Quest for a phenomenologically consistent low cutoff theory

TL;DR

This work presents a low-cutoff Randall–Sundrum framework where an exact discrete gauged symmetry $\mathbf{Z}_N$ eliminates dangerous baryon- and lepton-number–violating operators, while bulk fermion profiles generate the Yukawa hierarchy via wave-function overlap. Under plausible assumptions, it yields Dirac neutrinos with a total mass near $66\,\text{meV}$ and reproduces CKM/PMNS textures, making flavor observables the primary experimental probe. While higher-dimensional $\Delta F=2$ processes are safely suppressed, dipole operators impose stringent constraints that motivate either an elevated cutoff or additional flavor/CP structure to evade current bounds. The approach avoids domain-wall problems and offers avenues for cosmology and dark-matter connections, though further refinement of the flavor-CP sector is needed for complete phenomenological viability.

Abstract

The Randall-Sundrum model with the Higgs localized on the IR brane solves the gauge hierarchy problem. However, the associated low cutoff ($Λ\sim 10$ TeV) generically leads to unacceptably rapid nucleon decay and excessively large Majorana neutrino masses. Achieving consistency while simultaneously explaining the Yukawa hierarchy requires either a horizontal symmetry or a discrete gauged symmetry. We demonstrate that eliminating all dangerous operators within a horizontal symmetry framework must come with large and unattractive charge assignments, if possible at all. Hence, we consider an exact discrete gauged $\mathbf{Z}_N$ symmetry, with fermion mass hierarchies generated via wave function overlap. We employ this to reproduce the current Cabibbo-Kobayashi-Maskawa and Pontecorvo-Maki-Nakagawa-Sakata structures. Assuming universal five-dimensional Yukawa couplings, generation-blind profile for right-handed neutrinos and flat profile for the third generation SM doublets, it predicts Dirac neutrinos with a total mass $\sim 66$ meV. Since the $\mathbf{Z}_N$ charges must be generation blind, flavor observables serve as key probes.

Figures (5)

• Figure 1: Upper: the prediction of neutrino mass-square differences under different choices of generation-blind $c_\nu$. Here, the normal ordering is considered. The horizontal and vertical dashed lines, whose intersection is labeled by a green star, are measured values adopted from Ref. Esteban:2024eli. Lower: the scattered predictions on the neutrino mass sum in the normal order with different choices of $c_\nu$. The vertical dashed line is the measured $\Delta m_{21}^2 =74.9^{+1.9}_{-1.9}$ meV$^2$Esteban:2024eli.
• Figure 2: The prediction on the effective cutoffs of four-Fermi operators. The first eight operators from the left induce meson-antimeson oscillations \ref{['eq:meson_operators']}. The operator $(\bar{s}_{\rm L} \gamma^\mu d_{\rm L})(\bar{\nu} \gamma_\mu \nu)$ is responsible for the $K \to \pi \bar{\nu} \nu$. The $\mu \to e \gamma$ is described by $e(\bar{\mu}_{\rm L} \sigma_{\alpha \beta} e_{\rm R}) F^{\alpha \beta}$. The last operator corresponds to the electron EDM. The solid bars are the existing bounds adopted from Refs. Isidori:2010kgPolonsky:2024pccCrivellin:2017rmkCesarotti:2018huyAebischer:2020dsw. The error bars of predictions are $3\sigma$ range in the log scale. Here, all predictions are made by fixing $g_X^{\alpha\beta}=g_{IJKL}^{\alpha\beta \gamma \rho} =1$ and randomly sampling $\{g_X^{ij},g_{IJKL}^{ijkl}\}$ under the cutoff scale $\Lambda = 10$ TeV with bulk profiles in Table \ref{['tab:c_j']}.
• Figure 3: The prediction on effective cutoff scale on the tree level operator that induce $\mu \to e \gamma$ against assumptions on 5D Wilson coefficient $\Delta^{ij}$. The red dashed line is the current bound. We sample the $\Delta^{ij}$ with a Gaussian distribution centered at $\langle \Delta^{ij}\rangle$ whose standard deviation is $0.1 \times \langle \Delta^{ij}\rangle$ under the $\Lambda =10$ TeV. The error bars are $3\sigma$ range in the log scale.
• Figure 4: The parameter space for charges $n_Q$ and $n_\ell$ under the constraint from proton decay and Yukawa couplings \ref{['eq:yukawa_constraint']} for one generation only. Here we take the FN parameter $\lambda=0.17$Qiu:2023igq and the cutoff $\Lambda=10$ TeV. Shaded regions are excluded by proton decay, where $\Lambda_i$ in $n_{i,c}$\ref{['eq:n_i,c']} are taken from Ref. Beneito:2023xbk.
• Figure 5: The scattered predictions on the PMNS mixing angles and $CP$ phase in the normal order and with $c_\nu=1.395$. The horizontal and vertical dashed lines are measured values adopted from Ref. Esteban:2024eli. Note that the choice on $c_\nu$ does not affect the PMNS parameters here much, since they are mostly determined by $c_\ell$.