I have read this question:
Now EM forces are mediated by virtual photons.
Gravity is mediated by theoretical virtual gravitons.
The strong force is mediated by virtual gluons.
Now all these are massless bosons.
Yes I understand that virtual particles are just a mathematical formula to describe the effects of the force field.
But the weak force is different. It is mediated by massive particels, W and Z bosons.
And yes I understand that the massiveness of these bosons cause the short range of the weak force.
What I do not understand is how can virtual particles be massive and still mediate the force? It is not a real particle. How can something not real have rest mass while mediating an interaction? Virtual particles are just a mathematical model, how can they have rest mass? How do you experimentally prove that a virtual particle has rest mass?
Does the massiveness of the W and Z bozons mean that the weak force is fundamentally different from the other forces? How can virtual particles be massive while mediating an interaction?
How do we experimentally prove that virtual W and Z bozons have rest mass?