UPDATE May 13, 2022: We made an elementary error by assuming that the Higgs particle is free. It is not free: its lifetime is very short. The particle exists as an internal line of a Feynman diagram. In an internal line we do allow the loop diagrams below.
Do we have a problem with divergences? We have to check if the machinery which we developed in the last fall is able to remove the divergences.
A further observation: for very short wavelength particles, a Higgs particle in an internal line is "essentially free" because short wavelength phenomena are not "aware" of the interaction where the Higgs particle is taking part. We could argue that destructive interference removes all very short wavelength particles. This is a new way to understand the natural cutoff of high frequencies.
We need to check what kind of divergences occur in the diagrams below.
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In this blog we have argued that the Feynman diagrams above are forbidden for a free particle. A particle cannot do a Baron Munchausen trick and affect its own state alone, without any external interaction.
Our "sharp hammer" model explains this. There is perfect destructive interference for the reactions above. The energy, momentum, and the speed of the center of mass of the particle have to be conserved. There is nothing to witness that the reaction happened, and perfect destructive interference is possible.
Thus, there is no need to cancel anything.
Conjecture. We will never find any superpartners of particles.
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