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If I have a reaction (shown below), and I'm supposed to work out what the products will be, what would the lepton neutrino $\nu$ be? e.g electron neutrino: $$ \nu + p \to $$

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Hi Bob. I will give you a hint: lepton number conservation , if you are talking of the neutrino on the left. You have to take into account all the conservation laws for the possible products on the right, baryon number is also there, charge ... –  anna v Nov 4 '11 at 19:57
    
but protons don't have a lepton number? –  Bob Nov 4 '11 at 20:12
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@Bob: proton's lepton number is zero (because it is a baryon) –  Slaviks Nov 4 '11 at 21:43
    
Welcome to Physics.SE! This site supports LaTeX for formatting math by way of the MathJax javascript engine. There are some minimal hints in the FAQ and a lot has been said about LaTeX on-line. –  dmckee Nov 5 '11 at 2:07
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1 Answer

Put simply there is no unique answer, several possibilities are

  1. neutral current elastic scattering: $\nu + p \to \nu + p$
  2. neutral current resonant delta production: $\nu + p \to \nu + \Delta^+$
  3. charged current resonant delta production: $\nu + p \to e + \Delta^{++}$
  4. neutral current deep inelastic scattering: $\nu + p \to \nu + \text{lotsa stuff}$
  5. charged current deep inelastic scattering: $\nu + p \to e + \text{lotsa stuff}$
  6. $\cdots$

including a whole host of meson production reactions. A colleague of mine is trying to extract lambda production cross-sections from a the data set of a test-bed liquid argon time-projection chamber for her dissertation even now.

Pay particular attnetion to the difference between options 2 and 3 or 4 and 5. The distinction between them is better exhibited at vertex level where they represent

  • neutral current: $\nu + q \stackrel{\gamma,Z}{\to} \nu + q$
  • charged current: $\nu + d \stackrel{W}{\to} e + u$
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Your second reaction is wrong. Inverse beta decay: $\nu_e n \to e\; p$. As for neutrino-proton interaction it may be $\nu_e p \to e\; \pi^+ p\;$ or $\nu_\mu p \to \mu^-\pi^+p $ –  voix Nov 5 '11 at 7:50
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Your fourth reaction should be $\overline\nu_e p \to e^+\Delta^0$ –  voix Nov 5 '11 at 8:06
    
@voix Yes. Of course it should. In both cases. –  dmckee Nov 5 '11 at 15:02
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