Possible reactions / decays in the standard model

Question

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?

Answer 1

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 $CPT$