How the Fine-Structure Changes from ${\simeq } 1/137$ to ${\simeq }1/128$ at High Energies

Abstract

At present available high-energies such as at an energy corresponding to the mass of the neutral $Z^0$ vector boson, the fine-structure coupling attains a value ${\simeq } 1/128$ at $Q^2 = (M_{Z})^2=(91.188)^2\,\text {GeV}^2$ starting form the well known constant value of ${\simeq } 1/137$ at low $Q^2\simeq 0$, with the latter corresponding to a measurement of the fine-structure constant at large distances, say from an electron, in laboratory experiments.