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

Abstract

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. 16𝐻 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 16𝐻 with the 𝟏𝟔 dimensional fermion multiplet of 𝑆𝑂(10), i.e. 𝟏𝟔 𝟏𝟔 16𝐻 16𝐻 Λ . 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 𝜎 ( 1, 1, 0 ) −𝑇 ( 3, 1, 1 3 ) , and 𝐻( 1, 2,−1 2 ) − Δ( 3, 2, 1 6 ) , and 𝐻 −𝑇 can induce proton decay at tree level. Assuming that the Yukawa couplings of the 16𝐻 are comparable to those of the 126𝐻 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 𝑀𝑇 > 108 TeV, while 𝑀Δ could be as light as a few TeV𝑠.