Muon (g-2) : Vertex Corrections of Z0 Boson (2021.5)

Recently, the precise measurement of muon g-2 has been carried out at Fermilab, and they discovered a finite value of deviation of muon g-2 from electron. They say that the deviation should be of the order of one billionth. Even though the number is very small, this must be a historically important discovery in fundamental physics in that it should be related to some new physics.
The g-2 of electron is explained in terms of vertex corrections of photon on electron, and this theoretical model calculation is known to be a renormalization scheme in QED. This theoretical model was developed by Feynman, Tomonaga and others, and it became quite well-known since it could reproduce the experimental value of electron g-2 to a high accuracy. However, the renormalization scheme contains some divergence, and they renormalize the infinite quantity to the corresponding electron wave function. But this infinity should remain in the wave function, and it should be quite hard to believe that the renormalization scheme should hold true in real physics. Those people who may be interested in the renormalization scheme may read Cosmology and Field Theory .
The reason why the precise measurement of muon g-2 is considered to be extremely important should be related to the fact that the values of g-2 between electron and muon must be the same in QED calculations. This is clear since the g-2 is a dimensionless quantity and there is no dimensionful parameter in QED except lepton mass, and thus the g-2 prediction of electron and muon in QED must be identical to each other. Therefore, if there should be any finite difference between g-2 of two leptons, then it must indicate some new physics which is beyond simple QED predictions.
Now, what should be a new type of physics which may explain the deviation of muon g-2 from electron? We believe that this deviation should be explained by the vertex corrections of Z0 boson on muon as seen below.
Around 10 years ago, we published a field theory textbook with the title [ Fundamental Problems in Quantum Field Theory ( Bentham Publishers, 2013) ]. In chapter 5 of this textbook, we presented a brief explanation of the vertex corrections of Z0 boson on the muon g-2. At that time, we learned that the vertex corrections of Z0 boson on leptons has no divergence in spite of the fact that it should not be any gauge field theory. Or in other words, the field theory calculation of weak vector bosons does not find any divergences in the vertex corrections. This is really a surprising result. Indeed, we find a finite value of the vertex correction of Z0 boson on the muon g-2. Further, this finite number of vertex corrections of Z0 boson on the g-2 of muon is around the order of one billionth. At that time, we could never imagine that this small number might well be observed in future since muon life time is around the order of microsecond.
Here I upload a part of chapter 5 of the textbook of [ Fundamental Problems in Quantum Field Theory ( Bentham Publishers, 2013) ] for a limited time period so that graduate students can learn the theory of weak interactions in quantum field theory.

Textbook of Bentham Science Publishers : "5. Weak Interactions" PDF