a similar manner, in the present model the masses of the colored Higgs fields, as well as those of the second Higgs doublet $H_D$ and Higgsino $\tilde{h}$ of the SSM, are also at the intermediate scale. In the minimal $SU(5)$ GUT, the doublet Higgses $H_u$ and $H_d$ of the SSM are embedded in the fundamental representations of $SU(5)$ as $H = (H_u, H_C)$ and $\bar{H} = (H_d, \bar{H}_C)$. The superpotential of Eq. (\[eq:W\_eff\]) implies that the masses for all these fields are also of order $\tilde{m}$: $$M_{H_C} \sim M_{H_D} \sim M_{\tilde{h}} \sim O(\tilde{m}),
\label{eq:m-H_C}$$ except for the light Higgs doublet $h$ of the SM, which is environmentally selected to be of order the weak scale $v \ll \tilde{m}$. One might think that such low values for the colored Higgs masses are excluded by the proton decay constraints. This is, however, not the case as will be discussed in Section \[subsec:p-decay\]. In Fig. \[fig:spectrum\], we give a schematic depiction of the spectrum of the present model. In the figure, we have put the wino, $\tilde{W}$, to be at a TeV scale, since its mass may be environmentally selected to be in this range; see Section \[subsec:wino\] below.

[![A schematic depiction of 