Gauging the Shadow Sector with SO(3)

We examine the phenomenology of a low-energy extension of the Standard Model, based on the gauge group SU(3) ⊗ SU(2) ⊗ U(1) ⊗ SO(3), with SO(3) operating in the shadow sector. This model offers νe → νs and νμ → ντ oscillations as the solution of the solar and atmospheric neutrino problems. Moreover, it provides a neutral heavy shadow lepton X that could play the role of a cold dark matter particle. With the accumulated evidence for neutrino oscillations [1] comes the challenge of understanding the origin of neutrino mass. Since the simple Higgs triplet [2] is ruled out by LEP [3], most approaches centre on singlet fermions and some variant of the see-saw mechanism [4]. The question then arises how these new particles fit into the larger theory. One of the most novel proposals [5], inspired by E8 ⊗ E ′ 8 superstring theory, is that fermions, which are light because they are non-singlets under a low-energy “shadow gauge group” G ′ , could play an important role in this regard. The implementation of this idea, however, involves several specific assumptions: G ′ is isomorphic to the Standard Model SU(3) ⊗ SU(2) ⊗ U(1), with matter fields in the fundamental representation coming in three generations. None of these inputs are compulsory. In fact, in the superstring scenario, compactification yields E6 as the grand unified gauge group and it is also responsible for the generation structure, while the E ′ 8 is left intact and can break down to G ′ in many ways. Furthermore, even if one can identify SU(2) ′ × U(1) as a subgroup of G , there are still many possible matter representations [6] including neutral heavy shadow leptons which could mix with the active neutrinos. It is therefore important to explore other candidates for the low-energy group G ′ , in order to obtain a clearer picture on this issue. Thus, in this paper, we will examine G′ = SO(3), the Georgi-Glashow model [7], which being vector like, is anomaly free. We assume no generation replication and, since there is no information on the “charged” shadow leptons, we dispense with the artifice of putting in a mass by hand. The shadow leptons appear as triplets ~ ψL =  E X e ′−  L , ~ ψR =  E ν ′