The anomalous magnetic moment form factor $F(q^2)$ of an elementary fermion at $q^2=0$, calculated at one-loop, is $$F_2(0)=\frac{\alpha}{2\pi}.$$ At least at this order (order-$\alpha$), $F_2(0)$ does not have any dependence on the mass of the fermion. Within QED, $e^-, \mu^-, \tau^-$ all have the identical values of $F_2(0)$ at the lowest order. But do all charged leptons have the same value of $F_2(0)$ also at the higher orders? I would intuitively guess that there will be a mass dependence at some higher order. If so, what is the lowest order at which a mass-dependence of $F_2(0)$ arises theoretically?
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2$\begingroup$ Did you try to compute this at least at two-loop and see if the mass enters? Why guess when you can check? $\endgroup$– ACuriousMind ♦Commented Feb 24, 2022 at 14:20
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