Unification of Weak and Hypercharge Interactions at the TeV Scale

An $SU(3)_C \times SU(3)_W$ gauge theory in 5D is broken by orbifold compactification to the standard model gauge group $SU(3)_C \times SU(2)_L \times U(1)_Y$. The Higgs doublets are zero modes of bulk $SU(3)_W$ triplets and serve to normalize the hypercharge generator, apparently giving a tree-level prediction for the weak mixing angle: $\sin^2 \theta = 1/4$. The orbifold boundary conditions imply a restricted set of $SU(3)_W$ gauge transformations: at an orbifold fixed point only the transformations of $SU(2)_L \times U(1)_Y$ are operative. This allows quarks and leptons to be located at this fixed point, overcoming the longstanding problem of how to incorporate matter in a unified $SU(3)_W$ theory. However, this local, explicit breaking of $SU(3)_W$ symmetry in general destroys the tree-level prediction for the weak mixing angle. In the case that the electroweak theory is strongly coupled, it is shown that the prediction survives, and can be used to compute the scale of compactification: $1 - 2~{\rm TeV}$ without supersymmetry, and in the region of $3~{\rm TeV}$ for a supersymmetric theory. The experimental signature of electroweak unification into $SU(3)_W$ is a set of ``weak partners'' of mass $1/2R$, which are all electrically charged and are expected to be accessible at LHC. These include weak doublets of gauge particles of electric charge $(++,+)$, and a charged scalar. When pair produced, they yield events containing multi-charged leptons, missing large transverse energy and possibly Higgs and electroweak gauge bosons.