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I have read this question:

How it is possible to mediate a weak interactions by very heavy particle such as Boson?

How can a pion have a mass, given it's a "field mediator" and created/destroyed continuously?

Can virtual particle have mass?

Can/do Virtual Particles have mass/energy?

Why don't virtual particles violate conservation of mass/energy?

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?

Question:

  1. 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?

  2. How do we experimentally prove that virtual W and Z bozons have rest mass?

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  • $\begingroup$ Well, 'real' is a vague concept. If you consider a simplest process in EM, indeed, there's a necessity for virtual photons. On another hand, photons are stable particles which can propagate just like electrons. Presumably, same is true for gravitons. This is not true for gluons (at least, at low energies) - they are not color singlets. Weak bosons can propagate for some time but then they decay. I mean, there's no direct connection between massivenes/virtual/mediating an interaction except for the fact that in any interaction process you do have virtual particles at the fundamental level. $\endgroup$ – mavzolej Apr 16 at 4:37
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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?

As you have stated, virtual means mathematical tool. The four vector of a virtual particle changes according to the kinematics of the incoming and outgoing particles, mass can even be negative. What makes the difference at our time in the cosmos is that symmetry breaking has given a physical mass to free Z and W. This mass enters in the propagator representing the virtual particle in the Feynman diagram .

In both position space and momentum space propagators , the mass of the virtual particle enters in the denominator. When the virtual exchange has a small mass the total probability contributed to the interaction can be large, photon, electron (not to forget there are a lot of virtual particles in feynman diagrams).

propag

The variables are under the integral of the Feynman diagram. This is to show that the real mass of the virtual particle exchanged in the diagram enters in the denominator, thus when large, diminishing the probability of the interaction the Feynman diagram represents.

With the enormous mass of the Z and W the diagram is suppressed, which is what makes the weak interaction , low probability of the final integral calculation. Before symmetry breaking, all forces were equal in this sense as the masses are zero.

How do we experimentally prove that virtual W and Z bozons have rest mass?

Virtual are not experimentally measurable except by the calculation of the total probability for the experiment fitting the data, i.e. indirectly. The model of feynman diagrams for the calculations has been validated by all experiments up to now, and if we find a violation, we look for extensions of the standard model and not for a change in mathematics.

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