Revisiting lepton flavor violation: $τ$ and meson decays

TL;DR

This work investigates charged lepton flavor violation in the minimal Type-I seesaw with two heavy neutral leptons (HNLs), focusing on tau decays and meson channels using updated form factors, decay constants, and oscillation data. The authors derive BR formulas for τ → ℓM and τ → ℓMM' processes and analyze their dependence on HNL parameters, employing the Casas-Ibarra parametrization to map neutrino data to the mixing angles Θ and the combinations U_tot^2, x_α, and Λ_{αβ}. A key finding is that semileptonic tau decays, particularly τ → ℓρ and τ → ℓπ, can dominate over purely leptonic channels like τ → 3ℓ or τ → ℓγ in certain regions of parameter space, while heavy meson decays are far below experimental reach; non-decoupling Z-penguin contributions drive enhanced BRs at large M_N, though unitarity and perturbativity bounds cap the viable parameter space. The study provides indirect bounds by combining non-unitarity and universality constraints with loop-induced cLFV amplitudes, and identifies regions where next-generation experiments (e.g., Belle-II) could observe or constrain these processes. Overall, the results guide experimental priorities by highlighting tau-mediated semileptonic channels as promising probes of the minimal seesaw parameter space, while suggesting that broader model variants could open additional discovery opportunities.

Abstract

The minimal type-I seesaw model provides a simple explanation of neutrino flavor oscillations and induces charged lepton flavor violation (cLFV). Despite extensive previous studies, semileptonic cLFV channels remain underexplored. Using updated form factors, decay constants, and oscillation data, we revisit $τ$ and meson decay channels, performing a systematic comparison across the seesaw parameter space. Surprisingly, we find that decays such as $τ\to \ellρ$ can dominate over purely leptonic $τ$-sector probes, including $τ\to 3\ell$ and even $τ\to\ell\,γ$, in certain regions. In contrast, heavy-meson decays remain far below experimental sensitivity. Considering global constraints on the seesaw parameters, we derive branching ratios for the relevant cLFV processes and identify those within potential reach of next-generation experiments.

Figures (12)

• Figure 1: Ternary plot showing the allowed values of $x_\alpha$ consistent with neutrino oscillation data. The plot was done by letting $\delta$ and $\theta_{23}$ run free, and choosing the allowed regions of parameter space according to the values tabulated by NuFit 6.0. Esteban:2024eli.
• Figure 2: Feynman diagrams mediating cLFV processes with quarkonia.
• Figure 3: Regions of the parameter space where decoupling and non-decoupling. In the purplish regions is where the non-decoupling part dominates, the orange regions is where the decoupling part dominates, and in the white regions are where they are equally relevant. The black line shows the unitarity line from Urquia-Calderon:2024rzc, where everything to the right of it is not allowed.
• Figure 4: Comparison between the maximum allowed branching ratios, and current and prospective searches. For the values of current and prospective searches, see Table \ref{['tab:cLFV_decays_limits']}. We used the values that maximize each branching ratio (see main text).
• Figure 5: Maximal branching ratio for different $\tau$ decays in IO, compared with current bounds and prospective searches.