Weak mixing angle under U(1,3) colored gravity

Abstract

Colored gravity, based on 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 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 (sin2 θW) is predicted to exhibit about ~ 0.231 for lepton-lepton interactions (close to observations) and ~ 0.222 for hadron-lepton interactions, which is in 3σ tension with some observations. These findings open pathways for reconciling experimental data with colored gravity and suggest avenues for quantum correction studies.