Unification of weak and hypercharge interactions at the TeV scale

Abstract

A realistic SU(3)_C×SU(3)_W unified theory is constructed with a TeV sized extra dimension compactified on the orbifold S₁/Z₂, leaving only the standard model gauge group SU(3)_C×SU(2)_L×U(1)_Y unbroken in the low energy 4D theory. 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: sin²θ=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×U(1)_Y are operative. This allows quarks to be located at this fixed point, overcoming the longstanding problem of how to incorporate matter in a unified SU(3)_W theory. However, in general this local, explicit breaking of SU(3)_W symmetry, necessary for including quarks into the theory, destroys the tree-level prediction for the weak mixing angle. This apparent contradiction is reconciled by making the volume of the extra dimension large, diluting the effects of the local SU(3)_W violation. In the case that the electroweak theory is strongly coupled at the cutoff scale of the effective theory, radiative corrections to the weak mixing angle can be reliably computed, and used to predict the scale of compactification: 1–2 TeV without supersymmetry, and in the region of 3–6 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 multiple charged leptons, missing large transverse energy and possibly Higgs and electroweak gauge bosons.