Toward a q-Deformed Standard Model

Abstract

A gauge theory with an underlying SU_q(2) quantum group symmetry is introduced, and its properties examined. With suitable assumptions, this model is found to have many similarities with the usual SU(2)\times U(1) Standard Model, specifically, the existence of four generators and thus four gauge fields. However, the two classical symmetries are unified into one quantum symmetry, and therefore there is only a single coupling constant, rather than two. By incorporating a Higgs sector into the model, one obtains several explicit tree-level predictions in the undeformed limit, such as the Weinberg angle: $sin^2\Theta_{W} = 3/11$. With the Z-boson mass m_Z and fine structure constant alpha as inputs, one can also obtain predictions for the weak coupling constant, the mass of the W, and the Higgs VEV. The breaking of the quantum invariance also results in a remaining undeformed U(1) gauge symmetry.Comment: Version to appear in J. Geom. Phys. -reorganized and shortened, with minor stylistic change