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My question would be (as I couldn't find a website summarising it) to have a comprehensive list of how to check whether a particle interaction is allowed and if so, what interaction it is (or it would be expected to be)

To check whether a particle interaction is allowed:

  • J,Q and B have to be conserved (as well as the energy)

Is there something else?

To check which interaction it (most likely) is I don't have many Ideas..

  • Weak Interaction: Isospin not conserved, C or/and P not conserved, individual quark numbers not conserved

but what are the indicators for the strong/EM interaction? Or how do I rule them out?

e.g. how would I check whether $$\rho^0\longrightarrow e^+e^-$$ would be allowed as an EM interaction?

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    $\begingroup$ Introductory particle physics courses and textbooks do just that: the prepare students to answer just these questions; have you tried any such texts? $\endgroup$
    – Cosmas Zachos
    Commented Dec 13, 2022 at 15:38
  • $\begingroup$ @CosmasZachos I'm currently taking an introductory course for particle physics and we haven't learned how exactly we would distinguish strong from EM interactions - hence the question. We've learned when it's the weak interaction and obviously when photons/gluons are involved its EM/strong interaction but without those two indicators, we haven't been told how to figure out when it is EM and when it is strong interaction. On our sheets, the answers are always given as "EM or strong interaction" never which of the two in specific. $\endgroup$
    – Tabi
    Commented Dec 13, 2022 at 15:48
  • $\begingroup$ @CosmasZachos Okay.. I'm slightly confused now. In my Uni's script it literally says "Isospin is conserved in the strong and electromagnetic interactions but not in the weak interaction." So this is false? Also in the above example, why can it not be strong? If your first part of the answer refers to this - the isospin is conserved in this example, is it not? $\endgroup$
    – Tabi
    Commented Dec 13, 2022 at 16:10
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    $\begingroup$ @Tabi "why can it not be strong?". Does mediator of the strong interactions (gluon) interact with electrons? No, gluons only interact with objects that carry colour charge, i.e. quarks or other gluons. Does this answer your question? $\endgroup$
    – Martino
    Commented Dec 13, 2022 at 16:43
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    $\begingroup$ Leptons do not interact strongly. Isospin is violated by EM and leptons have no isospin. $\endgroup$
    – Cosmas Zachos
    Commented Dec 13, 2022 at 17:08

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$$\rho^0\longrightarrow e^+e^-$$ is allowed by the EM interaction, as it preserves J, P and C, but violates isospin, as EM does/can.

The photon has an isovector and an isoscalar piece, and isospin is only a symmetry (barely!) of the strong interactions, up to a small explicit breaking; it treats all members of an isomultiplet evenly; but electromagnetism notices the difference in charge among members of an isomultiplet and thereby treats them differently.

Leptons, like electrons, therefore, have no isospin (charge independence), since they don't interact strongly. Isospin is thus violated. So, unless you noticed some P or C mismatch in this reaction, it has to be electromagnetic.

As such, the decay rate must be suppressed by roughly $\alpha^2$ w.r.t. strong decays, over 4 orders of magnitude. This is presumably what your course wishes you to notice.

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