The fine structure constant alpha is said to be running
with energy as (from various QED textbooks)

1/alpha(E) = 1/alpha - (1/3 pi) ln (E^2/m^2)

where m is the electron mass, ln the natural logarithm,
and alpha without index is 1/137.036.

But many papers mention that at 90 Gev, alpha is around 1/128.
This is in contradiction with the above formula, which would give
a value of around 133 at 90 GeV.

Is the discrepancy due to the fact that the formula
misses the hadronic corrections?

As a result, what value is expected for alpha at
10^19GeV? Where can one look this up?

Frank