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

Saurabh K. Shukla

doi:10.1016/j.nuclphysb.2025.117034

paper

Constraining scalars of $1 6_{H}$ through proton decays in non-renormalisable $S O (10)$ models

arXiv:2403.14331 · doi:10.1016/j.nuclphysb.2025.117034

Abstract

Non-renormalisable versions of $S O (10)$ \, 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. $1 6_{H}$ 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 $1 6_{H}$ with the $16$ dimensional fermion multiplet of $S O (10)$ ,\, i.e. $\frac{16 16 1 6 _{H} 1 6 _{H}}{Λ}$ . 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 $σ (1, 1, 0) - T (3, 1, \frac{1}{3})$ , and $H (1, 2, - \frac{1}{2}) - Δ (3, 2, \frac{1}{6})$ , and $H - T$ can induce proton decay at tree level. Assuming that the Yukawa couplings of the $1 6_{H}$ are comparable to those of the $126_{H}$ of a realistic $S O (10)$ model and setting the cutoff scale to the Planck scale typically constrains the $B - L$ breaking scale to be $4 \sim 5$ 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 $S O (10)$ \, scenario, we find that $M_{T} > 1 0^{8}$ TeV, while $M_{Δ}$ could be as light as a few TeV $s$ .

arXiv comment28 Pages, 1 figure and 3 tables. version 2: References added, Published in Nuclear Physics B

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

Abstract

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Constraining scalars of $1 6_{H}$ through proton decays in non-renormalisable $S O (10)$ models