Low scale trinification symmetry through effects of dimension-5 operators in $E_6$ grand unified theory with and without supersymmetry

Abstract

We examine E6 GUT models (both SUSY and non-SUSY) with D-parity violating intermediate trinification symmetry (SU (3)C ⊗ SU (3)L ⊗ SU (3)R) (g3L = g3R) where the D-parity breaking is achieved by quantum gravity effect through dimension-5 operators. Inclusion of the gravitational effect significantly lowers the intermediate scale, being as low as 10 TeV. However with a given choice of the intermediate mass MI , the gauge unification mass MU as well as the GUT coupling constant are unaffected by the effects. The predicted value of MU is shown to be compatible with the accessible limit of the proton lifetime in presence of additional particles i.e. color octet scalars like (8, 2, 1 2 ) or (8, 1, 0) and electroweak triplet fermion (1, 3, 0) at the lower scales. The presence of color octet scalar with mass of the order of TeV may suppress the production of the Higgs boson through gluon fusion. The SU (2)L triplet fermion may behave like a stable dark matter. With reference to cosmological issue, it is expected that no strings or walls bounded by strings associated with D are generated, since the discrete D-parity is broken at the GUT scale.