A new electroweak and strong interaction unification scheme

• Published in: Physics letters. B Vol. 225; no. 1; pp. 143 - 147
• Main Author: Adler, Stephen L.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 13.07.1989
• ISSN: 0370-2693; 1873-2445
• DOI: 10.1016/0370-2693(89)91025-3

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 l L, l L c, ν L of each family as a 3 L representation of an electroweak SU(3) gauge group, and coupling the corresponding quarks as a second 3 L and two 3 R's or 3 L ∗'s. In the absence of strong interactions, the model predicts sin 2θ w = 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) × SU(12), and gives a corrected formula sin 2θ w = 1 4 + 1 3 α/α s at the SU(3) × SU(12) unification energy, which is computed to be 10 10.8±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. Extension 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.