Spectrum of color sextet scalars in realistic SO(10) GUT

Incorporation of the standard model Yukawa interactions in a grand unified theory (GUT) often predicts varieties of new scalars that couple to the fermions and lead to some novel observational effects. We assess such a possibility for the color sextet diquark scalars within the realistic renormalizable models based on $SO(10)$ GUT. The spectrum consists of five sextets; $\mathrm{\ensuremath{\Sigma}}\ensuremath{\sim}(6,1,\ensuremath{-}\frac{2}{3})$, $S\ensuremath{\sim}(6,1,\frac{1}{3})$, $\overline{S}\ensuremath{\sim}(\overline{6},1,\ensuremath{-}\frac{1}{3})$, $\mathcal{S}\ensuremath{\sim}(6,1,\frac{4}{3})$, and $\mathbb{S}\ensuremath{\sim}(\overline{6},3,\ensuremath{-}\frac{1}{3})$. Computing explicitly their couplings with the quarks, we evaluate their contributions to the neutral meson-antimeson mixing and baryon number-violating processes like neutron-antineutron oscillation. The latter arises because of a $B\ensuremath{-}L$ violating trilinear coupling between the sextets which also contributes to some of the quartic couplings and perturbativity of the same leads to strong limits on the sextet masses. Using the values of the $B\ensuremath{-}L$ breaking scale and Yukawa couplings permitted in the realistic models, we derive constraints on the masses of these scalars. It is found that $\mathrm{\ensuremath{\Sigma}}$ along with any of the remaining sextets cannot be lighter than the $B\ensuremath{-}L$ breaking scale, simultaneously. In the realm of realistic models, this implies no observable $n\text{\ensuremath{-}}\overline{n}$ oscillation in near future experiments. We also point out a possibility in which the sub-GUT scale $\mathrm{\ensuremath{\Sigma}}$ and a pair of $S$, allowed by the other constraints, can viably produce the observed baryon asymmetry of the Universe.