Light Colour-Triplet Higgs is Compatible with Proton Stability: An alternative approach to the doublet-triplet splitting problem

It is usually assumed that the proton stability requires the coloured triplet partner of the electroweak Higgs doublet to be superheavy (with a mass $\sim M_{GUT}$). We show that this is a very model-dependent statement and the colour triplet can be as light as the weak doublet without leading to the proton decay problem: instead of using the mass difference the splitting can occur between the doublet and triplet Yukawa coupling constants. In this scenario the GUT symmetry breaking automatically induces an extremely strong suppression $\sim M_W/M_{GUT}$ of the coloured Higgs effective Yukawa coupling; this happens without any fine--tuning, just because of the Clebsch factors. Conceptual differences of the above picture are: (1) an essentially stable proton: both $d = 5$ and $d = 6$ proton decay mediating operators are suppressed by the same factors $\sim (M_w/M_{GUT})^2$; (2) the possibility of solving the $\mu$ problem by the light gauge singlet field (this fact would lead to the destabilization of the hierarchy in the standard case); (3) the existence of the long--lived, light, coloured and charged supermultiplet in the 100 GeV mass region. We construct two explicit SO(10) examples with the above properties, with superpotentials most general under the symmetries.