The Running to Unification: A Study of the Evolution of the Weinberg Angle in the Standard Model
weak mixing angle. Gauge couplings. Standard Model.
In this work, we investigate the evolution of the Standard Model gauge couplings through Renormalization Group Equations (RGEs), with an emphasis on the behavior of the Weinberg angle at different energy scales. We used the PyR@TE package to derive and solve the RGEs at the 1-loop approximation level, using initial conditions extracted from the Particle Data Group. The couplings g1, g2, and g3 are analyzed, as well as the evolution of the parameter sin^2 θW (μ), discussing their variations across the energy scale. The results show that, although a partial convergence of the couplings occurs at high energies, the exact unification predicted by many Grand Unified Theories (GUTs) is not achieved within the minimal context of the Standard Model. This study provides a quantitative overview of the role played by the Weinberg angle in the analysis of the unification of fundamental forces.