Constraining scalars of 16H through proton decays in non-renormalisable SO(10) models

Non-renormalisable versions of SO(10) based on irreducible representations with lesser degrees of freedom, are free of running into the catastrophe of non-perturbativity of standard model gauge couplings in contrast to the renormalisable versions having tensors with many degrees of freedom. 16<inf>H</inf> is the smallest representation, participates in Yukawa Lagrangian at the non-renormalisable level, contributing to the charged and neutral fermion masses, and has six distinct scalars with different B−L charges. We computed the leptoquark and diquark couplings of different pairs of scalars stemming from all possible decomposition of the term resulting from the coupling of 16<inf>H</inf> with the 16 dimensional fermion multiplet of SO(10), i.e. [Formula presented]. Computing the tree and loop level contribution of different pairs to the effective dimension six, B−L conserving operators, it turns out only three pairs, viz [Formula presented], and [Formula presented], and H−T can induce proton decay at tree level. Assuming that the Yukawa couplings of the 16<inf>H</inf> are comparable to those of the 126‾<inf>H</inf> of a realistic SO(10) model and setting the cutoff scale to the Planck scale typically constrains the B−L breaking scale to be 4∼5 orders of magnitude less than the cutoff scale (Λ). Moreover, analysing the branching pattern of the leading two-body decay modes of the proton, we observed a preference for the proton to decay into second-generation mesons due to the hierarchical nature of Yukawa couplings. In a realistic SO(10) scenario, we find that M<inf>T</inf>>10⁸ TeV, while M<inf>Δ</inf> could be as light as a few TeVs.