SO(10) theory of R-parity and neutrino mass

TL;DR

This work constructs a supersymmetric SO(10) grand unified theory with exact R-parity through a renormalizable see-saw mechanism, using a minimal Higgs content ${S(54), A(45), Σ(126), Σ̄(126)}$ to realize sequential breaking to the MSSM. A detailed analysis of two symmetry-breaking patterns, the associated flatness conditions, and the complete particle spectrum is followed by a one-loop gauge-coupling unification study with multiple thresholds, revealing viable intermediate scales $M_R$ of order $10^{13}$–$10^{14}$ GeV and a lowered unification scale $M_X$ around $10^{15.5}$–$10^{16}$ GeV. The model predicts exact R-parity down to the MSSM, a stable LSP, and a neutrino mass structure that includes a potentially sizeable non-canonical term from higher-dimensional effects, with implications for proton-decay channels. Overall, the framework demonstrates how intermediate scales and light GUT states can coexist with successful unification and provides a concrete link between high-scale SO(10) breaking and low-energy phenomenology.

Abstract

We study the Higgs sector of a SO(10) grand unified theory which predicts exact conservation of R-parity at all scales and incorporates the see-saw mechanism. We find possible intermediate scales and light states compatible with the constraints coming from the running of the gauge couplings. Such a pattern could lower the SO(10) breaking scale, allowing the d=6 proton decay operators to be comparable in magnitude to the d=5 ones.

Figures (2)

• Figure 1: $M_C$, $M_R$ and $M_X$ vs. $1/\alpha_U$ for Chain A, with $M_s = 1$ TeV and $\epsilon = 1$, for $n=0$ and $1$.
• Figure 2: $M_C$ and $M_R$ vs. $M_s$ for Chain A, when $M_X$ is fixed at its lowest allowed value ($log(M_X/GeV)=15.5$) and $\epsilon = 1$, for $n=0$ and $1$. Dotted lines are the same plots for lowest and highest values of $\alpha_3$