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This will likely be easy for anyone experienced in particle physics, but I'm not. I'm asked to explain why it is impossible to construct a valid Feynman diagram using Standard Model vertices for the following processes:

$\nu_{\tau} + p \rightarrow \tau^{+} + n$

$\pi^{+} + \pi^{-} \rightarrow n + \pi^{0}$

I was already asked two similar problems, and those were clear since charge wasn't even conserved for those processes. But here I'm stuck. Can someone help me out? It's clear there are some concepts I'm not grasping.

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  • $\begingroup$ I don't know the answer but in the Pion case, I think it has to do with the approximate conservation of baryon number. $\endgroup$ – Brandon Enright Feb 6 '14 at 1:38
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    $\begingroup$ In the Tau Neutrino case, you have a matter neutrino (+1 lepton number) going to an anti-Tau (-1 lepton number). $\endgroup$ – Brandon Enright Feb 6 '14 at 1:39
  • $\begingroup$ is there any way to solve without recourse to conservation of baryon and lepton number? these problems are in the very first chapter of our text, and lepton/baryon number have certainly not been introduced yet $\endgroup$ – mikefallopian Feb 6 '14 at 1:45
  • $\begingroup$ Essentially all we have learned about Feynman diagrams is what constitutes a valid vertex $\endgroup$ – mikefallopian Feb 6 '14 at 1:46
  • $\begingroup$ Conservation of any particular quantum number is no different that conservation of charge. Charge is a quantum number. If there is another answer then I don't know it, but I'm absolutely no expert. $\endgroup$ – Brandon Enright Feb 6 '14 at 1:46
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As mentioned in the comments, both processes are disallowed due to conservation of quantum numbers. This is the only way to formally prove this. In order to avoid using the words lepton and baryon number conservation you can try to draw the diagrams for these process brute force. You won't succeed (because of these conservation laws), but this will help you find a reason why each process won't work.

Taking the first process as an example. To have a proton turn into a neutron would require emission of a $W$ boson (draw it and see...). Thus this $W$ boson has to combine with the neutrino to form a $\tau^+ $ for this diagram to be valid. However, this can't happen since a $W$ boson only couples neutrinos to $\tau ^-$.

It is easy to form a similar argument for the second process.

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