A virtual particle is a loop of two particles? Feynman cannot handle tunneling

In the previous blog post we conjectured that the virtual photon which mediates the electric pull between the nucleus and the electron is actually two real photons which move to opposite directions:

e- --------------->---------->-------
                    ^             |
                     |             | photons
                     |            v
Z --------------- >---------->-------

We make the photons real by adding enough energy to them so that the energy E and the momentum p carried by the photon match. From where do these photons get the energy? If the electron moves slowly, then it may not have enough kinetic energy to donate for the photons. Also, a slow electron spends more time near the nucleus and receives more momentum p. It looks like we have to borrow the energy from the vacuum.

The loop of photons bears some resemblance to a loop of a virtual electron and a virtual positron:
         ______
       /             \
      ^               |
e-   |               v    e+
       \_______/

If we want to make the pair real, we need to borrow energy from the vacuum.

In an earlier blog post, we defined a virtual electron as a real electron which has entered a high potential wall and has a negative kinetic energy.

One aspect is that when we have a system of particles, we cannot really define the energy of an individual particle. It is the system, whose energy we can calculate. Should we consider all particles real then and call the system virtual when the potential energy of the particles exceeds the total energy we gave to the system?

If we have a positron which tries to tunnel through the potential wall of a nucleus Z, it is not the positron which becomes virtual but the system Z e+ which becomes virtual. How do we handle this in a path integral? If we use the Schrödinger equation, the wave function of the positron will decay exponentially if it comes too close to the nucleus. Feynman propagators do not contain such exponentially decaying terms because they are free particle propagators.

We have found one of the reasons why the Feynman integrals for virtual particles diverge:

Feynman formulas do not take into account the fact that the probability amplitude of a path should decay exponentially if its kinetic energy is negative at some point.

An example is a photon whose energy is less than 1.022 MeV. Let the photon scatter from a nucleus Z.

Any path which contains an electron-positron pair has a negative kinetic energy (we interpret the rest mass of the pair potential energy) and the integral over the lagrangian should decay exponentially. The system is trying to tunnel through a potential wall.

But the Feynman formulas contain the product of the propagators of various photons, the nucleus, an elecron, and a positron. The propagators do not take into account the amount of energy that the system has initially available.

Feynman diagrams are about scattering processes where particles do not need to tunnel through ordinary potential walls like an electric potential. They may do that, though.

But in scattering there is tunneling through walls imposed by the energy of particle creation. No wonder Feynman integrals diverge in those cases as they cannot handle tunneling at all. The real question is why the formulas after renormalization give exquisitely accurate answers?