Problem 3. Particle physics-detecting neutrinos. Neutrinos can be detected by their interactions with electrons or nuclei. Suppose a muon neutrino Vụ hits an atom (so it could be interacting with either an electron, up quark, or down quark). The muon neutrino is transformed into some other type of particle, so it isn't in the final state. Our reaction is: Vu + (part of atom) → (unknown final state without vu) (a) Based on conservation of muon number, what particle must appear in the final state, since the muon neutrino has vanished? (b) What does conservation of charge have to say about the rest of the process? Can the (part of atom)' be unchanged, and if not, what about it has to change? (c) What are the two (complete) particle physics processes that could happen, consistent with the above two conservation laws, and with two particles in the final state? (Specifically, for each example, which part of an atom (e¯,u, d) appears in the initial state, and what two particles are in the final state?) (d) One of the processes should have quarks, and can also be written in terms of nucleons (p, n). Write it that way. (Only one of the quarks in the nucleon will actually interact.) (e) Assuming the atom is more or less at rest, is there a minimum amount of energy that the in- coming neutrino has to have for either of the examples you gave to actually happen? Why/why not? If there is, calculate it.

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