged lepton inside a water Cerenkov detector in Kamioka, name the type of interaction and calculate the minimum energy of the resulting charged particles for the process to be recorded in the detector. d) The Kamioka group has constructed an additional detector surrounding the main Water Cerenkov detector at the outside. This detector consists of outward facing photo multi- plier tubes which sit at the outer wall of the main detector and which are immersed in an additional water layer surrounding the main detector. Describe a potential purpose of this detector. Describe the interactions which happen in this new detector. Describe from which direction we would expect the particles which we want to detect with this new detector.