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As far as I know, the virtual particles that appear in Feynman diagrams are allowed to be outside of their mass hyperbola, namely \begin{equation} k^2 = \omega^2 - (\vec{p})^2 = m^2 \end{equation} So that the conservation laws are verified.

If this in mind (which I am not entirely sure it is), how can we know the mass of the interaction bosons?

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  • $\begingroup$ A "virtual particle" is a mathematical construct. It's not an actually measurable quantized energy exchange. Do you want to know if all the internals of a physical theory have to connect to measurable quantities? No, they do not. In lucky cases a single perturbation term (or better, order) like this can already account for the overwhelming majority of an effect, though, so one could be tempted to assign some "reality" to it. Isn't that the case for the anomalous magnetic moment of the electron where next to leading order is already "pretty good'? $\endgroup$
    – FlatterMann
    May 16 at 17:42
  • $\begingroup$ You find out the mass of the field external particles interacted with by seeing which external momentum for them gives the cross section a resonance. $\endgroup$
    – Connor Behan
    May 16 at 18:09
  • $\begingroup$ I understand. However, do these particles occur outside of virtual interactions? Then what defines them as true? How do we know they exist if they can only appear `virtually'? (Some of them). As in, how do we know they are true in contrast to for example phonons or holes in solid physics? $\endgroup$
    – dolefeast
    May 16 at 18:43

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