The existence of dark matter is evidenced by astrophysical observations, yet its nature remains a central question in particle physics. The discovery of a Higgs boson (H) with a mass of 125 GeV at the LHC has spurred investigations into its potential connection with physics beyond the Standard Model (BSM). Searches for elusive BSM particles coupled to the Higgs boson are motivated by the upper limit on the undetected Higgs boson decay branching ratio. One such particle is a massless dark photon (γd), a force carrier of an extra U(1)d gauge group in the dark sector. Dark photons could explain dark matter self-interactions, addressing the small-scale structure formation problem and the PAMELA-Fermi-AMS2 anomaly, and potentially enhance the light dark matter annihilation rate in asymmetric dark matter scenarios. A promising search strategy involves the Higgs boson decaying into a visible photon and a massless dark photon (H → γγd), detectable via missing transverse momentum (ETmiss). This paper combines searches for H → γγd using the full LHC Run 2 dataset (139 fb−1) recorded by the ATLAS detector at √s = 13 TeV, focusing on three final-state signatures: γ + ETmiss + VBF jets (VBF channel), γ + ETmiss + Z(ℓℓ, ℓ = e, μ) (ZH channel), and γ + ETmiss (ggF channel). The ATLAS detector, a multipurpose detector with near 4π coverage, is described, along with the Monte Carlo simulation used for signal and background modeling. The Higgs boson is assumed to be produced via gluon-gluon fusion (ggF), vector-boson fusion (VBF), and in association with a Z boson (ZH).

The CMS experiment has previously reported searches for Higgs boson decays into a photon and a dark photon using the ZH production mechanism (137 fb−1) and VBF production (130 fb−1). Earlier ATLAS and CMS searches using 8 TeV data also targeted the γ + ETmiss final state. This paper builds upon these previous analyses by combining three distinct channels, encompassing both Standard Model-like Higgs bosons and higher-mass Higgs bosons predicted in BSM theories, improving overall sensitivity and exploring a broader mass range.

The combined search utilizes three channels: VBF, ZH, and ggF. The VBF channel, based on Ref. [34], selects events with ETmiss > 150 GeV, two VBF jets with specific kinematic requirements (large pseudorapidity separation, large invariant mass, and non-back-to-back in azimuthal angle), an isolated photon (15 GeV < ETγ < max(110 GeV, 0.733 × mT)), and rejection of events with reconstructed leptons. Events are categorized into ten signal regions (SRs) based on mjj and mT. The ZH channel, from Ref. [35], selects events with two same-flavour, oppositely charged leptons (76 GeV < mℓℓ < 116 GeV), ETmiss > 60 GeV, and an isolated photon (ET > 25 GeV). A boosted decision tree (BDT) algorithm enhances sensitivity. The ggF channel reinterprets Ref. [36] using the RECAST technique, selecting events with ETmiss > 200 GeV and a leading photon (ETγ > 150 GeV) meeting isolation and η criteria. Four SRs are defined based on ETmiss ranges. Backgrounds are estimated using data-driven methods and Monte Carlo simulations. Systematic uncertainties, including those related to data-taking conditions, physics objects, and signal/background modeling, are considered and treated as correlated or uncorrelated as appropriate. The combination of the three channels is performed using a likelihood function that incorporates all systematic uncertainties. The profile-likelihood-ratio test statistic and the CLs method are used to derive upper limits on the parameters of interest.

The combined analysis yields an observed (expected) 95% confidence level (CL) upper limit on the branching ratio B(H125 → γγd) of 1.3% (1.5%). This represents a 29% (14%) improvement in sensitivity compared to the most stringent result from the VBF analysis alone. The observed (expected) 95% CL upper limits on the BSM Higgs boson production cross-section times B(HBSM → γγd) range from 16 fb (26 fb) for mH = 400 GeV to 1.0 fb (1.5 fb) for mH = 3000 GeV. Assuming a branching ratio B(HBSM → γγd) of 5% and theoretically predicted cross-sections, Higgs boson masses below around 1600 GeV (1500 GeV) are excluded. The combination with the VBF channel improves the cross-section times B(HBSM → γγd) limit by 33% (14%) at mH = 1500 GeV compared to the ggF channel alone. The results are further interpreted within a minimal simplified model, which introduces a generic messenger sector connecting the dark and observable sectors. This interpretation uses two free parameters (aα and ξ) and an interference parameter χ. The combined results, along with the ATLAS measurement of B(H125 → γγ) and the reinterpretation of the ATLAS search for H125 → invisible, constrain the allowed parameter space of the minimal simplified model, excluding regions particularly for χ = +1.

This combined search provides the most stringent constraints to date on Higgs bosons decaying into a photon and a massless dark photon. The combination of three distinct channels significantly improves the sensitivity compared to individual analyses, extending the reach to higher Higgs boson masses. The interpretation in the minimal simplified model context complements constraints from other searches, strengthening the overall picture of dark photon phenomenology. The observed limits on the branching ratio and cross-section times branching ratio exclude significant regions of parameter space, suggesting the absence of this type of decay within the tested ranges. The results highlight the importance of combining different analysis strategies to enhance the sensitivity to rare and elusive processes.

This paper presents a combined search for Higgs boson decays into a photon and a massless dark photon, setting the most stringent constraints to date. The combination of three channels improves sensitivity and extends the explored mass range. The results are also interpreted in a simplified model, providing complementary constraints to other searches. Future work could involve exploring alternative simplified models, investigating potential non-zero dark photon masses, and using even larger datasets from future LHC runs to further probe this parameter space.

The analysis relies on theoretical predictions and models for both signal and background processes, introducing inherent uncertainties. While efforts have been made to account for systematic uncertainties, it is important to note that unaccounted-for effects could potentially impact the results. The simplified model used for interpretation makes specific assumptions about the messenger sector; other models could yield different constraints.