arxiv: 2605.10699 · v1 · submitted 2026-05-11 · ✦ hep-ph · hep-ex· hep-th

Recognition: 2 theorem links

· Lean Theorem

Distinguishing Higgs portal and neutralino dark matter via vector boson fusion

Amit Chakraborty, Rafiqul Rahaman, Tathagata Ghosh

Pith reviewed 2026-05-12 04:03 UTC · model grok-4.3

classification ✦ hep-ph hep-exhep-th

keywords dark matterHiggs portalneutralinovector boson fusionLHCkinematic discriminationmissing transverse energy

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The pith

Vector boson fusion at the LHC can distinguish Higgs portal dark matter from neutralino dark matter at over 5 sigma using jet kinematics.

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

The paper tests whether vector boson fusion events at the LHC, with two jets and missing transverse energy, can separate Higgs portal scalar dark matter from neutralino dark matter. Polarization of the weak bosons produces softer transverse momenta for the jets in the Higgs portal case than in the neutralino case, while the rapidity gap and azimuthal angle between jets also differ. These features are fed into a Kolmogorov-Smirnov test after linear discriminant analysis, yielding separation above 5 sigma for the models examined. A sympathetic reader would care because the result shows collider data can actively discriminate between two popular dark matter candidates instead of only setting limits.

Core claim

In the 2j + missing ET final state from vector boson fusion, the transverse momentum distributions of the tagged jets are softer for Higgs portal dark matter due to the polarization properties of the weak bosons, while neutralino signals produce more energetic jets. The rapidity gap Δη and azimuthal angle difference Δφ also differ characteristically between the two scenarios. A Kolmogorov-Smirnov test applied after linear discriminant analysis quantifies that the signals are distinguishable with a confidence level exceeding 5σ.

What carries the argument

Polarization of weak bosons in VBF, which controls the transverse momentum spectra of the two tagging jets and supplies the kinematic variables Δη and Δφ that feed the statistical separation test.

If this is right

Higgs portal dark matter produces less energetic VBF jets in the transverse direction than neutralino dark matter.
The angular separations Δη and Δφ between jets add independent discriminating power between the two models.
Statistical tests confirm the signals can be told apart above 5 sigma for the benchmark parameters used.
Collider searches in the 2j + MET channel become a viable route for model discrimination rather than only exclusion.

Where Pith is reading between the lines

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

The same polarization-driven kinematic differences could be checked in other VBF-mediated processes at future colliders.
If the separation survives more realistic detector effects and background modeling, it would reduce dependence on direct-detection experiments for choosing between these dark matter candidates.
Accurate simulation of vector-boson polarization becomes essential for any new-physics search that relies on VBF jet properties.

Load-bearing premise

The separation depends on the specific weak-boson polarization and on the masses and couplings chosen for each dark matter model in the Monte Carlo simulation.

What would settle it

An LHC measurement that finds identical jet pT spectra and identical Δη-Δφ distributions for events selected as Higgs portal versus neutralino signals would falsify the claimed distinguishability.

Figures

Figures reproduced from arXiv: 2605.10699 by Amit Chakraborty, Rafiqul Rahaman, Tathagata Ghosh.

**Figure 2.** Figure 2: FIG. 2: Normalized distributions of the transverse momentum ( [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3: Normalized distributions for ∆ [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4: Normalized distributions of the LDA variable [PITH_FULL_IMAGE:figures/full_fig_p015_4.png] view at source ↗

read the original abstract

Understanding the nature of dark matter (DM) is a fundamental challenge in particle physics. In this paper, we investigate the potential of vector boson fusion (VBF) processes at the Large Hadron Collider (LHC) to demonstrate, as a proof of principle, the feasibility of distinguishing between different dark matter scenarios, focusing on Higgs portal DM (HPDM) and neutralino DM in the $2j + \not\!\! E_T$ final state and exploiting the distinctive kinematic features of the VBF jets and the missing transverse energy. Our study reveals that the polarization of weak bosons in VBF plays a crucial role in shaping the transverse momentum distributions of the tagged jets, with the jets being less energetic in the transverse direction for the Higgs portal scenario compared to the neutralino scenario. In addition, the kinematic variables $\Delta\eta$ and $\Delta\phi$ exhibit characteristic differences between the Higgs portal and neutralino DM signals, providing significant discriminating power between these scenarios. We further apply a Kolmogorov--Smirnov test using linear discriminant analysis to quantify the distinguishability of the signals and find that the Higgs portal signals can be differentiated from neutralino DM signals with a C.L. exceeding $5\sigma$, thereby establishing the viability of collider-based discrimination between dark matter models.

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 shows a proof-of-principle way to separate Higgs-portal DM from neutralino DM at the LHC using VBF jet kinematics driven by polarization differences, but the >5σ claim rests on MC modeling at fixed benchmarks.

read the letter

The main point is that this work uses vector boson fusion to try to tell Higgs portal dark matter apart from neutralino dark matter by looking at the kinematics of the two tagging jets in the 2j + missing ET channel. They report that a linear discriminant analysis plus Kolmogorov-Smirnov test gives more than 5 sigma separation. What is new here is the application of the VBF topology specifically to these two DM classes, highlighting how the production mechanism affects weak boson polarization. Higgs portal goes through s-channel Higgs exchange, which favors longitudinal polarizations and softer jet pT, while neutralino uses t-channel Z or W exchange with different helicity preferences. This leads to differences in pT(jet), Δη, and Δφ that they quantify with MC simulations at chosen parameter points. The paper handles this cleanly as a proof of principle and shows the statistical test working on the simulated distributions. That part is solid for what it is. The potential issue is that everything rests on those Monte Carlo samples accurately reflecting the polarization differences for the selected masses and couplings. If the generator modeling of the helicity structure is off, or if the benchmarks aren't representative, the distributions could overlap enough to lose the separation. The stress test note flags this correctly, and without analytic cross-checks or a parameter scan in the paper, it remains a concern. Backgrounds and detector effects would also need careful treatment in a full study. This is the kind of targeted phenomenology paper that could interest people running DM searches at the LHC. It deserves to go to peer review because it has a clear, testable claim and engages with real collider observables, even if the robustness needs more work.

Referee Report

2 major / 1 minor

Summary. The manuscript claims that vector boson fusion (VBF) at the LHC can distinguish Higgs portal dark matter (HPDM) from neutralino dark matter in the 2j + missing ET final state. It argues that s-channel Higgs exchange in HPDM versus t-channel Z/W exchange in neutralino DM produces different weak-boson polarization, leading to distinct jet pT, Δη, and Δφ distributions. Linear discriminant analysis (LDA) followed by a Kolmogorov-Smirnov (KS) test on Monte Carlo samples is reported to yield >5σ separation, establishing collider-based model discrimination as viable.

Significance. If the kinematic separation is robust, the result would be significant: it offers a concrete collider handle on two DM scenarios that often share similar signatures elsewhere, using polarization effects in VBF as the discriminator. The proof-of-principle approach and quantitative statistical test are strengths that could guide experimental analyses at the LHC.

major comments (2)

Abstract: the >5σ LDA+KS separation is obtained from Monte Carlo samples at specific (unspecified) benchmark masses and couplings. The manuscript provides no robustness scan over these parameters or over event-generator choices for weak-boson polarization fractions; because the claimed kinematic differences are stated to arise from polarization, the absence of such checks makes the central distinguishability claim load-bearing and currently unverified.
Abstract (method description): the polarization argument is presented as characteristic of the two Lagrangians, yet no analytic cross-check or generator-independent calculation of the helicity fractions is supplied. If the Monte Carlo modeling of longitudinal versus transverse modes is inaccurate for the chosen points, the pT(jet), Δη, and Δφ differences disappear and the KS test result is no longer guaranteed.

minor comments (1)

The abstract refers to 'characteristic differences' in Δη and Δφ without quoting the numerical ranges or showing example distributions; adding a brief quantitative statement or reference to a figure would improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address each major comment below and have revised the manuscript to incorporate additional checks and clarifications that strengthen the presentation of our results.

read point-by-point responses

Referee: Abstract: the >5σ LDA+KS separation is obtained from Monte Carlo samples at specific (unspecified) benchmark masses and couplings. The manuscript provides no robustness scan over these parameters or over event-generator choices for weak-boson polarization fractions; because the claimed kinematic differences are stated to arise from polarization, the absence of such checks makes the central distinguishability claim load-bearing and currently unverified.

Authors: We agree that the abstract emphasizes the benchmark results and that a robustness scan would strengthen the central claim. The specific masses and couplings are defined in Section III of the manuscript. As the work is a proof-of-principle study, the chosen points illustrate the kinematic separation arising from the different production mechanisms. In the revised manuscript we will add a limited scan over additional DM masses and couplings within the phenomenologically allowed range, confirming that the separation exceeds 5σ for the majority of tested points. For event-generator dependence, the polarization is determined at the matrix-element level by MadGraph5_aMC@NLO according to the respective Lagrangians; we will include a short statement on this and note consistency with standard electroweak polarization expectations. revision: yes
Referee: Abstract (method description): the polarization argument is presented as characteristic of the two Lagrangians, yet no analytic cross-check or generator-independent calculation of the helicity fractions is supplied. If the Monte Carlo modeling of longitudinal versus transverse modes is inaccurate for the chosen points, the pT(jet), Δη, and Δφ differences disappear and the KS test result is no longer guaranteed.

Authors: The referee is correct that the polarization difference follows directly from the Feynman diagrams of the two models: s-channel Higgs exchange in the Higgs-portal case versus t-channel Z/W exchange in the neutralino case. These structures produce distinct helicity amplitudes that can be derived analytically using the standard electroweak helicity formalism. Although the manuscript relies on Monte Carlo for the full simulation including parton showering, we will add a concise qualitative discussion of the expected longitudinal versus transverse fractions based on the tree-level diagrams and cite relevant literature on VBF polarization. This addition will make the origin of the kinematic differences more transparent while retaining the Monte Carlo results as the quantitative demonstration. revision: yes

Circularity Check

0 steps flagged

No circularity: distinction arises from independent Monte Carlo simulations of distinct DM Lagrangians

full rationale

The paper generates separate Monte Carlo samples for Higgs-portal DM (s-channel Higgs exchange) and neutralino DM (t-channel electroweak exchange) in the VBF + MET channel, extracts kinematic distributions (pT(jets), Δη, Δφ), trains an LDA discriminant, and applies a KS test to report >5σ separation. No parameter is fitted inside the paper to the target observable; the separation is an output of the differing helicity structures and benchmark choices in the two independent simulations. No self-citation is invoked as a load-bearing uniqueness theorem, no ansatz is smuggled, and no known result is merely renamed. The derivation chain is therefore self-contained against external benchmarks (standard MC generators and statistical tests).

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that Monte Carlo generators correctly capture the polarization of weak bosons in VBF and that the chosen benchmark points for each dark matter model are representative.

free parameters (1)

DM masses and couplings
Specific values for the Higgs-portal scalar and neutralino parameters are selected to define the signals; these are not derived from first principles but chosen to satisfy other constraints.

axioms (1)

domain assumption Standard Model weak-boson polarization and parton-shower modeling in Monte Carlo tools accurately reproduce the VBF jet kinematics.
The paper invokes this to translate model differences into observable jet pT and angular distributions.

pith-pipeline@v0.9.0 · 5533 in / 1317 out tokens · 52028 ms · 2026-05-12T04:03:59.118100+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear
polarization of weak bosons in VBF plays a crucial role... Effective W Approximation... PT(x,pT), PL(x,pT)... Kolmogorov–Smirnov test using linear discriminant analysis
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear
chosen benchmark points... mχ=130 GeV, mh2=275 GeV, cosα=0.95, λ=3... significance of approximately 5σ

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