Grand Unication in the Motor Theory: SU (5) Model with Renormalisation Group, Proton Decay, and Motor Modes

In this work,we present a detailed SU(5) grand unied model built upon the mo-tor theory. It is shown that compactication of ve motor dimensions with orbifoldprojections leads to the gauge group SU(5) with natural electric charge quantisationthrough the motor number n. A renormalisation group analysis of the convergenceof the coupling constants g1, g2, g3 is performed, including the contribution of motormodes (KK tower) . The unication energy is found to be MGUT ≈ 1.2 · 1016 GeVand the unied coupling α−G1UT ≈ 39.5 for Φ0 ∼ 10−3, consistent with classical SU(5)predictions. The mass of the X bosons is computed as MX ∼ MGUT . The protonlifetime,including contributions from motor modes, is estimated as τp ∼ 1035 years,in agreement with the Super-Kamiokande bound (τp > 1034 years) . It is also shownthat the fermion mass hierarchy arises from the dependence of Yukawa couplingson the radion Φ, reproducing the generation mass ratios. The model predicts newmotor copies of all SM particles with masses of order 100 GeV, accessible at HL-LHCand FCC-hh.