Testing the Froggatt-Nielsen Mechanism with Lepton Flavor and Number Violating Processes

TL;DR

This paper extends the Froggatt-Nielsen framework to the lepton sector, systematically mapping realistic FN textures across Dirac, Majorana via the Weinberg operator, and type-I seesaw neutrino mass generation. It couples the FN texture analysis to low-energy and collider observables by embedding FN-induced higher-dimensional operators in SMEFT and computing CLFV and $0\nu\beta\beta$ predictions, using a two-step texture-selection procedure driven by fits to leptonic masses and mixings. The results reveal texture-dependent patterns and correlations among CLFV channels, neutrino mass ordering, and $0\nu\beta\beta$ decay, with muon-sector processes offering the most promising probes and IO scenarios providing strong constraints on Dirac FN. The findings emphasize the FN mechanism’s power to link neutrino mass generation to testable leptonic observables and motivate joint quark–lepton analyses and explorations of extended scalar sectors to enhance experimental sensitivity.

Abstract

The Froggatt-Nielsen (FN) mechanism offers an elegant explanation for the observed masses and mixings of Standard Model fermions. In this work, we systematically study FN models in the lepton sector, identifying a broad range of charge assignments ("textures") that naturally yield viable masses and mixings for various neutrino mass generation mechanisms. Using these textures, we consider higher-dimensional operators consistent with a FN origin and find that natural realizations predict distinct patterns in lepton flavor- and number-violating observables. For Dirac and Majorana neutrinos, FN-related correlations can lead to detectable rates of charged lepton flavor violation at next-generation low-energy experiments. Majorana and type-I seesaw models predict measurable rates of neutrinoless double beta decay. Determination of inverted neutrino mass ordering would exclude the Dirac neutrino FN scenario. Only a small minority of purely leptonic FN models predict detectable flavor violation at future muon colliders, though it is possible that a combined analysis with the quark sector will reveal motivated signals. These findings highlight the power of the FN mechanism to link neutrino mass generation to testable leptonic observables, offering new pathways for the experimental exploration of lepton number and underscoring the importance of next-generation low-energy probes.

Figures (10)

• Figure 1: Average predicted CLFV decay rates for the 100 most realistic natural Dirac FN textures (gray lines), relative to each observable's current constraint. In each model, the flavor scale was chosen to saturate current experimental bounds at $\Lambda \sim 10^6$ GeV, thus fixing the other rates. Green shading indicates the reach of proposed future low-energy CLFV experiments, and the flavor-anarchic null texture is shown as a red line for comparison.
• Figure 2: Average predicted CLFV decay rates for the top most 100 realistic Majorana FN textures (gray lines), as in Fig. \ref{['fig: Dirac results']}. The top panel assumes that the scale of the Weinberg operator ($\Lambda_W$) coincides with the FN scale ($\Lambda$), fixing the predictions for CLFV signals from the imposed neutrino mass constraints. The ' predicted' neutrino scale for the null texture is set to $10^{14}$ GeV. The bottom panel assumes $\Lambda_W \neq \Lambda$, such as in FN type-II seesaw scenarios, where $\Lambda$ is instead chosen to saturate its most restrictive current experimental bound of $\Lambda \sim 10^6$ GeV.
• Figure 3: Effective Majorana mass $m_{ee}$ versus the mass of the lightest neutrino for the top 100 FN textures in the Majorana (top) and type-I seesaw (bottom) scenarios. The yellow- and blue-shaded regions indicate the allowed ranges for IO and NO, respectively, based on the current measured values for $\Delta m_{32}^2$ and $\Delta m_{21}^2$. The solid blue line indicates the strongest exclusion from current $0\nu\beta\beta$ searches, from KamLAND-Zen ParticleDataGroup:2022pth, while the dashed blue line marks the reach of the future $0\nu\beta\beta$ experiments nEXO nEXO:2021ujk and CUPID CUPID:2022wpt. The vertical red lines indicate the limits on $\min m_\nu$ in the IO and NO scenarios from current cosmological limits on $\sum m_\nu$. Error bars show the $1\sigma$ spread of predictions with $\delta_{\mathrm{max}}<2$.
• Figure 4: Comparison of the predicted branching ratio for $\mu \to 3 e$ and the conversion rate for $\mu$-$e$ conversion in Al for the first and the fifth Dirac FN textures in Table \ref{['tab: charges']}, assuming the FN scale $\Lambda$ saturates its current lower bound. The conversion rate is normalized to the muon capture rate in nuclei. Contours show areas containing 68% (solid) and 98% (dashed) of random coefficient choices with $\delta_{\mathrm{max}}<2$. Thus, these textures might be distinguished despite similar average predictions.
• Figure 5: Histograms of the $\eta$ parameter distribution for $1000$ trials that yield exact fits to the measured leptonic masses and mixings parameters. For each neutrino mass mechanism we show the result for the top-performing textures: for Dirac neutrinos (left), $X_L = \{6,5,5 \}$, $X_e=\{-3,-2,0\}$, $X_N = \{9,8,8 \}$; for Majorana (middle), $X_L = \{2,0,-1 \}$, $X_e=\{7,6,4\}$; and for type-I seesaw (bottom), $X_L = \{6,1,-1\}$, $X_e=\{7,7,6\}$, $X_N = \{3,0,-4 \}$.