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Search for dark photons in decays of Higgs bosons produced in association with Z bosons in proton-proton collisions at $\sqrt{s} =$ 13 TeV

T0 review · 1 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read No Higgs-to-dark-photon decays found; rate capped at 4.6 percent

desk verdict First dedicated H→invisible+massless dark photon limit from CMS, clean and standard; the single WZ normalization for two subcomponents is the one question I'd push. read the letter →

arxiv 1908.02699 v2 pith:7YQY4JXX submitted 2019-08-07 hep-ex

CMS Collaboration This is my paper · ORCID
classification hep-ex
keywords darkphotonHiggsbosonexoticdecayinvisiblemissingtransversemomentummassCLsupperlimitbinnedlikelihoodfit
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper asks whether the 125 GeV Higgs boson can decay to a single visible photon plus an invisible massless dark photon, a signature that would point to a charged dark sector. The search, using the full 2016–2018 proton-proton collision data recorded at 13 TeV (an integrated luminosity of 137 fb$^{-1}$), finds 14 candidate events against 13.3 expected from standard model background processes; there is no excess. Interpreting the null result in the dark-photon model gives the first upper limits on such Higgs decays: at 125 GeV the branching fraction is capped at 4.6% at 95% confidence, with 3.6% expected. Because some models allow this branching fraction up to about 5%, the search is sensitive to the most plausible signal rates and rules them out.

What carries the argument

The discriminating variable is the transverse mass $m_T=\sqrt{2 p_T^{\text{miss}} p_T^{\gamma}[1-\cos\Delta\phi(\vec p_T^{\text{miss}},\vec p_T^{\gamma})]}$ of the missing-transverse-momentum and photon system. Signal events from $H\to\gamma+\text{invisible}$ populate a Jacobian peak with an endpoint near $m_T\sim m_H$, while the dominant WZ, ZZ, and nonresonant backgrounds are flat or rise toward low $m_T$. The extraction is a binned maximum-likelihood fit to the $m_T$ distribution, split into low-$|\eta_\gamma|$ and high-$|\eta_\gamma|$ regions, with three data control regions (same-flavor lepton pairs, trilepton WZ, and four-lepton ZZ) fixing the background normalizations; a modified frequentist CLs procedure produces the limits.

What would settle it

Recompute the 95% confidence-level limit twice, once with the WZ background $m_T$ shape taken directly from the trilepton control-region data and once from simulation; if the two limits differ by more than the quoted systematic uncertainty, the background-shape assumption breaks. Alternatively, a dedicated data sample of WZ events with a fully identified third lepton, selected with the same missing-transverse-momentum and photon requirements as the signal region, would reveal any $m_T$ shape mismatch between data and simulation in the relevant phase space.

Watch

Extended reading notes

Core claim

The analysis targets the process $pp\to Z(\ell\ell)H$ with $H\to\gamma\gamma_D$, where $\gamma_D$ is a massless dark photon that escapes detection, leaving a final state of a same-flavor lepton pair, one isolated photon, and large missing transverse momentum. After event selection, 14 events are observed against 13.3 $\pm$ 3.8 expected background events, and a binned maximum-likelihood fit to the transverse-mass spectrum of the photon plus missing momentum finds no significant signal. At $m_H=125$ GeV, assuming the standard model ZH production cross section, the observed (expected) 95% confidence-level upper limit on the branching fraction $\mathcal{B}(H\to\text{invisible}+\gamma)$ is 4.6 (3.6)%. The same fit excludes the product $\sigma_{ZH}\times\mathcal{B}(H\to\text{invisible}+\gamma)$ from about 40 fb at 125 GeV to about 4 fb at 300 GeV, and the paper states these are the first limits on Higgs boson decays to final states that include an undetected massless dark photon.

Load-bearing premise

The limit assumes the simulated shapes of the $m_T$ distributions for the WZ and ZZ backgrounds are correct in the signal region, because the analysis normalizes those simulations in control regions containing only a handful of events and then relies on the same shapes to model the signal region.

Editorial extensions

If this is right

  • Any 125 GeV Higgs-like scalar with a branching fraction above 4.6% to a photon plus an invisible massless particle is excluded, independent of the specific dark-photon model details.
  • The exclusion extends to heavy neutral Higgs bosons, ruling out $\sigma_{ZH}\times\mathcal{B}(H\to\text{invisible}+\gamma)$ from about 40 fb at 125 GeV down to about 4 fb at 300 GeV.
  • Fitting the $m_T$ shape rather than counting events improves the expected sensitivity by 30–50%, showing that shape-based extraction is the effective route in this final state.
  • The irreducible standard model background from $H\to Z\gamma\to\nu\nu\gamma$ is below 0.1 events, so the search is limited by instrumental and reducible backgrounds, not by the standard model Higgs itself.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • I infer that the same analysis, applied to the full High-Luminosity LHC data set of roughly 3000 fb$^{-1}$, would push the branching-fraction limit below 1%, directly testing the ~5% benchmark that motivates the search.
  • The result can likely be reinterpreted for a massive dark photon: a nonzero $\gamma_D$ mass would shift the $m_T$ endpoint below $m_H$, so the existing limit curve could be recast as a constraint on the dark photon mass within the model.
  • The same-flavor control region used for nonresonant backgrounds contains only 3 events, so that background shape is validated on very sparse data; a future measurement with higher statistics in that region would be the most direct check on the quoted limit.
  • Combining this ZH-associated search with gluon-fusion production, as the earlier 8 TeV analysis did, could roughly double the signal acceptance and tighten the limit further.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

1 major / 4 minor

Summary. The paper reports a search by the CMS Collaboration for a Higgs boson produced in association with a Z boson and decaying to an undetected particle together with an isolated photon, focusing on the massless dark photon interpretation. The analysis uses the full 13 TeV data set of 137 fb^-1 and selects events with a Z->ll candidate, a high-pT photon, large missing transverse momentum, and low jet activity. A binned maximum-likelihood fit is performed on the transverse mass mT spectrum in the signal region together with three dedicated control regions (e-mu for nonresonant backgrounds, three-lepton for WZ, and four-lepton for ZZ), with separate bins in photon pseudorapidity. Background normalizations for the dominant WZ and ZZ processes are fitted to data, nonresonant backgrounds are estimated from an e-mu control region, and a set of experimental and theoretical systematic uncertainties is included. No significant excess over the standard model background is found: 14 events are observed against a total background estimate of 13.3 +/- 3.8. Upper limits at 95% CL are set on sigma_ZH times B(H->invisible+gamma) as a function of mH, and for mH=125 GeV, assuming the SM ZH production cross section, the observed (expected) limit on the branching fraction is 4.6% (3.6%).

Significance. If the result holds, this is the first experimental limit on a Higgs boson decay to a massless dark photon plus invisible particles in the ZH production channel. The analysis follows a well-established profile-likelihood strategy, uses data-driven control regions for the dominant backgrounds, and documents the systematic uncertainties. The result is of direct interest to dark-sector and BSM Higgs searches, and it provides a template for future searches of this signature. The paper is clearly written and the statistical methodology is sound. The main caveat is the validation of a subdominant WZ background component, discussed in the major comments.

major comments (1)
  1. [Section 5.2, Eq. (1)] The WZ background in the signal region contains two components: (a) events in which the electron from the W boson decay is misidentified as a photon, and (b) events in which the W lepton is not identified and a genuine hard photon is radiated. In the likelihood of Eq. (1), a single normalization parameter muWZ multiplies both components, and the three-lepton control region directly constrains only component (a), because it requires the W-decay lepton to be identified and used as the photon proxy. Component (b) is thus constrained only through its simulated ratio to component (a), and its mT shape is not validated by any data control region. Since WZ is the dominant background (8.1 +/- 2.0 out of a total of 13.3 +/- 3.8) and the observed limit corresponds to roughly eight signal events, an O(1) event shift in this background would change the mH=125 GeV limit by about 0.5 percentage points. The authors should report the relative contribution of component (b) and either validate it with a dedicated control region or assign an explicit systematic uncertainty to the ratio of the two components.
minor comments (4)
  1. [Section 6, Section 8] Signal samples are generated only at mH = 125, 200, and 300 GeV, while limits are shown as a continuous function of mH between 125 and 300 GeV. The paper should state how the signal acceptance and mT shapes are interpolated between the generated masses.
  2. [Section 7] The systematic uncertainties are described in the text, but a summary table listing each nuisance parameter, its prior, and its typical impact on the signal and background yields would improve the reproducibility and readability of the analysis.
  3. [Section 5.2] The sentence describing the electron-to-photon misidentification rate would be clearer if it specified whether the quoted 1-5% range is per-candidate and how it is applied as a function of |eta_gamma| and pT.
  4. [Table 2 and Figure 3] The signal predictions in Table 2 are quoted for a signal size of 0.1 sigma_ZH; for clarity, the corresponding branching fraction assumed for the signal should be stated explicitly in the table caption or text.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the analysis measures a signal strength as a free parameter in a likelihood fit against data, with backgrounds constrained by independent control regions and theory inputs from external references.

full rationale

The paper is a direct experimental search. The central result, the upper limit on the product of ZH production cross section and B(H -> invisible + gamma), is obtained from a binned maximum-likelihood fit in which the signal strength mu is a free parameter (Eq. 1) and no target quantity is defined in terms of a fitted parameter. The background normalizations (mu_Nonres, mu_WZ, mu_ZZ) are constrained by dedicated data control regions (e-mu, WZ three-lepton, ZZ four-lepton), and the signal shape and acceptance are taken from simulated ZH events normalized to external theory cross sections (Refs. [28, 29]). The dark-photon interpretation is imported from independent theoretical papers, not derived from the data or from self-citations by the experimental collaboration. The skeptical concern about the WZ background shape being validated only sparsely, while legitimate as a modeling risk, is not a circularity: it concerns the accuracy of an external simulation input, not a reduction of the conclusion to its own assumptions. No step in the derivation chain equates an output with an input by construction, and no self-citation is load-bearing for the main limit. The result is therefore self-contained as an experimental measurement, with no significant circularity.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The paper introduces no new physical entities. It measures an upper limit using standard statistical methods. The background normalizations are fitted nuisance parameters, not theoretical free parameters. The dark photon is a pre-existing theoretical construct, and the search is interpreted within that external model.

free parameters (3)
  • mu_Nonres
    Scale factor for the nonresonant WW and top quark background, determined from the e-mu control region in the simultaneous fit (Eq. 1).
  • mu_WZ
    Scale factor for the WZ background with a misidentified or lost lepton, determined from the three-lepton control region (Section 5.2).
  • mu_ZZ
    Scale factor for the ZZ background, determined from the four-lepton control region (Section 5.3).
assumptions (4)
  • domain assumption GEANT4 simulation accurately reproduces the CMS detector response to the final states considered.
    All Monte Carlo events are passed through a GEANT4-based detector simulation and reconstructed with the same algorithms as data (Section 3).
  • domain assumption POWHEG, MadGraph, and PYTHIA describe the signal and background kinematics accurately.
    NLO generators with NNPDF parton distribution functions are used to model signal and background processes (Section 3).
  • domain assumption The electron-to-photon misidentification rate, measured in Z to ee data, is valid for the signal region.
    The WZ background estimate relies on this rate (Section 5.2).
  • domain assumption The integrated luminosity measurements are correct to within the quoted uncertainties.
    Luminosity uncertainties of 2.3 to 2.5% are assigned per year (Section 7).

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Cite this review

Pith. "Pith review of Search for dark photons in decays of Higgs bosons produced in association with Z bosons in proton-proton collisions at $\sqrt{s} =$ 13 TeV." pith.science (2026). https://pith.science/paper/7YQY4JXX

@misc{pith2026190802699,
  author       = {Pith},
  title        = {Pith review of: Search for dark photons in decays of Higgs bosons produced in association with Z bosons in proton-proton collisions at $\sqrts =$ 13 TeV},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7YQY4JXX}},
  note         = {Machine review of arXiv:1908.02699}
}
abstract

A search is presented for a Higgs boson that is produced in association with a Z boson and that decays to an undetected particle together with an isolated photon. The search is performed by the CMS Collaboration at the Large Hadron Collider using a data set corresponding to an integrated luminosity of 137 fb$^{-1}$ recorded at a center-of-mass energy of 13 TeV. No significant excess of events above the expectation from the standard model background is found. The results are interpreted in the context of a theoretical model in which the undetected particle is a massless dark photon. An upper limit is set on the product of the cross section for associated Higgs and Z boson production and the branching fraction for such a Higgs boson decay, as a function of the Higgs boson mass. For a mass of 125 GeV, assuming the standard model production cross section, this corresponds to an observed (expected) upper limit on this branching fraction of 4.6 (3.6)% at 95% confidence level. These are the first limits on Higgs boson decays to final states that include an undetected massless dark photon.

Figures

Figures reproduced from arXiv: 1908.02699 by the authors.

Figure 1
Figure 1. A Feynman diagram for the production of the Z [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. The mT distributions for the eµ, WZ, and ZZ control regions after the simultaneous fit to data in the signal and control regions. Statistical and systematic uncertainties in the expected background yields are represented by the hatched band. Vertical bars represent data statistical uncertainties, while horizontal bars represent the bin widths. 7 Efficiencies and systematic uncertainties Several sources of systematic… view at source ↗
Figure 3
Figure 3. The mT distributions in the signal region for two mH values for events with |η γ | < 1 (left) and |η γ | > 1 (right), after the fit to data. The signal size corresponds to 0.1σZH for both values of mH shown. The signal processes are stacked on top of all backgrounds. Statistical and systematic uncertainties in the expected background yields are represented by the hatched band. Vertical bars represent data statistica… view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Expected and observed upper limits at 95% CL on the product of [PITH_FULL_IMAGE:figures/full_fig_p012_4.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Search for light long-lived neutral particles produced in $pp$ collisions at $\sqrt{s} =$ 13 TeV and decaying into collimated leptons or light hadrons with the ATLAS detector

    hep-ex 2019-09 accept novelty 5.0 of 10

    No evidence for displaced dark-photon jets is found, and 95% confidence limits exclude cross sections above about 4 pb for H to two dark photons with decay lengths from 1.5 mm to 307 mm.

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