Energy distribution of virtual particles?

Virtual particles are mathematical place holders of quantum numbers, under the integrals representing interactions, as depicted by Feynman diagrams. A simple example electron electron scattering, the first order diagram.

Only lines entering or leaving the diagram represent observable particles. Here two electrons enter, exchange a photon, and then exit. The time and space axes are usually not indicated. The vertical direction indicates the progress of time upward, but the horizontal spacing does not give the distance between the particles.

The intermediate line represents a virtual photon, i.e. it has all the quantum numbers of the photon, except its mass is off mass shell, it can have a mass other than the zero which is the mass of the photon. It is under an integral over the angles of possible scatters, and it has no meaning to ask about its velocity because it is just a mathematical trick.

The same is true in diagrams where the virtual particles are electrons or W or whatever in the table of the standard model. Within the integrals, they would be off mass shell, the four vector representing them taking variable momenta and energies, so no velocity could be calculated.

The energy distribution would depend on mathematics of the particular exact diagram.