What is the connection between the Lamb Shift and the g factor?

[raracon]

TL;DR

Trying to find a connection between these two (Lamb Shift and G factor aka anomalous magnetic moment)

German Wikipedia mentions that the g factor is one of the causes of the Lamb Shift. It does not say why and I am trying to find a connection between these two things. Any ideas?

 

[vanhees71]

The anomalous $g$ factor (devisions from 2 for elementary Dirac particles like the electron or muon) are due to the radiative corrections of the $e\bar{e}\gamma$ vertex function, which are also contributing to the Lamb shift of the hydrogen-atom levels.

 

[raracon]

The anomalous $g$ factor (devisions from 2 for elementary Dirac particles like the electron or muon) are due to the radiative corrections of the $e\bar{e}\gamma$ vertex function, which are also contributing to the Lamb shift of the hydrogen-atom levels.

Ah I see. And how are they contributing? What would change if they would not be there?