When viewing the above reference keep in mind the Little TOE view: That the electron is composed of three liberated Higgs lattice elements.
So you would like to determine the value of the fine structure constant from first principles? Then so you may. But first we need to understand the structure of the Higgs lattice.
Were the Higgs elements like uniform marbles that were all compressed into a very large universe, we might expect local regions to find a maximum density arrangement. Something like a regional close pack formation.
But the Higgs are not marbles. They are not fully restrained. And they are not round. Because the Higgs are not confined to a round zone they can pack more closely than marbles. They are more like dodecahedra. Further more, when a Higgs, or two, or more are dislodged from the lattice they can move through the lattice with very little resistance.
And the Higgs can reshape to warp the lattice around every dislocation. We call this effect gravity.
But, back to the lattice. This view of the lattice field, still and absolutely cold with close packing, is unreal. But with a temperature that yields Higgs cells in the shape of dodecahedra; displaced groups of Higgs, along with their dislocations are restricted in their freedom of motion. Guided by the six axes of the Higgs lattice.
Are you ready to calculate the probability that is the fine structure constant?