Group-Theoretical Determination of the Mixing Angle in the Electroweak Gauge Group

TL;DR

This paper uses group theory to analyze the electroweak gauge group, deriving a specific value for the Weinberg angle and discussing its implications for the relationship between fundamental constants.

Contribution

It provides a group-theoretical derivation of the Weinberg angle, showing it must be 1/2 under certain symmetry assumptions, which is a novel approach.

Findings

Derives $ heta_W$ as 45 degrees from group theory

Suggests the value is an asymptotic limit in the early universe

Indicates $e^2/g^2$ and $1-M_W^2/M_Z^2$ are unrelated

Abstract

The assumption that the Weinberg rotation between the gauge fields associated with the third component of the ``weak isospin" ($T_3$) and the hypercharge ($Y$) proceeds in a natural way from a global homomorphism of the $SU(2)\otimes U(1)$ gauge group in some locally isomorphic group (which proves to be $U(2)$), imposes strong restrictions so as to fix the single value $\sin^2\theta_W=1/2$. This result can be thought of only as being an asymptotic limit corresponding to an earlier stage of the Universe. It also lends support to the idea that $e^2/g^2$ and $1-M_W^2/M_Z^2$ are in principle unrelated quantities.