Why the vertex function affects the electron anomalous magnetic moment but not its charge? SOLVED!

On February 28, 2021, we asked the question in the title of this blog post.

https://www.fzu.cz/~kupco/QCD/2017/qcd06_anomalni_magneticky_moment.pdf

https://cluster28-files.instructure.com/files/1875~936399/download%3Fdownload_frd%3D1%26verifier%3DDTWO5WywHiDDO9YoFWCbyxFi6dpxJBZlug5SQAvx

Alexander Kupco (2017) and Matthew Schwartz (2012) have written derivations of the anomalous magnetic moment.

They use the Gordon decomposition, or identity, to divide the interaction into the Coulomb interaction and the magnetic interaction. It turns out that the vertex function only affects the magnetic part. That is, the vertex function has no effect when we measure the electron charge in the Millikan-Fletcher experiment, but it does have an effect when we measure the magnetic moment in a Penning trap.