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arxiv: 2605.13614 · v1 · submitted 2026-05-13 · ✦ hep-ex

Recognition: 2 theorem links

· Lean Theorem

Search for pair production of additional neutral scalars within the Inert Doublet Model in a final state with two electrons or two muons in proton-proton collisions at sqrt{s} = 13 TeV and 13.6 TeV

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Pith reviewed 2026-05-14 17:59 UTC · model grok-4.3

classification ✦ hep-ex
keywords Inert Doublet Modelneutral scalar pair productiondark matter candidatedilepton final statemissing transverse momentumCMSexclusion limitsLHC
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The pith

No significant excess observed in first dedicated search for inert doublet scalars, excluding masses up to 108 GeV

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

The paper carries out the first dedicated search for pair production of the additional neutral scalars H and A predicted by the Inert Doublet Model. Proton-proton collision data at 13 and 13.6 TeV are analyzed in a final state of two opposite-charge same-flavor leptons plus missing transverse momentum from the stable dark-matter candidate H. A parameterized neural network separates potential signal from Standard Model backgrounds. No excess above expected background is seen, allowing 95% confidence level exclusion limits to be placed in the m_H versus m_A plane.

Core claim

No significant excess of events is observed. Exclusion limits at 95% confidence level are set on the production cross section of the two new neutral scalars, H and A, expressed in terms of their masses m_H and m_A in the m_H vs. m_A plane. The observed exclusion region reaches m_H = 108 GeV for m_H-m_A = 78 GeV and, at m_H = 70 GeV, covers the range m_H-m_A = 40-90 GeV.

What carries the argument

Parameterized neural network that classifies events in the two-lepton plus missing transverse momentum final state arising from off-shell Z boson decay to H A pairs.

Load-bearing premise

Standard Model backgrounds are accurately modeled and subtracted, and the signal acceptance and efficiency for the Inert Doublet Model are correctly simulated across the scanned mass points.

What would settle it

Observation of a statistically significant excess of events in the neural-network signal-enriched region compared with the expected background.

Figures

Figures reproduced from arXiv: 2605.13614 by CMS Collaboration.

Figure 1
Figure 1. Figure 1: The IDM free parameters are subject to numerous theoretical and experimental constraints. In this work, the constraints that are applied follow Ref. [9], with more recent updates described in Refs. [10, 13, 17, 25, 33, 34]. The two-loop constraints on the scalar couplings presented in Ref. [13] are not applied, as the code is not publicly available, instead the leading-order (LO) values for constraints are… view at source ↗
Figure 1
Figure 1. Figure 1: Leading-order Feynman diagrams of: (left) HH [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Total signal cross section at LO obtained with M [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Distributions of key variables after the preselection and OCSF pair selection for 2016– [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Distributions of the pNN output for the data and the SM expectations in the SR [PITH_FULL_IMAGE:figures/full_fig_p020_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Distributions of the data and the SM expectations in all CRs after the background-only [PITH_FULL_IMAGE:figures/full_fig_p020_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Distributions of the pNN output for the data and the SM expectations in the SR [PITH_FULL_IMAGE:figures/full_fig_p021_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Distributions of the data and the SM expectations in all CRs after the background-only [PITH_FULL_IMAGE:figures/full_fig_p021_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: The 95% CL upper limit on σIDM as a function of mA − mH, for mH = 70 GeV, sepa￾rately for the (black circles) Run 2 and (red squares) Run 3 data sets. Limits are calculated with the IDM parameters mH± = mA + 50 GeV, λ2 = 1, and λ345 = 10−6 . The limits, however, are insensitive to the choice of the λ2 value, and to changes in mH± and λ345 within their allowed values [PITH_FULL_IMAGE:figures/full_fig_p022_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: The 95% CL exclusion limits in terms of mH and mA − mH. The red dashed lines indicate the ±1 standard deviation bands from experimental uncertainties, whilst the black dashed lines indicate the ±1 standard deviation bands from theoretical uncertainties in the signal samples. The exclusion limits from the LEP reinterpretation and relic density constraints are overlaid in green and yellow, respectively (see … view at source ↗
read the original abstract

A first dedicated search for pair production of new scalars predicted by the Inert Doublet Model is performed using proton-proton collisions. Data were collected with the CMS detector at the CERN LHC at $\sqrt{s}$ = 13 TeV and 13.6 TeV, corresponding to integrated luminosities of 138 fb$^{-1}$ and 35 fb$^{-1}$, respectively. Within this model, four additional scalar bosons (H, A, H$^+$, and H$^-$) are predicted. Through an additional discrete symmetry, the lightest new scalar, H, is stable, rendering it a viable dark matter candidate. These candidates can originate from quark-antiquark annihilation producing an offshell Z boson that decays to a pair of the new scalars. The target final state consists of exactly two opposite-charge same-flavour leptons (electrons or muons), with missing transverse momentum due to the stable neutral scalars, and very little hadronic activity. A parameterised neural network is used to separate the signal from the standard model background. No significant excess of events is observed. Exclusion limits at 95% confidence level are set on the production cross section of the two new neutral scalars, H and A, expressed in terms of their masses, $m_\mathrm{H}$ and $m_\mathrm{A}$, in the $m_\mathrm{H}$ vs. $m_\mathrm{A}$ plane. The observed (expected) exclusion region reaches $m_\mathrm{H}$ = 108 (106) GeV for $m_\mathrm{H}-m_\mathrm{A}$ = 78 (76) GeV and at $m_\mathrm{H}$ = 70 GeV, covers the range of $m_\mathrm{H}-m_\mathrm{A}$ = 40$-$90 (35$-$90) GeV.

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

2 major / 3 minor

Summary. The manuscript reports the first dedicated search for pair production of neutral scalars H and A predicted by the Inert Doublet Model in proton-proton collisions at 13 TeV (138 fb^{-1}) and 13.6 TeV (35 fb^{-1}) with the CMS detector. The analysis targets the final state of exactly two opposite-sign same-flavor leptons, large missing transverse momentum, and low hadronic activity. A parameterized neural network discriminates signal from Standard Model backgrounds (primarily Drell-Yan, WW, and non-prompt leptons). No significant excess is observed, and 95% CL exclusion limits are placed on the production cross section in the m_H vs. m_A plane, with the observed (expected) exclusion reaching m_H = 108 (106) GeV at m_H - m_A = 78 (76) GeV.

Significance. If the background modeling holds, this provides the first dedicated constraints on the Inert Doublet Model in this channel, directly limiting the viable parameter space for the stable scalar H as a dark matter candidate. The combination of two datasets at different energies and the parameterized NN approach for scanning the mass grid are strengths that enable broad coverage without post-hoc adjustments. The null result yields clean, interpretable exclusion contours.

major comments (2)
  1. [Section 7] Background estimation section: the manuscript relies on simulation for the dominant backgrounds in the high-MET, low-jet signal region; a dedicated table or figure quantifying the post-fit yields, shape agreement in control regions, and systematic uncertainties on MET tails and non-prompt leptons for both datasets is needed to substantiate the subtraction accuracy underlying the observed limits.
  2. [Section 6] Parameterized neural network (Section 6): while the approach is efficient for the mass grid, the training/validation procedure across mass points and the response in the low-jet regime should be shown with explicit overtraining checks and efficiency curves to confirm that discrimination power does not introduce bias in the low-mass exclusion region.
minor comments (3)
  1. [Abstract] Abstract: the phrasing 'covers the range of m_H-m_A = 40-90 (35-90) GeV' at m_H=70 GeV should be clarified to specify whether this is a continuous exclusion band or discrete points.
  2. [Figures] Figure captions: specify the exact integrated luminosities and center-of-mass energies for each dataset when showing limit contours or NN output distributions.
  3. [Section 8] Notation: ensure consistent use of m_H and m_A throughout, including in the limit-setting description.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and positive assessment of our work. We address each of the major comments below and have incorporated the suggested additions into the revised manuscript.

read point-by-point responses
  1. Referee: [Section 7] Background estimation section: the manuscript relies on simulation for the dominant backgrounds in the high-MET, low-jet signal region; a dedicated table or figure quantifying the post-fit yields, shape agreement in control regions, and systematic uncertainties on MET tails and non-prompt leptons for both datasets is needed to substantiate the subtraction accuracy underlying the observed limits.

    Authors: We agree with the referee that providing more detailed validation of the background estimation is important. In the revised manuscript, we have added a dedicated table (Table 7) that quantifies the post-fit yields in the signal region and relevant control regions for both the 13 TeV and 13.6 TeV datasets. Additionally, we include a new figure (Figure 8) showing the shape agreement in control regions for the MET distribution, along with an expanded discussion of the systematic uncertainties associated with the MET tails and non-prompt lepton backgrounds. These updates substantiate the accuracy of the background subtraction used in deriving the observed limits. revision: yes

  2. Referee: [Section 6] Parameterized neural network (Section 6): while the approach is efficient for the mass grid, the training/validation procedure across mass points and the response in the low-jet regime should be shown with explicit overtraining checks and efficiency curves to confirm that discrimination power does not introduce bias in the low-mass exclusion region.

    Authors: We thank the referee for this valuable suggestion. In the revised manuscript, we have expanded Section 6 to include a detailed description of the training and validation procedure for the parameterized neural network across the different mass points. We now present explicit overtraining checks, including comparisons of training and test performance metrics, and efficiency curves as a function of jet multiplicity to demonstrate the network's response in the low-jet regime. These additions confirm that the discrimination power is robust and does not introduce any bias in the low-mass exclusion region. revision: yes

Circularity Check

0 steps flagged

No circularity: direct data-to-simulation comparison sets experimental limits

full rationale

The paper reports a standard LHC search for new scalars in the Inert Doublet Model. Observed events in the two-lepton + MET + low-jet final state are compared to simulated SM backgrounds (Drell-Yan, WW, non-prompt leptons) and IDM signal samples. A parameterized neural network separates signal from background, but its training uses simulated samples independent of the final observed counts. No excess is seen, and 95% CL exclusion contours in the m_H–m_A plane are extracted from the data via standard statistical procedures. No equation, fit, or claim reduces by construction to its own inputs; no self-citation chain is load-bearing for the central null-result or limit-setting step. The analysis chain is externally falsifiable against the recorded LHC datasets and is therefore self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The search depends on the Inert Doublet Model predictions for signal and on standard assumptions about background modeling and detector response; no new free parameters or invented entities are introduced beyond the model being tested.

axioms (2)
  • domain assumption Standard Model background processes are correctly modeled in simulation for the two-lepton plus missing transverse momentum final state.
    Background estimation relies on this to identify any excess.
  • domain assumption The Inert Doublet Model correctly predicts the production cross sections and decay modes of H and A.
    Signal efficiency and acceptance are calculated within this framework.
invented entities (1)
  • Inert scalars H, A, H+, H- no independent evidence
    purpose: Additional scalars including a stable dark matter candidate.
    These particles are predicted by the Inert Doublet Model under test; the paper does not introduce them.

pith-pipeline@v0.9.0 · 5664 in / 1341 out tokens · 53034 ms · 2026-05-14T17:59:41.745704+00:00 · methodology

discussion (0)

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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/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    A parameterised neural network is used to separate the signal from the standard model background. No significant excess of events is observed. Exclusion limits at 95% confidence level are set on the production cross section of the two new neutral scalars, H and A, expressed in terms of their masses, m_H and m_A, in the m_H vs. m_A plane.

  • IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    The target final state consists of exactly two opposite-charge same-flavour leptons (electrons or muons), with missing transverse momentum due to the stable neutral scalars, and very little hadronic activity.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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