Weak mixing angle under $\text{U}(1, 3)$ colored gravity

TL;DR

This paper investigates colored gravity based on U(1,3) symmetry, predicting the weak mixing angle and exploring its implications for unifying fundamental interactions, with results close to experimental values but with some tension.

Contribution

It introduces a novel colored gravity model based on U(1,3) symmetry that predicts the weak mixing angle and incorporates standard model interactions.

Findings

Predicted weak mixing angle for leptons: ~0.231

Predicted weak mixing angle for hadron-lepton interactions: ~0.222

Results are within 3σ of experimental observations

Abstract

Colored gravity, based on $\text{U}(1,3)$ symmetry, emerges naturally in the complexification of Lorentzian manifolds and integrates U(1) electromagnetism as a subcase. This work explores the viability of also including strong and electroweak interactions under the $\text{U}(1,3)$ gauge group of colored gravity. We identify specific generators linked to leptonic and quark interactions and embed the standard Higgs mechanism. Crucially, the weak mixing angle ($\sin^2\theta_W$) is predicted to exhibit about $\sim0.231$ for lepton-lepton interactions (close to observations) and $\sim0.222$ for hadron-lepton interactions, which is in 3$\sigma$ tension with some observations. These findings open pathways for reconciling experimental data with colored gravity and suggest avenues for quantum correction studies.