A hierarchy of gauge hierarchies

We investigate the possibility that there is no intrinsic mass scale below the Planck mass msup(p), and that both stages of symmetry breaking in grand unified theories may be generated by radiative corrections. In such a scheme it is plausible that 1 >> msub(x)/msub(p) >> msub(w)/msub(x), where the subscript X denotes the superheavy bosons in grand unified theories. This hierarchy of gauge hierarchies arises because the X bosons get their masses from Higgs representations with larger non-abelian charges than the Higgs responsible for the W and Z masses. In a specific SU(5) model, we find that msub(x)/msub(p) is naturally O(10-5), whereas msub(w)/msub(x) can be much smaller. However, it can only be achieved in SU(5) at the expense of one unnatural condition on the Higgs potential. (orig.)