Saturday, July 9, 2016

A formula for α

On page 4 of "Naturally Speaking" by G.F. Giudice, after a short list of numerological formulas for the fine-structure constant α, one finds a formula for α according to physical orthodoxy, i.e. grand unification. I reproduce it here for the edification of passing numerologists: 

α = { αs sin2θW (b1−b3)+3/5 cos2θW (b3−b2) } / (b1−b2) + higher-order terms.

"Here, the fine-structure constant α, the strong coupling constant αs and the weak mixing angle θW are evaluated at the same renormalization scale and b1,2,3 are the gauge β-function coefficients. Higher-order terms cannot be neglected to achieve a prediction that matches the experimental accuracy."