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If we are in the Standard Model and we have the following processes:

$$e^+ + e^- \to \mu + \mu^-\\ p + p \to K^+ + \Sigma^+ \\ p + n \to \Lambda^0 + \Sigma^+ \\ e^+ + e^- \to u + \tilde{t} $$

And the following decay processes:

$$ \mu^- \to e^-\gamma\\ \tau^- \to e^- + \nu_{\tau} + \tilde{\nu}_e \\ \Sigma^+ \to K^+ + \Lambda^0 \\ \Xi^- \to n + \pi^-\\ p \to e^+ \pi^0\\ \Lambda^0 \to p + \pi^- $$

Assuming that the initial energy is sufficient, which processes can happen and which cannot? Of course not all of the above processes are possible. What is a quality that helps me decide whether one of the above processes or decays can or cannot happen, i.e flavor quantum number, or something similar.

But the problem is that for example for the first process, that of electron positron into muon and anti muon, I know that the process can happen for sufficient initial energy, but I know that because it can be experimentally proven. How can I know that the process happen, without the need of an experiment?

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    $\begingroup$ You surely aren't asking for someone to do your (easy!) homework for you. Show your work on the kinematics of the first reaction you claim you are only asking about. $\endgroup$ Jun 17 at 15:11
  • $\begingroup$ I never asked for someone to solve it. I asked if there are other qualities other then the flavor quantum number that can help me decide whether the process can be done or no. And if I need different qualities for each of them, or that one is enough for all. At what point I asked for a solution ? $\endgroup$
    – imbAF
    Jun 17 at 15:16
  • $\begingroup$ What are you asking then? If the quantum numbers on the left and right match, and if the energy-momentum jibes, what, exactly is troubling you? You might clarify your question. Show your work on energy/momentum constraints. $\endgroup$ Jun 17 at 15:24
  • $\begingroup$ One recommendation we have in the lecture is to observe the flavor quantum number. That is one way of solving the problem. But I was curious to know if there are other ways, quantities that one can observe and decide whether the process can happen or no. Hence the reason why I listed all the processes, to make it clear about what I am speaking. It's me wanting to know more then one way of solving the same problem,I guess $\endgroup$
    – imbAF
    Jun 17 at 15:26
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    $\begingroup$ Does the second one conserve baryon number? The 3rd and 4th flavor, etc... $\endgroup$ Jun 17 at 15:29
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To summarize, whether a reaction/decay is allowed or forbidden in the SM, the following laws/quantum numbers needs to be checked.

  1. Energy, momentum and angular momentum

  2. Charge conservation

  3. Baryon number & lepton number and lepton family number also

  4. Quark flavors $s, c, b $ & $t$

  5. Isospin ($I$) & $I_3$

  6. Parity ($P$), charge conjugation ($C$), $CP$, time reversal ($T$) and $CPT$

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