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arxiv: 2606.03809 · v1 · pith:VHLSD46Unew · submitted 2026-06-02 · ✦ hep-ph · hep-ex

Probing lepton flavor mixing in W_R searches with machine learning at the LHC

Jin-Man Cai , Gang Li This is my paper

Pith reviewed 2026-06-28 09:15 UTC · model grok-4.3

classification ✦ hep-ph hep-ex
keywords left-right symmetric modelheavy Majorana neutrinosmachine learningLHC searcheslepton flavor mixingKeung-Senjanovic processdilepton final states
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The pith

A deep neural network improves sensitivity to right-handed W bosons and heavy neutrinos by incorporating lepton flavor mixing in LHC searches.

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

The paper examines the effects of right-handed lepton flavor mixing on the production and decay of heavy Majorana neutrinos in the left-right symmetric model. It focuses on the Keung-Senjanović process at the LHC, using a deep neural network to analyze same-sign and opposite-sign dilepton plus jets final states across unmixed, maximal-mixing, and PMNS-like scenarios. The DNN analysis yields higher expected significance than prior cut-based methods, resulting in stronger projected exclusion limits on the masses of the right-handed W boson and heavy neutrino. Run 2 data already constrains parts of the mixing parameter space, while the high-luminosity LHC is projected to reach even smaller mixings and potentially exclude standard mixing patterns. The work also maps out overlaps with low-energy charged lepton flavor violation searches.

Core claim

In the unmixed scenario the DNN improves expected significance over ATLAS cut-based analyses, producing stronger exclusion limits; the combined dilepton analysis at the HL-LHC excludes m_WR up to 6.7 TeV and m_NR up to 4.4 TeV under maximal mixing (6.3 TeV and 4.1 TeV under PMNS-like mixing), while Run 2 already rules out sizable regions of the |V_e1|–|V_μ1| plane.

What carries the argument

A deep neural network classifier trained on kinematic features of the dilepton-plus-jets final state from the Keung-Senjanović process to separate signal under three lepton-flavor-mixing benchmarks from Standard Model backgrounds.

If this is right

  • LHC Run 2 data already excludes large fractions of the electron-muon mixing plane for the heavy neutrino.
  • HL-LHC running will reach smaller mixing values and can rule out both maximal and PMNS-like patterns.
  • Future charged-lepton-flavor-violation experiments can probe overlapping or stronger regions of the same mixing parameter space.

Where Pith is reading between the lines

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

  • If the reported DNN performance persists with real data, comparable networks could be applied to other beyond-Standard-Model signatures that depend on flavor structures.
  • Refinements in background modeling or additional input features could push the mass reach beyond the values quoted for the HL-LHC.

Load-bearing premise

The simulated background shapes, parton showers, and detector responses used to train and validate the neural network accurately describe real LHC data.

What would settle it

An observed distribution of DNN output scores in signal regions that deviates from the predicted background-plus-signal template by an amount large enough to remove the claimed exclusion reach on m_WR and m_NR.

Figures

Figures reproduced from arXiv: 2606.03809 by Gang Li, Jin-Man Cai.

Figure 1
Figure 1. Figure 1: Feynman diagram of the Keung-Senjanovi´c process [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Comparison of the HT distributions in the e ±e ± channel between the simulated backgrounds (red) and the ATLAS results (blue) from [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Signal and background efficiencies for the SS dilepton searches as a function of the DNN score threshold. The left [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: 95% C.L. constraints on [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: shows the constraints in the |Ve1|–|Vµ1| plane for two benchmark points: (mWR , mNR ) = (5 TeV, 3 TeV) at LHC Run 2 and (6 TeV, 3 TeV) at the HL-LHC. For the LHC Run 2 benchmark, the ex￾clusion region is characterized by p |Ve1| 2 + |Vµ1| 2 ∼ 0.8–0.85. For the HL-LHC benchmark, the increased center-of-mass energy and integrated luminosity compen￾sate for the impact of the larger mWR . Consequently, the sen… view at source ↗
Figure 6
Figure 6. Figure 6: Comparison of LHC and CLFV constraints on [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
read the original abstract

Right-handed lepton flavor mixing in the left-right symmetric model directly affects the production and decay of heavy Majorana neutrinos $N_R$, yet its impact on collider searches remains less explored. Using a deep neural network (DNN), we analyze the Keung-Senjanovi\'c process $pp \to W_R \to \ell_\alpha N_R \to \ell_\alpha \ell_\beta jj$ with $\ell_{\alpha,\beta}=e,\mu$ at LHC Run~2 and the HL-LHC, considering both same-sign and opposite-sign dilepton channels. We adopt three benchmark mixing scenarios: unmixed, maximal-mixing, and PMNS-like. In the unmixed scenario, the DNN improves the expected significance over the cut-based analyses performed by ATLAS, leading to stronger exclusion limits. For the combined $\ell\ell$ analysis, the HL-LHC can exclude $m_{W_R}$ and $m_{N_R}$ up to $6.7$ ($6.3$)~TeV and $4.4$ ($4.1$)~TeV, respectively, under maximal (PMNS-like) mixing. LHC Run~2 already excludes a significant portion of the $|V_{e1}|\text{--}|V_{\mu1}|$ plane, and the HL-LHC will probe even smaller mixing values, possibly ruling out both the maximal and PMNS-like patterns. Finally, we investigate complementarities with low-energy charged lepton flavor violation processes, where future searches can overlap with or exceed the LHC 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.

Referee Report

1 major / 2 minor

Summary. The paper applies a deep neural network to the Keung-Senjanović process pp → W_R → ℓ_α N_R → ℓ_α ℓ_β jj (ℓ = e, μ) in the left-right symmetric model, incorporating three lepton-flavor-mixing benchmarks (unmixed, maximal, PMNS-like). It reports that the DNN improves expected significance relative to ATLAS cut-based analyses in the unmixed case and projects HL-LHC combined-ℓℓ exclusion reaches of m_WR up to 6.7 (6.3) TeV and m_NR up to 4.4 (4.1) TeV under maximal (PMNS-like) mixing; Run-2 data already constrain part of the |V_e1|–|V_μ1| plane.

Significance. If the simulation-based results hold, the work supplies concrete, quantitative projections that illustrate how machine-learning classifiers can extend the LHC reach for heavy right-handed gauge bosons and Majorana neutrinos while accounting for flavor-mixing effects, and it maps the complementarity with low-energy CLFV searches. The explicit numerical limits and the three-scenario comparison constitute a useful reference for experimental planning.

major comments (1)
  1. [results / methods (implied by abstract)] The headline improvement in expected significance and the HL-LHC exclusion contours (abstract and results section) are obtained exclusively from DNN scores evaluated on Monte Carlo samples for signal and background. No systematic variations of parton-shower tunes, hadronization parameters, or fast-detector response are reported, nor is a data-driven validation of the background modeling described; this assumption directly underpins the quoted 6.7 TeV and 4.4 TeV reaches and must be quantified before the numerical claims can be considered robust.
minor comments (2)
  1. [model / benchmarks] Clarify the precise definition of the three mixing benchmarks (unmixed, maximal, PMNS-like) with explicit values or ranges for |V_e1| and |V_μ1| in a dedicated subsection or table.
  2. [analysis] Specify the DNN architecture, training/validation split, and any regularization or early-stopping criteria used to avoid over-training on the MC samples.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful review and the constructive comment on the robustness of our projected limits. We address the major comment below.

read point-by-point responses

  1. Referee: The headline improvement in expected significance and the HL-LHC exclusion contours (abstract and results section) are obtained exclusively from DNN scores evaluated on Monte Carlo samples for signal and background. No systematic variations of parton-shower tunes, hadronization parameters, or fast-detector response are reported, nor is a data-driven validation of the background modeling described; this assumption directly underpins the quoted 6.7 TeV and 4.4 TeV reaches and must be quantified before the numerical claims can be considered robust.

    Authors: We agree that the quoted exclusion reaches rely on Monte Carlo samples without explicit systematic variations or data-driven background validation. This is a phenomenological projection study whose primary aim is to quantify the improvement of the DNN classifier relative to cut-based methods and to explore flavor-mixing effects. A full experimental analysis would require those elements. In the revised manuscript we will add a dedicated paragraph discussing the expected size of parton-shower and hadronization uncertainties (based on standard tune variations) and will explicitly state that the numerical limits are indicative projections rather than final experimental results. We will also clarify that data-driven validation lies outside the scope of this theoretical work. revision: yes

Circularity Check

0 steps flagged

No significant circularity; limits derived from independent MC simulations

full rationale

The paper trains a DNN on Monte Carlo samples of signal (W_R, N_R) and background processes generated from theoretical models, then computes expected significances and HL-LHC exclusion contours from the DNN output score distributions on those same simulations. This is the standard simulation-based limit-setting procedure and does not reduce any reported limit or significance to a quantity fitted from the target data by construction. No equations equate the final contours to inputs via self-definition, no load-bearing self-citations justify uniqueness theorems, and no ansatz is smuggled in. The chain remains self-contained against external benchmarks such as ATLAS cut-based results.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

The central projections rest on standard Monte Carlo modeling of the LRSM process plus three discrete mixing benchmarks; no new particles beyond the established WR and NR of the left-right symmetric model are introduced, and the mixing parameters are scanned rather than fitted to the LHC data itself.

free parameters (1)
  • mixing parameters |Ve1|, |Vμ1|
    Scanned over the plane to produce exclusion contours; values are not derived from first principles but chosen as benchmarks.
axioms (1)
  • domain assumption Standard parton distribution functions, parton showering, and detector simulation accurately model the Keung-Senjanović signal and SM backgrounds at 13 TeV.
    Invoked when translating DNN output into expected significance and mass limits.
invented entities (1)
  • right-handed W boson (WR) and heavy Majorana neutrino (NR) no independent evidence
    purpose: Mediators of the Keung-Senjanović process whose masses and couplings are being constrained.
    These are standard fields of the left-right symmetric model; the paper does not postulate additional new entities.

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discussion (0)

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