Flavor Symmetry and Proton Decay in PeV-Scale Supersymmetry

TL;DR

This study analyzes flavor symmetry and proton decay in a PeV-scale SUSY framework with heavy sfermions and TeV-scale gauginos/Higgsinos, incorporating right-handed neutrinos and a Froggatt-Nielsen mechanism to generate Yukawa hierarchies and suppress baryon-number-violating operators. A Bayesian formalism is used to combine constraints from flavor-changing and CP-violating observables, proton-decay limits, and Yukawa fits, exploring multiple FN charge benchmarks. The results show that certain FN assignments (notably A- and G-type) can simultaneously accommodate SM Yukawas and suppress dimension-five proton decay, while Planck-suppressed operators without FN protection can be severely constrained; the proton lifetime predictions vary by channel and model, with Hyper-Kamiokande sensitivity potentially testing a substantial portion of the parameter space. Cosmological considerations of a Wino LSP and AMSB dynamics further constrain the allowed mass scale, suggesting $m_0$ in the PeV range is viable but delicate to balance with dark-matter abundance and cosmology. Overall, the work highlights the necessity of a multi-messenger approach—encompassing flavor, CP, proton decay, and cosmology—to probe the flavor structure and unification prospects of SUSY beyond the TeV scale.

Abstract

Supersymmetry beyond the TeV scale offers several theoretical and phenomenological advantages, such as accommodating the observed Higgs mass and alleviating the flavor and CP problems. However, flavor and CP observables still impose stringent constraints even at the PeV scale, motivating a systematic study of flavor symmetries in this regime. In this work, we investigate nucleon decay induced by dimension-five operators in supersymmetric standard models and examine how flavor symmetries, particularly of the Froggatt-Nielsen type, can suppress these operators. We perform a Bayesian analysis combining flavor, CP, and proton-decay observables to quantify the allowed parameter space and identify characteristic predictions. Our results demonstrate that a multi-messenger approach, integrating flavor, CP, and baryon-number-violating observables, is essential for probing the underlying structure of supersymmetry beyond the TeV scale.

Figures (10)

• Figure 1: Effective dimension-six baryon-number violating operators generated by dressing the dimension-five baryon-number violating operators by the sfermion-gaugino/Higgsino loops. The gray blob denotes the dimension-five operator and black dot represents the mass insertion of the gauginos or Higgsinos.
• Figure 2: Flavor- and CP-violating processes arising from squark mass matrices.
• Figure 3: (a) Prior distributions of the Yukawa couplings and fermion mixings. The shaded regions correspond to the $1\sigma$ (light green) and $2\sigma$ (dark green) ranges predicted by the priors, with the measured values indicated for comparison. (b) Bayes factor as a function of $m_0$ for different experimental constraints, including FCNC bounds from meson mixing, fermion EDM limits, and proton-decay constraints for $\Lambda_B = 10^{16}\,\mathrm{GeV}$ and $\Lambda_B = M_{\mathrm{Pl}}$. Dashed lines represent the projected sensitivities of Hyper-Kamiokande.
• Figure 4: Prior distributions of the Yukawa couplings and fermion mixings for representative FN charge assignments. Model $N$ corresponds to the no-FN scenario shown in Fig. \ref{['fig:NcaseYukawa']}. The shaded bands indicate the $1\sigma$ and $2\sigma$ ranges derived from the priors, with the experimentally measured values overlaid for comparison.
• Figure 5: Bayes factors for the $A$-type benchmarks.