Can Virtual particles be knocked on shell (become real)? I have read these questions:
Can virtual particles be 'boosted' into becoming real particles by fields other than gravity?
where dmckee specifically mentions J/Ψ meson production as a clear example when a pair of virtual particles is knocked on shell from the nucleon see.
and where annav says "With the above background it is evident that virtual particles turn into real when they acquire mass and keep their quantum numbers: The photon hitting an electron and exchanging a virtual electron with the field of some atom (through a virtual photon or Z) creates a pair by the electron becoming real."
Can virtual particles become real?
where Solenodun Paradoxus says " But it is only an analogy, and it has its limitations. Most of the newbie questions about virtual particles can and should be addressed in the full mathematical framework which is interacting Quantum Field Theory. Any kind of explanation involving virtual particles is just hand-waving."
and Arnold Neumaier says "Virtual particles have no dynamics. The latter is always tied to a state, which - unlike virtual particles - necessarily respects causality. Hence they cannot ''become'' anything."
And I got curious, but confused. Some answers say:


*

*it is not possible, 

*some answers say it is possible (J/Ψ meson production), 

*some say it is only possible as far as we say that virtual particles mediate forces between real particles, so they have real effects.
I would like to settle this for good.
Question:


*

*Which one is it really:


*

*Virtual particles can be knocked on shell and become real

*Virtual particles can never become real

*Virtual particles have real effects on real particles
 A: One has to keep clear what elementary particle physics is about. It is about modeling mathematically the behavior of elementary particles so that predictions can be made and validated by future experiments.
The models are quantum mechanical, i.e. probabilistic, using the field of complex numbers and the tools of integration and differentiation. Given the upper and lower limits in the integrals under consideration, real numbers can be predicted for observations. 
The calculations were  simplified by Feynman when he discovered the representation with diagrams of the scattering process. 

This is the simplest process, the intermediate line is called a photon because it has the quantum numbers of a photon, even though  the mass given by the four vector is variable. The variable mass is what gives the line the title virtual.
The photon of the above diagram cannot become real, by real meaning on mass shell, because the total reaction would have the zero energy of the mass of the photon.
This type of  diagram for e+e- scattering describes the experimental plot, with different virtual exchanges

It models very well the measured crossections, where one sees that as the energy of scattering approaches certain values resonances appear with specific masses that can be fitted and assigned quantum numbers and a real number for the mass from fitting the resonance shape. In this sense only, of continuity in the mathematical model, one can say that virtual particles become real, as the energy scans the on mass shell range.

Virtual particles can be knocked on shell and become real

No,virtual particles are  just a tool in the mathematics describing the interaction, transferring the quantum numbers from the initial state to the final state.  

Virtual particles can never become real

Their only reality is in the mathematical formula describing the model that will give the real numbers to compare with experiment.

Virtual particles have real effects on real particles

Virtual particles exist in the mathematics that describes interactions of real particles. They are a mathematical tool, as much as integrals themselves. They affect the calculations, but cannot be experimented upon in the lab because they only have a mathematical existence, useful in keeping track of quantum numbers.
