I'm revising for an exam and looking at a few exercises, one of which starts with

Consider the charged-current interaction between a muon neutrino with one of the valence quarks of the proton.

We did not discuss things like in detail in the course, so I looked at the solution to get a hint. The first sentence in the solution is

At first order, the charged-current process must be $\nu_\mu d\rightarrow \mu^-u$

  • Why's that? Why can't the neutrino interact with an up-quark?

  • Where do the flavour changes in both sectors come from?


All of charge, lepton number and lepton-flavor number should be conserved in the reaction.

  • Because the reaction is charged-current, the neutrino will be converted into a charged lepton and because it is a neutrino (and not an anti-neutrino) it must be a negatively charged lepton (to conserve lepton number).
  • That means that the quark involved must be changed to another quark with a charge that is 1 unit more positive than it started, so you have to interact with a $-1/3$ quark.

At low enough energies you only see the valence content of the nucleon, so you have to pick the down quark. Presumably the author is assuming this case.

At higher energies you can also interact with the sea and strange and bottom quarks also become accessible.


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