Vanishing corrections on the intermediate scale and implications for unification of forces

Abstract

In two-step breaking of a class of grand unified theories including SO(10),we prove a theorem showing that the scale $M_I$ where the Pati-Salam gauge symmetry with parity breaks down to the standard gauge group,has vanishing corrections due to all sources emerging from higher scales $ μ>M_I$ such as the one-loop and all higher loop effects,the GUT-threshold,gravitational smearing,and string threshold effects. Implications of such a scale for the unification of gauge couplings with small Majorana neutrino masses are discussed.In string inspired SO(10) we show that $M_I \simeq 5\times 10^{12}$,needed for neutrino masses,with the GUT scale $M_U \simeq M_{str}$ can be realized provided certain particle states in the predicted spectum are light.