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I know the kind of interaction occurring in very common reaction. For example, I know that the interaction:

$e^- + e^+ \longrightarrow \mu^+ + \mu^-$

is driven by the electromagnetic force (there is a $\gamma$ in the Feynman's diagram).

But in general, given only the formula, on which criteria can I relay to find the type of interaction (strong, weak, EM) occurring?

Has it something to do with the characteristics of the mediators? I know that the W,Z bosons have defined electric charge, mass, ..., but I can't understand how this can help me in finding the interaction.

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is driven by the electromagnetic force (there is a γ in the Feynman's diagram).

you are putting the cart in front of the horse. Interactions are defined by their strength. Stronger, i.e. most probable is the strong interaction and the crossections, i.e. probability distributions , are much larger than the electromagnetic interaction, which is larger than the weak interaction first seen in decays. This table of fundamental forces makes this clear, where the exchanged particle is on the rightmost column.

Many Feynman diagrams for the processes exist for your example, since the crossection diagrams are a perturbative expansion, with photon exchanges and Z exchanges, and depending on the energy and the particles involved different diagrams (see page 5) become dominant in the expansion. Photon exchanges are the electromagnetic contribution, Z exchanges are the weak contribution to the crossection.

Thus the only rule of thumb for picking out the dominant diagram, which will characterize the interaction, depends on the energy of the interaction under study. For low energies the exchanged Z is very much off mass shell, in your example, and the weak contribution is depressed. On the Z energy the weak contribution is dominant. One has to calculate the Feynman diagrams and fit the specific data with the theoretical calculation. This is a summary of the way the electroweak interactions have been studied.

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