arxiv: 2604.27716 · v1 · submitted 2026-04-30 · ✦ hep-ph · astro-ph.CO· hep-ex

Recognition: unknown

Theoretical and Experimental Constraints in the μ--τ Four-Lepton Sector of the SMEFT: implications to neutrino self interactions

Aadarsh Singh , G. D'Ambrosio , Sudhir K. Vempati

Authors on Pith no claims yet

Pith reviewed 2026-05-07 05:44 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.COhep-ex

keywords SMEFTfour-lepton operatorsneutrino self-interactionsHubble tensionNA64μmuon-tau sectoreffective field theory

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The pith

Bounds on μ-τ four-lepton SMEFT operators limit the effective neutrino coupling G_eff many orders of magnitude below the value needed for strong self-interactions motivated by the Hubble tension.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper derives upper limits on three Warsaw-basis four-lepton operator coefficients in the muon-tau sector by combining perturbative unitarity bounds, positivity sum rules, NA64μ experimental results, and global electroweak fits. These limits are then mapped onto an effective four-neutrino coupling strength G_eff that governs neutrino self-interactions. The resulting G_eff values lie many orders of magnitude below the strongly interacting regime that has been proposed to ease the Hubble tension. This rules out heavy-mediator ultraviolet completions of strong ν_μ–ν_μ and ν_μ–ν_τ self-interactions inside the dimension-six SMEFT framework when cancellations between operators are absent, while leaving light-mediator scenarios untouched by the present analysis.

Core claim

Translating the bounds from unitarity, positivity, NA64μ, and global fits onto the effective four-neutrino coupling G_eff yields 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 cosmologically motivated light-mediator scenarios unconstrained.

What carries the argument

The Warsaw-basis dimension-six four-lepton operators with coefficients [C_ℓℓ]_{2222}, [C_ℓℓ]_{2233}, and [C_ℓℓ]_{2332}, which simultaneously control charged-lepton scattering processes and neutrino self-interactions through their mapping to G_eff.

If this is right

Global fits dominate constraints on [C_ℓℓ]_{2222} and [C_ℓℓ]_{2332}, while NA64μ leads for [C_ℓℓ]_{2233}.
The unitarity bound for the [C_ℓℓ]_{2233} direction becomes relevant near collider energies of 200 GeV.
Renormalization-group evolution from 1 GeV to 30 TeV alters the coefficients by at most 10 percent.
The derived SMEFT bounds on a leptophilic L_μ - L_τ Z' reproduce existing dedicated analyses.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Cosmological models invoking strong neutrino self-interactions to resolve the Hubble tension must rely on light mediators or mechanisms outside the standard dimension-six SMEFT description.
Improved sensitivity at future muon beam experiments could further restrict the parameter space for neutrino self-interacting scenarios.
The analysis highlights the complementarity between collider, fixed-target, and cosmological probes for neutrino self-interactions.

Load-bearing premise

The central claim depends on the absence of tuned cancellations among the four-lepton operators and on the dimension-six SMEFT remaining valid without important higher-dimensional contributions at the scales of interest.

What would settle it

An experimental observation or cosmological inference that requires a four-neutrino coupling G_eff at the level needed to address the Hubble tension, while remaining consistent with the absence of new physics beyond dimension-six operators, would falsify the exclusion.

Figures

Figures reproduced from arXiv: 2604.27716 by Aadarsh Singh, G. D'Ambrosio, Sudhir K. Vempati.

**Figure 1.** Figure 1: FIG. 1: Scalar- (orange) and vector-dominated (green) view at source ↗

**Figure 3.** Figure 3: summarizes the interplay between experimental bounds and the unitarity line as a function of √ s. The red line is Eq. (7), horizontal bands are the NA64µ current and projected bounds for Cˆ2222 ℓℓ and [Cℓℓ]2233, and the blue lines are the global-fit limits on Cˆ2222 ℓℓ and [Cℓℓ]2332. For reference we mark the center-of-mass energies of existing and proposed colliders such as LEP, FCC-ee [30, 84], CEPC [3… view at source ↗

**Figure 4.** Figure 4: FIG. 4: Combined experimental and theoretical constraints. view at source ↗

**Figure 5.** Figure 5: FIG. 5: Constraints on the mediator–neutrino coupling view at source ↗

read the original abstract

We study the dimension-six SMEFT four-lepton operators in the $\mu$--$\tau$ 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$\mu$ 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$\mu$ 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 $\nu_{\mu}$--$\nu_{\mu}$ and $\nu_\mu$--$\nu_\tau$ 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 $L_\mu - L_\tau$ $Z'$ UV completion. Our SMEFT-based current and projected NA64$\mu$ bounds reproduce the dedicated $Z'$ analyses already available in the literature.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper maps existing SMEFT bounds onto G_eff and excludes heavy-mediator UV completions for strong νμ-νμ and νμ-ντ self-interactions that could address the Hubble tension, provided no tuned cancellations occur.

read the letter

The main takeaway is that current constraints on the three relevant four-lepton operators already force the effective neutrino self-coupling G_eff many orders of magnitude below the strongly interacting regime needed for a Hubble-tension resolution via heavy mediators. The exclusion holds inside the dimension-six SMEFT and without cancellations between operators, while light-mediator scenarios remain untouched by this analysis. The authors also note that their bounds on a leptophilic Lμ-Lτ Z' reproduce existing dedicated results. What is new is the explicit translation of the Warsaw-basis coefficients [C_ℓℓ]2222, [C_ℓℓ]2233, and [C_ℓℓ]2332 into G_eff together with the direct statement ruling out those heavy-mediator completions. The work does the standard pieces well. It combines perturbative unitarity from partial-wave analysis, positivity sum rules, the NA64μ limit, and the Falkowski et al. global fit, while showing that RG evolution from 1 GeV to 30 TeV shifts the coefficients by at most 10 percent. The global fit dominates two directions and NA64μ the third, with unitarity only becoming competitive near 200 GeV for one coefficient. The soft spots are limited and already flagged. The central claim depends on the absence of tuned cancellations, which the paper states explicitly. Most of the numerical strength comes from external inputs rather than fresh data or calculations. Everything is kept inside dimension-six SMEFT, so higher-dimensional operators are outside the stated scope. No internal inconsistencies appear in the mapping or the running. This paper is useful for people working on neutrino self-interactions, SMEFT applications to cosmology, or leptophilic Z' models. A reader who wants a concrete bridge between laboratory bounds and the Hubble tension will get a clear quantitative picture. It deserves a serious referee because the methods are established, the caveats are stated, and the connection to cosmology is timely. I would send it to peer review; external checks on the G_eff translation and any overlooked mixing would be worthwhile.

Referee Report

1 major / 3 minor

Summary. The paper analyzes dimension-six SMEFT four-lepton operators in the μ–τ sector, focusing on the Warsaw-basis coefficients [C_ℓℓ]_{2222}, [C_ℓℓ]_{2233}, and [C_ℓℓ]_{2332}. It derives bounds from perturbative unitarity via 2→2 partial-wave analysis, spin-summing positivity sum rules, NA64μ data, and the global fit of Falkowski et al. (2017). RG evolution between 1 GeV and 30 TeV shifts the coefficients by ≤10%. These bounds are mapped to the effective four-neutrino coupling G_eff, yielding values many orders of magnitude below 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 dim-6 SMEFT and without tuned operator cancellations, while leaving light-mediator scenarios unconstrained. The paper also comments on bounds for a leptophilic L_μ–L_τ Z' completion.

Significance. If the central mapping and bounds hold, the work provides a robust, first-principles constraint on SMEFT operators linking charged-lepton scattering to neutrino self-interactions. It rules out a class of heavy new-physics explanations for cosmological tensions (Hubble) in the absence of cancellations, while correctly leaving light-mediator options open. The combination of unitarity, positivity, and existing experimental inputs adds value beyond individual bounds, and the explicit qualification of the no-cancellation assumption is a strength.

major comments (1)

Abstract and G_eff translation paragraph: The central claim that the bounds exclude heavy-mediator UV completions of strong self-interactions is qualified by 'in the absence of tuned cancellations between operators' and 'within the validity of the dimension-six SMEFT'. While the qualification is stated, the manuscript does not quantify the degree of tuning required to evade the bounds or demonstrate that such cancellations are non-generic in plausible UV models. This is load-bearing for the exclusion statement and should be addressed with a brief example or estimate.

minor comments (3)

Section on positivity sum rules: The phrase 'spin-summing positivity sum rules' is used without a specific reference or derivation sketch; adding a short equation or citation to the standard forward-scattering sum-rule technique would improve clarity for readers unfamiliar with the method.
RG running discussion: The statement that coefficients are modified by up to 10% is given, but the direction (increase or decrease) and which specific coefficient receives the largest shift are not detailed. A one-sentence breakdown or table entry would make the 10% figure more transparent.
Notation: The operator coefficients are written as [C_ℓℓ]_{ijkl} throughout; confirming that the indices follow the standard Warsaw-basis convention (with explicit SU(2) contraction) in a footnote or appendix would prevent any ambiguity for readers.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive feedback. We address the major comment below and will incorporate the requested clarification in the revised manuscript.

read point-by-point responses

Referee: Abstract and G_eff translation paragraph: The central claim that the bounds exclude heavy-mediator UV completions of strong self-interactions is qualified by 'in the absence of tuned cancellations between operators' and 'within the validity of the dimension-six SMEFT'. While the qualification is stated, the manuscript does not quantify the degree of tuning required to evade the bounds or demonstrate that such cancellations are non-generic in plausible UV models. This is load-bearing for the exclusion statement and should be addressed with a brief example or estimate.

Authors: We thank the referee for highlighting this point. The qualification regarding tuned cancellations is central to our exclusion of heavy-mediator scenarios, and we agree that a brief quantification strengthens the presentation. In the revised manuscript we will expand the G_eff translation paragraph (and update the abstract if space permits) with a short example. We will observe that, in generic UV completions without additional symmetries or fine-tuned relations among operators, the three Warsaw-basis coefficients are expected to be generated with comparable magnitudes. The existing bounds on linear combinations of these coefficients then directly limit G_eff to values many orders of magnitude below the strongly interacting regime. Achieving the cosmologically motivated G_eff while remaining consistent with charged-lepton data would therefore require cancellations among the operator contributions at a level that is non-generic without additional structure; we will illustrate this by comparing the naive bound (no cancellation) to the target value. This addition keeps the manuscript focused while addressing the load-bearing nature of the qualification. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation relies on external data and first-principles scattering constraints

full rationale

The paper derives bounds on Warsaw-basis coefficients [C_ℓℓ]_{2222}, [C_ℓℓ]_{2233}, and [C_ℓℓ]_{2332} from the external global fit of Falkowski:2017pss, NA64μ experimental data, perturbative unitarity via 2→2 partial-wave analysis, and spin-summing positivity sum rules. RG evolution is a standard perturbative calculation shifting coefficients by ≤10%. The mapping of these bounds to the effective four-neutrino coupling G_eff follows directly from the standard SU(2)_L expansion of the operators into the neutrino sector, without any re-fitting or self-referential definition. The central exclusion of heavy-mediator UV completions is explicitly conditioned on the absence of tuned cancellations and the validity of dim-6 SMEFT, with no load-bearing self-citations or ansatz smuggling. The reproduction of existing Z' bounds is a consistency check, not a derivation step. All load-bearing inputs are independent of the paper's own fitted values or prior claims by the same authors.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The analysis rests on the standard SMEFT framework, perturbative unitarity in 2-to-2 scattering, and the validity of the dimension-six truncation; no new free parameters are introduced beyond the operator coefficients being bounded, and no new particles or forces are postulated.

axioms (2)

domain assumption Validity of the dimension-six SMEFT truncation up to collider and cosmological scales without dominant higher-dimensional contributions
Invoked when translating bounds to UV completions and when stating the exclusion of heavy-mediator scenarios.
standard math Perturbative unitarity and positivity of 2-to-2 scattering amplitudes in the EFT
Used to derive the unitarity line and spin-summed positivity constraints on the Wilson coefficients.

pith-pipeline@v0.9.0 · 5709 in / 1678 out tokens · 37135 ms · 2026-05-07T05:44:22.915080+00:00 · methodology

discussion (0)

Reference graph

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