A new electroweak and strong interaction unification scheme

I explore the consequences of requiring the electroweak gauge group to contain an SU(2) subgroup rotating the charged fermions to their antiparticles. This is implemented by coupling the leptons lL, lLc, νL of each family as a 3L representation of an electroweak SU(3) gauge group, and coupling the corresponding quarks as a second 3L and two 3R's or 3L*'s. In the absence of strong interactions, the model predicts sin2θW=1/4 at the electroweak unification energy. Since the electroweak SU(3) does not commute with the color SU(3) group, the minimal consistent electroweak-strong gauge group is obtained from the closure of their commutator algebra. This has been determined to be the 151-generator semi-simple Lie algebra SU(3)xSU(12), and gives a corrected formula sin2θw=1/4+1/2α/αs at the SU(3)xSU(12) unification energy, which is computed to be 1010.8±0.8 GeV. Unification in the simple group SU(15) is attained at an energy approximately a factor of 10 higher. To cancel anomalies in the closure group, it is necessary to double the fermion content by adding ''mirror'' families with the roles of left- and right-handed electroweak couplings reversed with respect to the original families. Extensions of the model and embeddings in SO(32) are discussed; in particular, the group SU(15) with two families of fermions and mirror fermions can be embedded in SO(32) with all fermions in the adjoint 496 representation. (orig.)