Secondary mass scales in grand unification theory

It is shown for the example of SO(10) that for a general grand unification model different scalar fields having identical transformation properties with respect to the group SU(3)xSU(2)xU(1) may have the vacuum expectation values different in the order of magnitude, in the case of a multi-stage symmetry breaking. All possible schemes of the group SO(10) breaking are analysed. and the vacuum expectation values are estimated for a wide set of the scalar multiplets. An interesting consequence is the mass relation msub(b)=msub(tau) (above the unification mass), which is independent of the contents of the scalar fields interacting with fermions in the SO(10) model. The relations msub(d)=msub(e) and msub(s)=msub(μ) may be broken strongly