The QCD Coupling Parameter Derived from the Uncertainty Principle and a Model for Quark Vacuum Fluctuations

Abstract

The magnitude of the strong interaction is characterized by $\alpha_s$, the coupling parameter in Quantum Chromodynamics (QCD), a parameter with an unexplained value in the Standard Model. In this paper, a candidate explanation for $\alpha_s$ is derived from (1) the lifetime of quark-antiquark pairs in vacuum fluctuations given by the Uncertainty Principle, (2) the variation of $\alpha_s$ as a function of energy in QCD, and (3) classical relativistic dynamics of the quarks and antiquarks. A semiclassical model for heavy quark-antiquark vacuum fluctuations is described herein, based on (2) and (3). The model in this paper predicts the measured value of $\alpha_s(M_{Z^0})$ to be 0.121, which is in agreement with recent measurements within statistical uncertainties.