Vanishing threshold uncertainties and prediction for proton decay in non-supersymmetric $E_6$ GUT with intermediate trinification symmetry

We consider a class of non-supersymmetric $E_6$ Grand Unified Theories (GUTs) with trinification symmetry $SU(3)_C \times SU(3)_L \times SU(3)_R\times D$ ($D$ denoted as D-parity for discrete left-right symmetry) at the highest intermediate scale and establish a useful theorem that the electroweak mixing angle $\sin^2\theta_W$ has vanishing contributions due to one-loop GUT threshold corrections arising from every class of superheavy particles. This theorem can be extended to show that the one loop GUT threshold correction vanishes at the intermediate mass scale $M_I$ due to the presence of the discrete symmetry between the left and right handed Higgs fields. We quantify the effect of one loop GUT threshold corrections at the intermediate mass scale $M_I$ and the unification mass scale $M_U$ for the model. We observe that the modified $M_U$, provides crucial predictions on proton lifetime which can be verifiable within the foreseeable experiments.