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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.27716 |
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Table of Contents:
- We study the dimension-six SMEFT four-lepton operators in the $μ$--$τ$ sector. These operators control both charged-lepton scattering and neutrino self-interactions, the latter being weakly constrained by direct laboratory probes despite their importance for cosmological tensions. We compare three classes of constraints on the Warsaw-basis coefficients $[C_{\ell\ell}]_{2222}$, $[C_{\ell\ell}]_{2233}$, and $[C_{\ell\ell}]_{2332}$. We use perturbative unitarity from $2\!\to\!2$ partial-wave analysis, spin-summing positivity sum rules, and the experimental bounds from NA64$μ$ and the global fit~\cite{Falkowski:2017pss}. We find that the global fit dominates for $[C_{\ell\ell}]_{2222}$ and $[C_{\ell\ell}]_{2332}$, while NA64$μ$ provides the leading bound on $[C_{\ell\ell}]_{2233}$, with the unitarity line for this direction entering the range of collider energies near $200~\mathrm{GeV}$. Renormalization-group running between $1~\mathrm{GeV}$ and $30~\mathrm{TeV}$ modifies these coefficients by up to $10\%$. Translating these bounds onto the effective four-neutrino coupling $G_\mathrm{eff}$, we find values many orders of magnitude smaller than the strongly interacting regime motivated by the Hubble tension; this excludes heavy-mediator UV completions of strong $ν_μ$--$ν_μ$ and $ν_μ$--$ν_τ$ self-interactions within the validity of the dimension-six SMEFT and in the absence of tuned cancellations between operators, while leaving the cosmologically motivated light-mediator scenarios unconstrained by this analysis. Finally, we comment on the bounds these coefficients place on a leptophilic $L_μ- L_τ$ $Z'$ UV completion. Our SMEFT-based current and projected NA64$μ$ bounds reproduce the dedicated $Z'$ analyses already available in the literature.