Intermediate mass scales in the new SO(10) grand unification in the one-loop approximation

Chang, Mohapatra, and Parida have recently developed a new approach to SO(10) grand unification where D-parity breaking (at scale $M_P$) and SU(2${)}_{\mathrm{R}}$ breaking are decoupled. We have extended their one-loop analysis of the intermediate mass scales in the new SO(10) grand unification. We derive the general formulas for ${\sin }^2$ ${\mathrm{\theta }}_{\mathrm{W}}$(${\mathrm{M}}_{\mathrm{W}}$) and α($M_W$)/${\alpha }_s$($M_W$) for all breakings of SO(10) and examine the constraints these formulas place on the mass scales of the theory for the different chains. We identify only two (marginal) chains that lead to detectable values of the intermediate mass scales when $M_P$=$M_X$, the grand unification scale.