We presume that the spin-related component in the coupling constant e, associated with vacuum polarization, is: An electromagnetic coupling with a magnetic moment.
So, including a first anomaly term, we make the following guess, similar to Gordon decomposition:
Γ(a) = 1 + [a (1 +a/2π)],
One could in principle derive an, exact to all order, value for the observable a value with unlimited precision:
1/a = 137.035999528369196 (←やや大きい)
"A non-perturbative derivation of the exact value of the SU(2) coupling value g from the standard Electroweak Lagrangian itself"