Determine the scalar spectrum from the extended scalar potential

Determine the masses and spectrum of the dark-colored scalar fields $\phi_\nu$, $\phi_d$, $\phi_\ell$, $\phi_u$, $\phi_q$, and $\phi_e$ from a detailed analysis of the scalar potential, including the mechanism responsible for doublet–triplet splitting.

Background

The scalar multiplets $\Phi$ and $H$ contain fields with widely different expected roles and mass scales. For example, $H_d$ must remain near the electroweak scale, whereas the colored triplets $T_d$ and $T_u$ must be very heavy to satisfy proton-decay constraints. The dark-colored scalar components are likewise sensitive to whether the mechanism solving the doublet–triplet splitting problem applies to them. Because the scalar potential is not specified, the paper adopts alternative mass assumptions rather than deriving the spectrum. A concrete potential analysis is therefore needed to establish which portal interactions can remain phenomenologically relevant.