Global restrictions to the Mixing Angle $\theta_W$

TL;DR

This paper presents a topological argument suggesting the theoretical value of the electroweak mixing angle differs from its experimental measurement, implying they may only align in the early universe before symmetry breaking.

Contribution

It introduces a topological perspective to explain the discrepancy between the theoretical and experimental values of $ heta_W$, challenging the conventional identification of these definitions.

Findings

Theoretic value of $ heta_W$ is 1/2 based on topological arguments.

Experimental value of $ heta_W$ is approximately 0.23 from electroweak measurements.

The two definitions of $ heta_W$ may only coincide in the early universe before symmetry breaking.

Abstract

We provide the theoretic value 1/2 for the quantity $\sin**2\theta_W=e**2/g**2$, as opposite to the experimental value of $\sin**2\theta_W=1-M_W**2/M_Z**2 \sim 0.23$, in the electro-weak gauge group $SU(2)\otimes U(1)_Y$. The arguments we use are of topological nature and have to do with natural requirements of globality in the transformations of the gauge algebra. This results supports the idea that the two definitions of $\sin**2\theta_W$ cannot be simultaneously identified except, maybe, in an asymptotic limit corresponding to an earlier stage of the Universe, before the spontaneous symmetry breaking had taken place.