Insights on the Cosmic Origin of Matter from Proton Stability

TL;DR

This work presents a minimal, anomaly-free extension of the Standard Model in which proton stability is guaranteed by an infrared gauged symmetry $U(1)_{X_p}$ that breaks to a residual $\mathbb{Z}_9$ discrete gauge symmetry, enforcing $\Delta B \equiv 0 \pmod{3}$. The model links proton stability to lepton flavor non-universality and simultaneously yields a high-scale type-I seesaw for neutrino masses, minimal thermal leptogenesis, and a Majoron dark matter candidate arising from the broken $U(1)_{X_p}$; the Majoron remains light due to gravitationally suppressed breaking of the accidental global symmetry, protected by the gauge structure. The cosmological implications include rich topological defect dynamics (cosmic strings and domain walls) whose fate depends on the symmetry-breaking history, producing potential gravitational wave and CMB signatures. The framework makes concrete, testable predictions for neutrino textures, $0\nu\beta\beta$ decay, X-/gamma-ray lines, neutrino telescopes, and cosmological observables, while avoiding proton decay and offering a unified narrative for visible and dark matter origins.

Abstract

We investigate the phenomenology of a model in which the proton is rendered absolutely stable by an IR mechanism that remains robust against unknown quantum gravity effects. A linear combination of baryon number and lepton flavors is gauged and spontaneously broken to a residual $\mathbb{Z}_9$ discrete gauge symmetry enforcing a strict selection rule: $ΔB = 0\,(\mathrm{mod}\,3)$. Despite its minimal field content, the model successfully accounts for established empirical evidence of physics beyond the SM. High-scale symmetry breaking simultaneously provides a seesaw mechanism explaining the smallness of neutrino masses, minimal thermal leptogenesis, and a viable phenomenology of the majoron as dark matter. Any cosmic string-wall network remaining after inflation is unstable for numerous charge assignments. Lepton flavor non-universality, central to the construction, leads to predictive neutrino textures testable via oscillation experiments, neutrinoless double beta decay, and cosmology. The model motivates searches in $X$- and $γ$-ray lines, neutrino telescopes, and predicts CMB imprints.

Figures (9)

• Figure 1: One of the two solutions for the Majorana phases as a function of the lightest neutrino mass and Dirac phase $\delta_{ \mathrm{CP}}$. Upper and lower rows are for $\alpha$ and $\beta$, respectively. The columns correspond to the three models allowed by the current data: $e$-IO, $\mu$-NO, and $\tau$-NO. The remaining neutrino parameters are fixed to their central values from Ref. Esteban:2024eli. The future $2\sigma$-sensitivity of DUNE on $\delta_{ \mathrm{CP}}$-NO is denoted in dashed purple lines, assuming $\delta_{{ \mathrm{CP}}}$ is the current central value preferred by the global fits. See Section \ref{['sec:PMNS']} for details.
• Figure 2: Predictions for the $0\nu\beta\beta$ effective Majorana mass $m_{\beta\beta}$ as a function of the lightest neutrino mass for different scenarios. The color bands represent the two possible solutions for the Majorana phase, with $\delta_{ \mathrm{CP}}$ fixed to its current best-fit value in each scenario: $e$-specific IO (cyan–purple), $\mu$-specific NO (yellow–green), $\tau$-specific NO (red–blue), and the excluded $\tau$-specific IO model (orange–purple). See Section \ref{['sec:PMNS']} for details.
• Figure 3: Thermalization rate $\Gamma/H$ of the process $NN\to \textrm{SM}\, \textrm{SM}$ via $Z'$ interactions as a function of $z=M_{N_1}/T$ (left) and as a function of $M_{N_1}$ and $M_Z$ at $z=1$ (right). The black lines mark where $\Gamma/H =1$. We have plotted a benchmark scenario with the gauge symmetry charges $X_p$ determined by $(m,n) = (\vcenter{\hbox{[1]{$-$}}} 8, 3)$ and a coupling $g_X = 0.02$. See Section \ref{['sec:leptogenesis']} for details.
• Figure 4: Numerical scan of the UV parameters for different scenarios, where all points reproduce the low-energy neutrino data within $3\sigma$. We show the relevant quantities for leptogenesis: the mass of the lightest RHN versus $\tilde{m}_1$ (left) and the baryon-to-photon ratio (right). The black line in the left panel encloses the parameter region identified in Ref. Giudice:2003jh, where successful leptogenesis is possible. On the right, the observed value of the baryon-to-photon ratio is also shown. See Section \ref{['sec:leptogenesis']} for details.
• Figure 5: $\Gamma/H$ of the $t$-channel $N_1\, N_1\to a \, a$ (left) and the freeze-in yield as a function of $z=M_{N_1}/T$ (right), where we assume that only the lightest RHN is in thermal equilibrium. In both figures, we assume $v_1/v_2=0.1$.