arxiv: 2604.12755 · v1 · submitted 2026-04-14 · ✦ hep-ph

Recognition: no theorem link

Probing muon anomaly and lepton flavor violation with scalar leptoquarks in the 331LHN model

D. T. Binh , V. H. Binh , H. T. Hung , Duong Van Loi

Authors on Pith no claims yet

Pith reviewed 2026-05-10 15:29 UTC · model grok-4.3

classification ✦ hep-ph

keywords leptoquarksmuon anomalous magnetic momentlepton flavor violation331LHN modelYukawa couplingsscalar particlescollider phenomenology

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The pith

A singlet scalar leptoquark added to the 331LHN model fully accounts for the muon anomalous magnetic moment discrepancy while respecting lepton flavor violation limits.

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

The paper extends the SU(3)_C × SU(3)_L × U(1)_X model with neutral leptons by adding scalar leptoquarks and works out their Yukawa couplings to fermions. It shows that one singlet leptoquark can generate the entire 4.2σ excess in the muon magnetic moment reported in 2021, requiring its mass to sit above roughly 1.8 TeV. Updated 2025 lattice results tighten that lower bound to 6 TeV. The same couplings are then bounded by charged-lepton flavor violation rates and μ–e conversion data, forcing them into a normal hierarchical pattern. Pair production of the leptoquark at the LHC is suppressed at these masses, but the paper maps how future colliders would extend the reach.

Core claim

The authors determine the allowed scalar leptoquark multiplets and their Yukawa interactions, then demonstrate that a color-triplet singlet state produces loop diagrams sufficient to explain the full Δa_μ discrepancy. With m_S ≳ 1.8 TeV (or ≳ 6 TeV under the 2025 value), the model remains consistent with LHC direct-search limits and yields Yukawa matrices that satisfy all low-energy LFV observables when arranged in normal hierarchy.

What carries the argument

The singlet scalar leptoquark and its Yukawa interactions with leptons, which generate one-loop contributions to the muon anomalous magnetic moment and to lepton-flavor-violating processes.

If this is right

The leptoquark mass is forced above 1.8 TeV (6 TeV with 2025 data) to match Δa_μ without violating existing collider bounds.
The Yukawa couplings must follow a normal hierarchical pattern to satisfy all LFV and μ–e conversion constraints simultaneously.
QCD pair production of the singlet at the LHC yields signal rates too small for discovery at multi-TeV masses.
Future hadron colliders can push the discovery reach for this state well beyond current LHC limits.

Where Pith is reading between the lines

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

If the muon anomaly persists, the required mass range points to a relatively narrow window where both precision flavor experiments and high-energy colliders can test the same particles.
The normal hierarchy in the Yukawas may be linked to the neutrino-mass generation mechanism already present in the 331LHN model, offering a possible common origin for lepton masses and the anomaly.
Non-observation of the leptoquark at future colliders would require either a larger mass or additional suppression mechanisms not explored in this extension.

Load-bearing premise

The scalar leptoquark loop terms dominate the muon anomaly with negligible interference from other sectors of the 331LHN model, and the Yukawa couplings can be chosen freely to fit both the anomaly and flavor-violation data.

What would settle it

A future high-precision measurement that brings the muon anomalous magnetic moment back into agreement with the Standard Model prediction, or the direct observation of a leptoquark with mass below 1.8 TeV at the LHC.

Figures

Figures reproduced from arXiv: 2604.12755 by D. T. Binh, Duong Van Loi, H. T. Hung, V. H. Binh.

**Figure 2.** Figure 2: FIG. 2: Allowed parameter space for the one-loop contributions to ∆ [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3: Allowed parameter space consistent with the experimental bound on [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4: Allowed parameter space consistent with the experimental bounds on [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5: Allowed parameter space consistent with the experimental bounds on [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6: Tree-level diagram contributing to the [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗

**Figure 7.** Figure 7: FIG. 7: Allowed parameter regions for [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗

read the original abstract

We extend the $SU(3)_C \times SU(3)_L \times U(1)_X$ model with neutral leptons (331LHN) by introducing scalar leptoquarks. We determine the particle content of the leptoquark multiplets and their Yukawa interactions with fermions. We find that a singlet leptoquark can fully account for the $4.2\sigma$ discrepancy in the muon anomalous magnetic moment $\Delta a_\mu^{2021}$. The corresponding leptoquark mass is constrained to be $m_S \gtrsim 1.8$~TeV, consistent with current LHC bounds. We further consider the updated $\Delta a_\mu^{2025}$ based on recent lattice QCD results, which strengthen the lower bound to $m_S \gtrsim 6$~TeV. Combining $\Delta a_\mu$ with low-energy leptonic observables, including charged lepton flavor violation and the $\mu$--$e$ conversion rate, we constrain the viable parameter space. The allowed leptoquark Yukawa couplings exhibit a normal hierarchical pattern under all constraints. We also investigate the collider phenomenology of the singlet leptoquark, showing that its QCD-driven pair production leads to suppressed signal rates at the LHC for multi-TeV masses, while future hadron colliders can significantly extend the discovery reach.

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 adds a singlet scalar leptoquark to the 331LHN model, derives mass lower bounds of 1.8 TeV or 6 TeV to fit the 2021 or 2025 muon anomaly, and finds a normal hierarchical Yukawa pattern once LFV and conversion bounds are imposed.

read the letter

The core result is that one specific leptoquark singlet can reproduce the observed Delta a_mu while staying consistent with current LHC limits and low-energy LFV data. The authors update the target anomaly value with the newer lattice QCD input and show how the allowed Yukawa couplings tighten into a normal hierarchy under the combined constraints. They also sketch the pair-production cross section at hadron colliders, noting that multi-TeV masses suppress the signal at the LHC but remain reachable at future machines. That update and the explicit combination of g-2 with mu-e conversion and LFV branching ratios are the concrete additions to the existing literature on leptoquarks in 331-type models. The calculations appear to follow standard one-loop formulas for the magnetic moment and the usual effective-operator treatment for LFV, which is fine for a phenomenological study. The collider section is brief but uses known QCD production rates, so it does not introduce new technical issues. The main soft spot is the assumption that the leptoquark loop can be treated in isolation. The 331LHN model already contains extra scalars, neutral leptons, and a Z' that can contribute to a_mu at the same order; the paper does not quantify their size once the leptoquark Yukawas are fixed to the anomaly value. If those contributions are comparable or interfere destructively, the quoted mass bounds shift. The hierarchical pattern is also an output of the fit rather than an input prediction from the gauge structure. The work is aimed at readers already interested in 331 extensions or leptoquark explanations of precision anomalies. It is a competent parameter-space scan that updates prior bounds with the 2025 anomaly number and adds LFV cuts. I would send it to peer review so referees can verify the loop integrals and check whether the other sectors were properly bounded or shown to be sub-dominant.

Referee Report

2 major / 2 minor

Summary. The paper extends the 331LHN model with scalar leptoquarks, identifies the singlet as capable of explaining the full 4.2σ muon g-2 discrepancy via its one-loop contribution, derives mass lower bounds m_S ≳ 1.8 TeV (2021 value) or ≳ 6 TeV (2025 lattice update), constrains the Yukawa couplings with LFV and μ-e conversion data to obtain a normal hierarchical pattern, and examines suppressed LHC pair-production signals with improved reach at future colliders.

Significance. If the leptoquark loop dominates without significant interference from other 331LHN sectors, the work supplies a concrete, testable link between the muon anomaly, LFV observables, and collider signatures within a motivated extension of the Standard Model. The combination of multiple low-energy constraints to restrict the parameter space and the explicit collider phenomenology are positive features.

major comments (2)

The central claim that the singlet scalar leptoquark 'fully accounts' for Δa_μ rests on its isolated one-loop contribution matching the target value. The manuscript does not quantify or bound the additional one-loop contributions to a_μ from the model's Z', bileptons, and other scalars once the leptoquark Yukawas are fixed to reproduce the anomaly while satisfying LFV bounds; this omission is load-bearing for the dominance assumption.
The allowed Yukawa couplings are first adjusted to fit Δa_μ and subsequently restricted by LFV observables, so the reported 'normal hierarchical pattern' is an output of the fitting procedure rather than a direct consequence of the gauge structure or anomaly equations. This should be stated explicitly when presenting the viable parameter space.

minor comments (2)

The abstract and introduction cite the 2025 lattice update to Δa_μ but do not provide the explicit reference or the numerical shift used; this should be added for reproducibility.
In the collider section, the statement that QCD-driven pair production leads to 'suppressed signal rates' for multi-TeV masses would benefit from a brief comparison to the corresponding cross-section values or a reference to the parton-level calculation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major point below and indicate the revisions we will implement to strengthen the presentation.

read point-by-point responses

Referee: The central claim that the singlet scalar leptoquark 'fully accounts' for Δa_μ rests on its isolated one-loop contribution matching the target value. The manuscript does not quantify or bound the additional one-loop contributions to a_μ from the model's Z', bileptons, and other scalars once the leptoquark Yukawas are fixed to reproduce the anomaly while satisfying LFV bounds; this omission is load-bearing for the dominance assumption.

Authors: We appreciate the referee's observation. The manuscript demonstrates that the singlet leptoquark can generate the full Δa_μ discrepancy through its one-loop diagram once its Yukawas are fixed by the anomaly and LFV data. In the 331LHN model the Z' and bilepton contributions depend on independent parameters (masses, mixing angles, and additional Yukawas) that are not determined by the leptoquark sector. These contributions can be rendered subdominant by taking sufficiently heavy masses or small mixings while remaining consistent with existing bounds. To make the dominance assumption explicit, we will add a short discussion with order-of-magnitude estimates of the other contributions under the same LFV constraints, showing that viable regions exist where the leptoquark term dominates. revision: yes
Referee: The allowed Yukawa couplings are first adjusted to fit Δa_μ and subsequently restricted by LFV observables, so the reported 'normal hierarchical pattern' is an output of the fitting procedure rather than a direct consequence of the gauge structure or anomaly equations. This should be stated explicitly when presenting the viable parameter space.

Authors: We agree with the referee. The normal hierarchical pattern is obtained after imposing both the Δa_μ requirement and the LFV bounds; it is not enforced by the gauge structure or by the anomaly equations alone. In the revised manuscript we will explicitly note, when presenting the allowed parameter space, that the hierarchy is a phenomenological outcome of the combined constraints rather than a direct prediction of the model. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained parameter fitting

full rationale

The paper extends the 331LHN model by adding scalar leptoquarks, derives their Yukawa interactions from the gauge structure, computes the one-loop contribution to Δa_μ, and scans the resulting Yukawa parameter space against LFV and conversion bounds. The 'normal hierarchical pattern' is reported as a feature of the surviving region after these external constraints are imposed; it is not presented as a first-principles prediction that equals the input by construction. No self-citation chain, self-definitional loop, or renamed fitted quantity is exhibited in the provided text. The central claim that a singlet leptoquark can reproduce the anomaly is achieved by explicit choice of couplings within the model, which is standard and externally falsifiable against LHC and low-energy data.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 1 invented entities

The central claim rests on introducing new scalar particles whose couplings are fitted to data and on assuming the base 331LHN model without re-deriving its gauge structure or fermion assignments.

free parameters (2)

Leptoquark Yukawa couplings
Adjusted to reproduce the muon anomaly and then constrained by LFV rates
Leptoquark mass m_S
Lower bound extracted from fitting Δa_μ

axioms (2)

domain assumption Validity of the 331LHN gauge structure and fermion content
The paper extends this model without deriving its particle spectrum from first principles
standard math Standard one-loop formulas for magnetic moment and flavor violation
Adapted from QED/electroweak calculations to include the new leptoquark vertices

invented entities (1)

Scalar leptoquark singlet no independent evidence
purpose: To generate the required contribution to muon g-2 and mediate LFV processes
Postulated as an extension to fit the observed anomaly; no independent evidence provided

pith-pipeline@v0.9.0 · 5562 in / 1740 out tokens · 59185 ms · 2026-05-10T15:29:05.066226+00:00 · methodology

discussion (0)

Reference graph

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