I've tried to ask this question before, but I've never quite got a satisfying answer so I'm going to simplify my question.
As I understand it, virtual particles are just 'internal legs of a Feynman diagram' and are thus unobservable and we can in fact consider them purely as a 'convenient way of organising a perturbative expansion' and not as actual particles themselves.
The propagator used for virtual particles is given by $\frac{1}{p^2-m^2}$ for the momentum $p$ (which is conserved on the Feynman vertices) and mass $m$ of the virtual particle.
I understand that virtual particles are 'off-mass-shell' such that $p^2 \neq m^2$, so by 'mass of virtual particle' I'm just referring to the quantity m being used in the propagator
- The mass of a virtual particle is related to its maximum range of its Yukawa potential. i.e. $m \propto \mu$ for $\mu$ in $U\propto \frac{e^{-\mu r}}{r}$
My question is, if virtual particles are in a sense a 'convenient fudge' to aid in perturbation calculations. Why does the variable 'm' being used in the propagator always seem to have the same value as a mass of a particle which we can detect in other situations as real and not virtual.
It seems like a massive coincidence to me that a mass of a virtual particle, which we we just defined as related to $\mu$ for convenience in studying interactions, would also always be able to be detected as an 'external leg' particle itself.
So ultimately my question is, why do we never have forces with $\mu$ that don't happen to be related to the mass of an actual real particle. It there some deep theorem to all this?
I'm guessing there might be, since I have heard explnations online like 'the Higgs boson has nothing to do with giving particles mass, the Higgs field does, and the fact that the field exists means the excitation (namely the Higgs boson) must exist'.