In this paper, we propose a novel extension of the Standard Model of particle physics, based on the trinification gauge group $SU(3)_C \times SU(3)_L \times SU(3)_R$. Symmetry breaking is achieved using a bi-adjoint Higgs field (transforming under the left- and right-handed subgroups) along with a more conventional bi-triplet to ensure the correct breaking and pattern of fermion masses. To preserve a discrete $Z_2$ symmetry (T-parity), we also introduce a right-handed triplet to completely break trinification symmetry to the Standard Model. The minimization conditions and conditions for the boundedness of the potential for this model are calculated. Additionally, the Standard Model quantum charges of the 64-component Higgs field are determined and mass matrices for the gauge bosons are constructed. The survival of T-parity ensures the stability of dark matter candidates in the model; the details of such candidates and the generation of neutrino masses are left to future work.
"Trinification with a Bi-Adjoint Higgs Field,"
Macalester Journal of Physics and Astronomy: Vol. 11:
1, Article 5.
Available at: https://digitalcommons.macalester.edu/mjpa/vol11/iss1/5