Science, Faculty of
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Physics and Astronomy, Department of
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The European Physical Journal C. 2024 Jul 26;84(7):742
The Author(s)
ATLAS Collaboration
Presented is the search for anomalous Higgs boson decays into two axion-like particles (ALPs) using the full Run 2 data set of 140 fb−1 of proton-proton collisions at a centre-of-mass energy of 13 TeV recorded by the ATLAS experiment. The ALPs are assumed to decay into two photons, providing sensitivity to recently proposed models that could explain the (g − 2)μ discrepancy. This analysis covers an ALP mass range from 100 to 62 GeV and ALP-photon couplings in the range 10−7 TeV−1 < Caγ γ / < 1 TeV−1, and therefore includes signatures with significantly displaced vertices and highly collinear photons. No significant excess of events above the Standard Model background is observed. Upper limits at 95% confidence level are placed on the branching ratio of the Higgs boson to two ALPs in the fourphoton final state, and are in the range of 10−5 to 3 × 10−2, depending on the hypothesized ALP mass and ALP-photon coupling strength.
Eur. Phys. J. C (2024) 84:742 https://doi.org/10.1140/epjc/s10052-024-12979-0Regular Article - Experimental PhysicsSearch for short- and long-lived axion-like particles inH → aa → 4γ decays with the ATLAS experiment at the LHCATLAS CollaborationCERN, 1211 Geneva 23, SwitzerlandReceived: 7 December 2023 / Accepted: 2 June 2024© CERN for the benefit of the ATLAS Collaboration 2024Abstract Presented is the search for anomalous Higgsboson decays into two axion-like particles (ALPs) using thefull Run 2 data set of 140 fb−1 of proton-proton collisions ata centre-of-mass energy of 13 TeV recorded by the ATLASexperiment. The ALPs are assumed to decay into two pho-tons, providing sensitivity to recently proposed models thatcould explain the (g − 2)μ discrepancy. This analysis coversan ALP mass range from 100 to 62 GeV and ALP-photoncouplings in the range 10−7 TeV−1 < Caγ γ / < 1 TeV−1,and therefore includes signatures with significantly displacedvertices and highly collinear photons. No significant excessof events above the Standard Model background is observed.Upper limits at 95% confidence level are placed on thebranching ratio of the Higgs boson to two ALPs in the four-photon final state, and are in the range of 10−5 to 3 × 10−2,depending on the hypothesized ALP mass and ALP-photoncoupling strength.Contents1 Introduction . . . . . . . . . . . . . . . . . . . . . .2 The ATLAS detector . . . . . . . . . . . . . . . . . .3 Data set and simulated events . . . . . . . . . . . . .4 Object reconstruction and event selection . . . . . . .4.1 Object reconstruction . . . . . . . . . . . . . . .4.2 Event selection and categorization . . . . . . . .5 Background estimation . . . . . . . . . . . . . . . . .5.1 Two-photon final states in the search for long-lived axion-like particles . . . . . . . . . . . . .5.2 Three- and four-photon final states in the searchfor long-lived axion-like particles . . . . . . . . .5.3 Four-photon final states in the search for promptlydecaying axion-like particles . . . . . . . . . . .5.4 Background estimate summary . . . . . . . . . .6 Systematic uncertainties . . . . . . . . . . . . . . . .6.1 General experimental uncertainties . . . . . . . .6.1.1 Uncertainties due to displaced ALP decays e-mail: atlas.publications@cern.ch6.2 Uncertainties on the background estimation . . .6.3 Impact of theory uncertainties . . . . . . . . . . .7 Results . . . . . . . . . . . . . . . . . . . . . . . . .8 Conclusion . . . . . . . . . . . . . . . . . . . . . . .References . . . . . . . . . . . . . . . . . . . . . . . . .1 IntroductionAxion-like particles (ALPs), or more generally light (pseudo)scalars, are represented as gauge-singlets beyond the Stan-dard Model (SM) that can couple to the 125 GeV Higgsboson [1,2], and appear in many well-motivated extensions ofthe SM, e.g., the next-to-minimal supersymmetric standardmodel [3,4]. These include models that address the baryonasymmetry of the universe [5,6], offer a solution to the nat-uralness problem [7,8], or provide insights into the natureof dark matter [9–14]. ALPs and light bosons produced inHiggs boson decays could also be mediators to dark sectorsthat do not otherwise couple to the SM [15].A combination of ATLAS measurements of Higgs bosonproperties using 139 fb−1 of data constrains the branchingratios into invisible and undetected states to be B(H →invisible) < 10.7% and B(H → undetected) < 12% at95% confidence level (CL) [16,17]. Combined measure-ments of Higgs boson couplings performed by the CMSCollaboration using 138 fb−1 of data set upper limits ofB(H → invisible) < 16% andB(H → undetected) < 16%at 95% CL [18]. These results allow potentially large branch-ing fractions into beyond-the-standard-model (BSM) parti-cles, B(H → BSM), such as ALPs.In Ref. [19] it has been argued that if the ALP, denoted asa in the following, couples to at least some SM particles withcouplings of order (0.01–1)TeV−1, its mass must be above1 MeV. Taking into account the possibility of a long-livedALP, large regions of so far unconstrained parameter spacecan be explored by searches for exotic, on-shell Higgs bosondecays into two ALPs. In particular, this includes the param-eter space in which ALPs can explain the observed discrep-0123456789().: V,-vol 123 742 Page 2 of 31 Eur. Phys. J. C (2024) 84:742 ancy between the measurement [20–22] and the theoreticalprediction [23,24] of the anomalous magnetic moment ofthe muon [19]. It was suggested that subsequent ALP decaysinto photons provide unprecedented sensitivity to the ALP-photon couplings in the mass region above a few MeV, evenif the relevant ALP-photon couplings are loop suppressedand the a → γ γ branching ratios are significantly less than100% [19].This paper presents a search for decays of the 125 GeVHiggs boson into two ALPs in proton–proton (pp) collisionsat the LHC [25]. The search is sensitive to events whereeach a-boson decays into two photons. For the first time,a dedicated search for long-lived a → γ γ decays with asignificantly displaced vertex within the tracking system ofthe ATLAS detector is performed, allowing a large regionof the parameter space of the ALP-photon coupling Caγ γ tobe probed. Previous searches for H → aa → 4γ signatureswere performed by the ATLAS [26] and CMS Collaborations[27,28], but assumed promptly decaying ALPs and hencewere valid only up to decay lengths of a few centimeters.The decay length scales with τa ∝ 2/(m3a |Caγ γ |2), wherema is the ALP mass and , the new physics scale, is assumedto be in the TeV range [19]. The limits obtained here for ALPmasses ma > 15 GeV are about one order of magnitude morestringent than previous ATLAS analyses using 8 TeV data,and reach sensitivies similar to or slightly better than previousanalyses from CMS using 132 fb−1 of√s = 13 TeV data.The paper is structured as follows. A brief discussion ofthe ATLAS detector and an overview of the Monte Carlo(MC) samples and data sets used are given in Sects. 2 and 3.Object reconstruction and the event selection are described inSect. 4, where special focus is given to the reconstruction ofcollimated photon signatures and to the categorization of thefinal state topologies that can be reconstructed in the detector.The background estimates are discussed in Sect. 5, followedby a description of the dominant systematic uncertainties inSect. 6, in particular those that involve the reconstruction ofphotons with a displaced production vertex. The statisticalinterpretation and the final results are summarized in Sect. 7.The paper closes with a brief conclusion in Sect. 8.2 The ATLAS detectorThe ATLAS detector [29] at the LHC covers nearly the entiresolid angle around the collision point.1 It consists of aninner tracking detector surrounded by a thin superconduct-1 ATLAS uses a right-handed coordinate system with its origin at thenominal interaction point (IP) in the centre of the detector and the z-axis along the beam pipe. The x-axis points from the IP to the centre ofthe LHC ring, and the y-axis points upwards. Cylindrical coordinates(r, φ) are used in the transverse plane, φ being the azimuthal anglearound the z-axis. The pseudorapidity is defined in terms of the polaring solenoid, electromagnetic and hadron calorimeters, and amuon spectrometer incorporating three large superconduct-ing air-core toroidal magnets.The inner-detector system (ID) is immersed in a 2 T axialmagnetic field and provides charged-particle tracking in therange of |η| < 2.5. The high-granularity silicon pixel detec-tor covers the vertex region and typically provides four mea-surements (hits) per track, the first hit normally being in theinsertable B-layer (IBL) installed before Run 2 [30,31]. Itis followed by the silicon microstrip tracker (SCT), whichusually provides eight measurements per track. These sili-con detectors are complemented by the transition radiationtracker (TRT), which enables radially extended track recon-struction up to |η| = 2.0. The TRT also provides electronidentification information based on the fraction of hits (typ-ically 30 in total) above a higher energy-deposit thresholdcorresponding to transition radiation.The calorimeter system covers the pseudorapidity rangeof |η| < 4.9. Within the region |η| < 3.2, electromag-netic calorimetry is provided by barrel and endcap high-granularity lead/liquid-argon (LAr) calorimeters, with anadditional thin LAr presampler covering |η| < 1.8 to cor-rect for energy loss in material upstream of the calorime-ters. Hadron calorimetry is provided by the steel/scintillator-tile calorimeter, segmented into three barrel structures within|η| < 1.7, and two endcap copper/LAr hadron calorimetersup to |η| < 3.2. The solid angle coverage is completed withforward copper/LAr and tungsten/LAr calorimeter modulesoptimised for electromagnetic and hadronic energy measure-ments, respectively.The muon spectrometer (MS) comprises separate trig-ger and high-precision tracking chambers that measure thedeflection of muons in the magnetic field generated by thesuperconducting air-core toroidal magnets. The field integralof the toroids ranges between 2.0 and 6.0 Tm across most ofthe detector. Three layers of precision chambers, each con-sisting of layers of monitored drift tubes, cover the region|η| < 2.7, complemented by cathode-strip chambers in theforward region. The muon trigger system covers the rangeof |η| < 2.4 with resistive-plate chambers in the barrel, andthin-gap chambers in the endcap regions.Events of interest for this analysis are selected usingdedicated di-photon triggers. The first-level of the triggersystem is implemented in custom hardware, followed by ahigh-level trigger [32] where further selections are made byalgorithms implemented in software. The first-level triggeraccepts events from the 40 MHz bunch crossings at a ratebelow 100 kHz, which the high-level trigger further reducesin order to record events to disk at about 1 kHz.angle θ as η = − ln tan(θ/2). Angular distance is measured in units of R ≡ √( η)2 + ( φ)2.123Eur. Phys. J. C (2024) 84:742 Page 3 of 31 742 An extensive software suite [33] is used in MC simulation,in the reconstruction and analysis of real and simulated data,in detector operations, and in the trigger and data acquisitionsystems of the experiment.3 Data set and simulated eventsThis analysis uses pp collision data collected by the ATLASexperiment from 2015 to 2018 with a centre-of-mass energyof√s = 13 TeV. After data quality requirements [34]the full data set corresponds to an integrated luminosity of140.1 ± 1.2 fb−1 [35]. The lowest-threshold unprescaled di-photon triggers are used to select events for further analysis,as discussed in Sect. 4.2.The main background contributions stem from multijetprocesses, where jets might be misidentified as photons, aswell as Standard Model multiphoton processes [36]. How-ever, MC simulation does not capture the full backgroundshape observed in data and therefore a fully data-drivenbackground estimation has been employed. Simulated eventsare used to validate the data-driven background estimationtechniques described in Sects. 5.1–5.2, and to model Higgsboson decays into photons for both signal and backgroundprocesses. Background events from continuum 3γ , 4γ andγ γ production, neglecting any interference effects with theH → γ γ decay, are generated using Sherpa 2.2.8 and Sherpa2.2.4 [37–39], respectively, with the AZNLO set of tunedparameters [40] and the NNPDF30 [41] set of parton distribu-tion functions (PDF). Production of the Higgs boson throughgluon–gluon fusion (ggF) and vector-boson fusion (VBF)processes is modelled at next-to-leading order (NLO) usingPowheg- Box v2 [42–44] interfaced with Pythia 8.186 [45]using the AZNLO tune and NNPDF30 PDF. The change inselection efficiency between ggF and VBF and other Higgsboson production mechanisms is at the percent level, so itsimpact is negligible. Thus, all signal (H → aa → 4γ ) sam-ples use the ggF Higgs boson production mechanism andhave their cross-sections scaled to the total Higgs boson pro-duction cross-section predicted by a next-to-next-to-next-to-leading-order QCD calculation with NLO electroweak cor-rections applied [46–49].Signal samples are produced for ALP masses in the rangeof 0.1 GeV–62 GeV, with a spacing of 0.1 GeV in the rangeof 0.1 GeV–0.5 GeV, a spacing of 0.5 GeV in the range of0.5 GeV–5 GeV and a spacing of 1 GeV in the range of5 GeV–62 GeV, assuming  = 1 TeV. The full set of masspoints is simulated for four different values of the couplingCaγ γ : 1, 0.01, 5×10−4 and 10−5. Samples of simulated sig-nal events are generated using Powheg- Box v2 at NLO forthe Higgs production and Pythia 8.212 to simulate the decayinto ALPs and the subsequent decay into photons employinga generic 2HDM model [50]. For hadronisation and partonshowering, Pythia 8.212 is used as well, with the AZNLOtune and the CTEQ6L1 PDF set [51].Different pile-up conditions due to additional pp interac-tions in the same and neighbouring bunch crossings are sim-ulated by overlaying the hard-scattering event with inelasticpp events generated by pythia8.186 using the NNPDF2.3loPDF set [52] and the A3 tune [53]. Differences between thesimulated and observed distributions of the number of inter-actions per bunch crossing are corrected by reweighting thesimulated events to match the data distribution.All MC samples use a full simulation of the ATLASdetector [54] based on geant [55] to reproduce the detec-tor response. Corrections are applied to the simulated eventsto match the photon selection efficiencies, energy scale andresolution to those determined in data.4 Object reconstruction and event selectionThe experimental signature of H → aa → 4γ dependssignificantly on the ALP mass and on its coupling to pho-tons, Caγ γ . ALP masses below 3.5 GeV dominantly yieldcollimated photon signatures, which are reconstructed asone energy cluster in the electromagnetic calorimeter. Thephotons originating from the decays of axion-like particleswith higher masses can typically be resolved by the ATLAScalorimeter system and the ATLAS identification algorithms.The Caγ γ coupling determines the lifetime and hence thedistance the ALPs travel after being produced, so the searchfor H → aa → 4γ is divided into two sub-searches: asearch for promptly decaying ALPs corresponding to cou-plings Caγ γ ≥ 0.1 and a search for long-lived ALPs thatis optimised for smaller couplings. Coupling values smallerthan Caγ γ = 10−7 cannot be probed within this analysissince they yield ALP lifetimes that imply a decay outside ofthe detector volume for all ALP masses considered.4.1 Object reconstructionPhotons are reconstructed from topologically connected clus-ters [56] of energy deposits in the electromagnetic calorime-ter in the region |η| < 2.5 where a distinction to electrons isprovided by the tracking system. Only photon candidateswithin |η| < 2.37 are used in this analysis to allow theusage of a track based isolation variable. The transition regionbetween the barrel and endcap electromagnetic calorimeters,1.37 < |η| < 1.52, is excluded due to poor resolution of thecalorimeter in this area. The analysis does not distinguishbetween photons converting into e+e− pairs and unconvertedphotons.Photon candidates are defined by the lateral shower pro-file of the energy deposits in the first and second electromag-netic calorimeter layers and by the fractional energy leakage123 742 Page 4 of 31 Eur. Phys. J. C (2024) 84:742 into the hadron calorimeter. The analysis uses different pho-ton identification criteria for different regions of the signalparameter space. Standard ‘Tight’ and ‘Loose’ photon iden-tification criteria [57,58], which are tuned for converted andunconverted photons separately, are applied in final stateswhere individual photons can be separately reconstructed.Axion-like particles with small masses, e.g., ma < 3.5 GeV,decay predominantly into a pair of highly collimated pho-tons, which are reconstructed as single photon object. Forthese merged photon objects, the standard photon identifica-tion is not efficient. Hence, a neural network (NN)-based clas-sification approach is developed. A first classifier is trainedto separate real photon signatures, single or collimated, from‘fake photons’ that come from multijet background. A secondclassifier is then trained to separate single-photon signaturesfrom collimated signatures. Both classifiers use eight shower-shape variables relevant for photon identification [58]. Thetraining data sets are based on single- and collimated-photonsignatures from simulation and fake-photon candidates fromdata; the fake-photon candidates are selected by invertingthe requirement on several isolation observables. If a pho-ton passes a minimum threshold of the output neurons ofboth classifiers, it is labelled as a ‘merged’ photon. The per-formance of the classifier is shown in Fig. 1. Due to coarsepointing resolution of the calorimeter it is not possible toreconstruct displaced secondary vertices from ALP decays.The photon energy is reconstructed using the nominalATLAS reconstruction and calibration procedures [59]. Theenergy of photon candidates that are identified as collimatedphoton signatures is corrected by adding the measured clus-ter energies in the calorimeter within a cone of R = 0.2around the photon, if not yet associated with the photon.To further improve the rejection of misidentified photons,a track-based variable pisoT is defined as the scalar sum of thetransverse momenta of all tracks with transverse momentum(pT) above 1 GeV that originate from the primary vertex andare within a cone of R = 0.2 around the photon candi-date with transverse energy EγT . Isolated photons must havepisoT /EγT < 0.05. A calorimeter-based isolation requirementis not used due to its large signal rejection for collimatedphoton signatures.4.2 Event selection and categorizationEvents are selected using one of two di-photon triggers [60],each of which requires two reconstructed photon candidates.The first trigger requires a minimum transverse energy of35 GeV for the leading photon and 25 GeV for the sub-leading photon where both photons must satisfy the onlineLoose or Medium identification criteria [60], depending onthe data-taking period. The alternative trigger requires thateach photon satisfy the Tight identification criteria and havea transverse energy of at least 22 GeV. The terms ‘leading’and ‘subleading’ refer to the photon candidate with the high-est and second-highest transverse energy, respectively. Pho-ton candidates in the event must have a minimum transverseenergy corresponding to the trigger threshold for the leadingand subleading photons and at least 15 GeV for any addi-tional photon. For H → aa → 4γ events with Caγ γ = 1and at least two selected photon candidates, the average trig-ger efficiency is larger than 60% for all ALP masses. This stillholds for Caγ γ = 10−5 and ma > 50 GeV, while for smallermasses the trigger efficiency decreases down to 30 %. Thetrigger efficiency drops for decreasing ALP masses as colli-mated photon signatures often fail the isolation requirementat trigger level, which is based on calorimeter informationrather than tracks.Signal events are fully reconstructed if all four photonsare detected. However, some of the photons might be out ofdetector acceptance and some might not be reconstructed.The lifetime of the ALPs depends on their mass and cou-pling to photons, as shown in Sect. 1. Some examples arelisted here: assuming a coupling of Caγ γ = 10−4 a mass ofma = 1 GeV (ma = 10 GeV) yields a lifetime of cτ = 25 m(cτ = 25 mm). For Caγ γ = 10−5 the lifetime increasesby a factor of hundred. Missing photons as well as pairs ofcollimated photons being reconstructed as one photon resultin fewer reconstructed photons. At least two reconstructedphoton candidates are required for the analysis. Further clas-sification is based on the number and types of reconstructedphotons.Each event is classified into one of the five categoriesaccording to their experimental signature, in the followingorder: (1) events with four reconstructed photons, where allphotons satisfy the Loose identification and at least one sat-isfies the Tight identification, fall into the four-single (4S)category. (2) events with three reconstructed photons, whereall photons satisfy the Tight identification, fall into the three-single (3S) category. (3) events with two merged photon can-didates fall into the two-merged (2M) category. Additionalloose photon candidates are likely to originate from back-ground processes and are ignored, with negligible impact onthe rate of falsely identified signal events. (4) events with twophoton candidates, where one satisfies the merged classifica-tion and the other satisfies the Loose identification, fall intothe one-merged-one-single (1M1S) category. This categoryaccepts events where the merged classification of two pho-tons is not efficient. (5) events with exactly two photons thatsatisfy the Tight identification but without any further photoncandidates that satisfy the Loose identification fall into thetwo-single category (2S), which is dominated by events fromthe H → γ γ process.Only the most sensitive categories are used for the ALPsearch. For long-lived ALPs with masses ma ≥ 3.5 GeVthe 3S and 4S categories provide the most sensitivity. Long-lived ALPs with ma < 3.5 GeV yield collimated photon123Eur. Phys. J. C (2024) 84:742 Page 5 of 31 742 Fig. 1 Output of the neural network classifier to distinguish a real from fake photons, and b single from merged photonssignatures where the 2M, and 1M1S categories provide thelargest sensitivity.The 3S and 4S categories allow for the reconstruction ofthe ALP mass, ma , since at least one photon pair stems fromthe decay of an ALP for the signal process. Separate neuralnetworks were trained for the three- and four-photon cat-egories to select the correct photon pairing(s). The inputsto the networks are the invariant masses of all photon paircombinations and differences in their transverse energies anddirections. The training sample consists of both correct andwrong photon combinations. The combinations are based onMC signal samples for all ALP masses and couplings. Inthe 3S category, the invariant mass of the photon pair that ispredicted to stem from the same mother particle is definedas the reconstructed ALP mass mrecoa , while the average ofboth resulting invariant masses is defined as mrecoa in the 4Scategory.The signal region selection uses the invariant mass of allphoton candidates, denoted by mrecoinv , which is expected topeak around the Higgs boson mass for signal processes. Thesignal regions for all categories and searches are defined tocontain at least 90% of the reconstructed signal contributionin simulated data. For the two-photon categories (2M, 1M1Sand 2S), the signal region is defined by the invariant massrequirement 115 GeV < mrecoinv < 130 GeV around the Higgsboson mass.The 3S and 4S categories also require the reconstructedALP mass mrecoa to fall within a window around the gener-ated ALP mass, whose size varies depending on the masspoint being tested. In general, the requirements on mrecoinv arelooser in the 3S category since one photon typically escapesdetection, leading to a wider mrecoinv spectrum. The mrecoa dis-tribution also enables the definition of a control region in databy inverting the mass requirement on mrecoa .In the search for promptly decaying ALPs only the 4S cat-egory is used when estimating the limits on the signal process,as it has by far the largest sensitivity. In this case the cate-gory is defined by tightening the selection cuts so that at leastthree out of the four photons satisfy the Tight identificationrequirements and is labelled 4Sp. Promptly decaying ALPsare only considered for ma > 5 GeV, where a significantincrease in sensitivity over the search for long-lived ALPs isobserved. Table 1 summarizes the signal region definitionsfor all ALP mass hypotheses ma .5 Background estimationThe main background contributions stem from multijet pro-cesses, where jets might be misidentified as photons, aswell as Standard Model multiphoton processes. However,as the simulation does not capture the full background shapeobserved in data we rely on a fully data driven backgroundestimate.The signal is expected to peak in mrecoinv , the invariant massof the selected photons, near the Higgs boson mass, m H =125 GeV, in all categories and searches. The mrecoinv sidebandsare used for the background estimate in the signal region andfor the estimation of spurious signal effects.5.1 Two-photon final states in the search for long-livedaxion-like particlesThe distribution of mrecoinv in all two-photon categories (2M,1M1S, 2S) is fitted over a mass range from 100 to 150 GeV,region excluding the signal region. A suitable fitting functionshould describe the data in the sidebands, provide an unbi-ased estimate of the background in the signal region, and123 742 Page 6 of 31 Eur. Phys. J. C (2024) 84:742 Table 1 Definition of the signal region for different event categories in the prompt and long-lived searchModel parameters Signal region definitionLong-lived ALP search: Caγ γ < 0.12M, 1M1S and 2S categories0.1 GeV ≤ ma < 3.5 GeV 115 GeV < mrecoinv < 130 GeV3S category 4S category3.5 GeV ≤ ma < 10 GeV 105 GeV < mrecoinv < 130 GeV 120 GeV < mrecoinv < 130 GeV0 GeV < mrecoa < 10 GeV 0 GeV < mrecoa < 12 GeV10 GeV ≤ ma < 25 GeV 100 GeV < mrecoinv < 125 GeV 120 GeV < mrecoinv < 130 GeV6 GeV < mrecoa < 26 GeV 8 GeV < mrecoa < 28 GeV25 GeV ≤ ma < 40 GeV 100 GeV < mrecoinv < 125 GeV 120 GeV < mrecoinv < 130 GeV20 GeV < mrecoa < 40 GeV 23 GeV < mrecoa < 43 GeV40 GeV ≤ ma ≤ 62 GeV 90 GeV < mrecoinv < 115 GeV 120 GeV < mrecoinv < 130 GeV30 GeV < mrecoa < 65 GeV 38 GeV < mrecoa < 65 GeVPrompt ALP search: 0.1 < Caγ γ < 14Sp category5 GeV ≤ ma < 25 GeV 120 GeV < mrecoinv < 130 GeV|ma − mrecoa | < 1 GeV25 GeV ≤ ma < 40 GeV 120 GeV < mrecoinv < 130 GeV|ma − mrecoa | < 2 GeV40 GeV ≤ ma < 50 GeV 120 GeV < mrecoinv < 130 GeV|ma − mrecoa | < 3 GeV50 GeV ≤ ma < 55 GeV 120 GeV < mrecoinv < 130 GeV|ma − mrecoa | < 5 GeV55 GeV ≤ ma ≤ 62 GeV 120 GeV < mrecoinv < 130 GeV|ma − mrecoa | < 8 GeVproduce small uncertainties on the yields of spurious sig-nals. This is ensured by defining validation regions that usesimilar requirements to those of the signal region but rejectsignal events. Simulated samples of two-photon continuumprocesses and a data-driven validation region are studied. Thelatter is defined using the nominal signal selection and clas-sification, but inverting the isolation cut on the photon candi-dates, thus yielding a multijet-enhanced data sample.2 Thesevalidation regions are chosen to cover any scenario betweena background composed purely of di-photon events and abackground consisting of mis-identified multijet events.A Landau function gives unbiased background estimatesin the signal region of both validation samples and pro-vides χ2 per number of degrees of freedom around unity(χ2/ndf ≈ 1) in all sideband regions for the 2S and 1M1Scategories. It is expected that the background shape in the 2Mcategory differs from the 2S and 1M1S categories, due to thedifferent background composition after the requirements onthe NN-based classifiers. A second-order polynomial pro-2 It is ensured that there is no overlap with the training data of theNN-based photon identification classifiers.vides a good description of all validation regions of the 2Mcategory. Variations of the background estimates using dif-ferent fitting functions and different fitting ranges are used todefine systematic uncertainties and are discussed in Sect. 6.The H → γ γ process contributes not in the sideband butin the signal region as irreducible background, significantlyin the 2S category and to a negligible extent in the 2M and1M1S categories. Its contribution and shape are estimated byMC predictions.Figure 2 shows the mrecoinv spectra including the sidebandfit for the signal selection for the 2M and 1M1S categories,respectively. The expected signal shape for an ALP withma = 0.5 GeV and Caγ γ = 0.01 is also shown for illus-tration.5.2 Three- and four-photon final states in the search forlong-lived axion-like particlesThe background estimation in the long-lived ALPs searchesalso employs a sideband fit using the mrecoinv spectrum in the3S and 4S categories.123Eur. Phys. J. C (2024) 84:742 Page 7 of 31 742 Fig. 2 mrecoinv distribution for the nominal signal selection for the a1M1S and b 2M category. The nominal sideband fitting function isshown as the blue dashed line. The background, estimated from a fit inthe side-band regions, and its systematic uncertainty is shown as a bluehistogram for both cases. The green dotted line shows the alternative fit-ting function used to estimate the spurious signal uncertainty (discussedin Sect. 6). The expected signal shape for ma = 0.5 GeV, Cayy = 0.01is also shown with an arbitrary normalization. The signal region selec-tion on mrecoinv is indicated using vertical dashed lines. The contributionfrom H → γ γ is negligible and not visible in the figures. The lowerpanels show the data divided by the estimated continuum background,where the shaded area indicates the uncertainty on the background esti-mationPolynomials of third and second order serve as the nominalbackground fitting functions for the 3S and 4S categories,respectively, where the fits are carried out in the range of80–150 GeV and 105–145 GeV, excluding the signal region.First, the suitability of the sideband functions for backgroundestimation in both categories is tested on three- and four-photon continuum MC samples. Next, the sideband functionsand corresponding background estimates are validated usingan orthogonal set of data events in which the requirement onthe reconstructed ALP mass is inverted.This inverted sample can be used as a validation region,since the shape of background events should not change witha different choice of ALP mass apart from minor kinematicchanges in the mrecoinv distribution. The multi-photon MC sam-ples are used to correct for this kinematic effect.The chosen fitting functions yield a χ2/ndf close to unityin all validation regions and the estimated background usingthese validation regions is consistent with the observed num-bers of background events from the signal region sidebands.Systematic uncertainties due to the choice of the backgroundfunction and the fitting range are discussed in Sect. 6. Figure3 depicts the mrecoinv spectrum for various ALP mass searches,and shows the sideband fitting functions, the estimated back-ground in the signal region, and the expected signal shapefor two Caγ γ coupling parameters.5.3 Four-photon final states in the search for promptlydecaying axion-like particlesThe number of selected events in the 4Sp category of thesearch for promptly decaying ALPs, also defined in the mrecoinvvs. mrecoa plane, is significantly lower than that in the analysisoptimised for long-lived ALPs due to the stricter rejection offake-photon signatures using more stringent selection crite-ria such as Tight photon identification. To further suppressbackground contributions in the signal region, a tight selec-tion around the ma model parameter, as discussed in Sect. 4,is imposed. The size of the signal regions for each ALP massare shown in Table 1. The background in the signal regionof the search for promptly decaying ALPs is estimated bycounting the events around the signal region in the mrecoinv -mrecoa plane, extending the signal region by ± 5 GeV in themrecoinv dimension and by 1.5 times the signal region widthin the mrecoa dimension. Due to the low statistics, the totalnumber of background events in the shaded sideband areais scaled by the ratio of the areas of the signal region to thesideband region to estimate the number of background eventsin the signal region, as illustrated in Fig 4. This is equivalentto assuming a flat background distribution in the plane.123 742 Page 8 of 31 Eur. Phys. J. C (2024) 84:742 Fig. 3 mrecoinv distribution for the nominal signal selection for the 4S cat-egory. The nominal sideband fitting function is shown as the blue dashedline. The background, estimated from a fit in the side-band regions, andits systematic variation (obtained from a fit with reduced range) is shownas the blue histogram. The green dotted line shows the alternative fit-ting function which is used to estimate the spurious signal uncertainty(discussed in Sect. 6). The four subfigures show different ALP massranges: a 3.5 GeV < ma < 10 GeV, b 10 GeV < ma < 25 GeV,c 25 GeV < ma < 40 GeV, d 40 GeV < ma < 62 GeV. The sig-nal region selection on mrecoa is applied while the signal region selec-tion on mrecoinv is indicated as dashed lines. The expected signal shapesfor ma = 5 GeV, Cayy = 0.01; ma = 5 GeV, Cayy = 5 · 10−4;ma = 15 GeV, Cayy = 0.01; ma = 15 GeV, Cayy = 5 · 10−4;ma = 35 GeV, Cayy = 0.01; ma = 35 GeV, Cayy = 10−5; ma =50 GeV, Cayy = 0.01; ma = 50 GeV, Cayy = 10−5;is shown witharbitrary normalization. The lower panels show the data divided by theestimated continuum background, where the shaded area indicates theuncertainty on the background estimationAs an alternative background estimate, the size of the con-trol region is taken to be 2.5 times the signal region insteadof the 1.5 times used in the nominal background estimate.The difference between the nominal and the alternative back-ground estimates is used as a systematic uncertainty. Fig-ure 4 shows distributions in the mrecoinv -mrecoa plane for eventsselected in the search for promptly decaying ALPs, with thesideband regions shown for the search parameters ma = 10GeV and ma = 40 GeV. The validity of this procedure wastested using simulated multi-photon samples confirming thatthe associated statistical and systematic uncertainties coverpotential shape differences.5.4 Background estimate summaryTable 2 summarizes the data and the expected backgroundcontribution in the signal region for the different categories.The acceptance times selection efficiency of a signal event inany of the categories is largely dependent on the ALP massand coupling parameters under investigation. It ranges from123Eur. Phys. J. C (2024) 84:742 Page 9 of 31 742 Fig. 4 mrecoinv vs. mrecoa for the 4Sp categories in the search for promptlydecaying ALPs, for a simulated pp → 4γ sample and b for data. Thesignal (sideband) regions are indicated by solid lines (shaded areas)for the searches for ALPs with masses of 10 GeV and 40 GeV. Eventswithin the signal region are shown with filled markers, those outsidewith open markers9 to 23% for low ALP masses (ma < 5 GeV) and largecouplings (Caγ γ = 1) and is around 13% for large ALPmasses (ma ≈ 60 GeV) at all studied couplings. The largestfraction of events are already cut by the trigger due to therelatively high trigger thresholds. A future reduction of thetrigger thresholds could significantly improve the analysisacceptance.6 Systematic uncertaintiesThe systematic uncertainties are assessed below, and theirimpact on the results is discussed in Sect. 7. First the gen-eral experimental uncertainties are discussed, where specialattention is given to the uncertainties arising from the dis-placed decay of long lived ALPs. Then the uncertaintiesimpacting the background estimation are detailed followedby a discussion of the relevant theoretical uncertainties.The experimental systematic uncertainty ranges, depend-ing on the category and the hypothesized ALP mass andcoupling, from 6.5% to 18% for most categories, with theexception of the 4S category where the uncertainty rises to40% for masses ma < 15 GeV and small couplings Caγ γdue to low statistics and large contributions from the pho-ton identification uncertainties. The theoretical uncertaintyis around 6% for all categories.6.1 General experimental uncertaintiesThe following general experimental systematics are appliedto the signal model.The uncertainty in the combined 2015–2018 integratedluminosity is 0.83% [35], obtained using the LUCID-2 detec-tor [61] for the primary luminosity measurements, com-plemented by measurements using the inner detector andcalorimeters.To evaluate any impact on the expected signal yield due toimperfect modelling of pile-up, the average number of pile-up interactions is varied in the simulation. The correspondinguncertainty is below 1%.The trigger efficiency used to select events is evaluated insimulation and data using a bootstrap method and radiativeZ -boson decays [60]. The difference between data and sim-ulation, which ranges from 2 to 3%, is taken as a systematicuncertainty.The systematic uncertainties from the standard photonidentification and isolation efficiencies are estimated follow-ing the prescriptions in Ref. [58]. They affect the di-photonselection efficiency and are evaluated by varying the cor-rection factors for photon selection efficiencies in simula-tion by their corresponding uncertainties. The experimentaluncertainties in the photon energy scale and resolution areobtained as described in Ref. [58]. These variations produceuncertainties below 3% on the expected number of events inthe signal region in the search for promptly decaying ALPs.The uncertainties of the NN-based classifiers are estimatedby comparing their identification performance using Z → eeevents in simulation and data, where the electron shower-shape variables are used as the network input variables. Verygood agreement of the network output between data and sim-ulation is observed. The residual differences are fully propa-gated as uncertainties on the expected signal yields and pro-123 742 Page 10 of 31 Eur. Phys. J. C (2024) 84:742 Table 2 Overview of the number of observed events in the search forlong-lived ALPs (left) and selected mass points from the search forprompt ALPs (right) in comparison to the expected number of back-ground events. The uncertainty on the background estimate includesstatistical and systematic uncertainties as described in Sect. 6Long-lived ALP search Prompt ALP searchCategory Events Background estimate Category Events Background estimateCaγ γ < 0.1 0.1 < Caγ γ < 12M 9917 10,000 ± 200 4Sp (ma = 5 GeV) 2 0.35 ± 0.271M1S 113,875 113,100 ± 700 4Sp (ma = 10 GeV) 0 0.24 ± 0.182S 632,484 634,000 ± 1500 4Sp (ma = 15 GeV) 1 0.24 ± 0.283S (3.5 GeV ≤ ma < 10 GeV) 4782 4800 ± 100 4Sp (ma = 20 GeV) 0 0.24 ± 0.283S (10 GeV ≤ ma < 25 GeV) 3166 3200 ± 100 4Sp (ma = 25 GeV) 0 0.24 ± 0.283S (25 GeV ≤ ma < 40 GeV) 3843 3900 ± 150 4Sp (ma = 30 GeV) 0 0.60 ± 0.273S (40 GeV ≤ ma ≤ 62 GeV) 5389 5600 ± 90 4Sp (ma = 35 GeV) 0 1.31 ± 0.764S (3.5 GeV ≤ ma < 10 GeV) 15 14 ± 3 4Sp (ma = 40 GeV) 2 1.55 ± 0.944S (10 GeV ≤ ma < 25 GeV) 9 4 ± 2 4Sp (ma = 45 GeV) 2 3.23 ± 0.954S (25 GeV ≤ ma < 40 GeV) 21 19 ± 3 4Sp (ma = 55 GeV) 7 2.84 ± 1.514S (40 GeV ≤ ma ≤ 62 GeV) 54 54 ± 6 4Sp (ma = 62 GeV) 4 4.52 ± 1.50duce normalisation uncertainties of up to 15% in the 2M and1M1S categories, respectively.6.1.1 Uncertainties due to displaced ALP decaysThe uncertainties related to photon identification and energyreconstruction for photons produced with displaced vertices– i.e., those arising from long-lived ALP decays – are esti-mated by studying the decays of long-lived hadrons, mainlykaons with transverse momentum pT > 10 GeV, which canbe reconstructed as displaced tracks in the ATLAS trackingsystem. The daughter tracks from these decays, which origi-nate from a displaced vertex, can be matched to reconstructedclusters in the electromagnetic calorimeter. A comparison ofthe shower shapes predicted by simulations to those fromdata for signatures with displaced vertices can then be usedto estimate systematic uncertainties in photon reconstruction.The MC prediction of the shower shapes of hadronic particlesalso relies on the correct description of particle multiplici-ties and energies. To correct for any mismatch of particlecomposition in data and simulation, scale factors are derivedfrom the differences between data and MC predictions forshower-shape variables of tracks close to the primary vertex(z0 < 20 mm and d0 < 1 mm, where z0 and d0 are thelongitudinal distance from the IP and the impact parameter,respectively). These deviations are taken as a nominal biasand are used to correct tracks originating from a distancebetween 20 mm < z0 < 500 mm and 1 mm < d0 < 80 mmfrom the primary vertex (medium regime), and tracks with anorigin further than z0 > 500 mm and d0 > 80 mm from theinteraction point (far regime). These systematic uncertaintiesare used additionally for all photons stemming from a dis-placed decay. The systematic uncertainty from the modellingof the NN classifier that discriminates real photons from fakesdue to displaced photon vertices is 3%. The correspondinguncertainties from the modelling of the photon identificationand the second NN, which discriminates between mergedand resolved photons, ranges from 4 to 23%, depending onthe displacement.Long-lived hadrons are also utilized to estimate system-atic uncertainties in energy reconstruction. The observed dif-ferences in the momentum over energy ratio between theprompt, medium and far regimes are found to be negligiblecompared to the nominal energy reconstruction uncertainty.Systematic uncertainties in identifying the correct ALPpairing are mainly caused by variations in the photon energyscale corrections within their uncertainties. The final impacton the number of reconstructed events in a particular ALPmass signal region is less than 5% and hence negligible.6.2 Uncertainties on the background estimationThe continuum background processes are estimated fromdata and are subject to uncertainties related to the potentialbias arising from the selected background model, as detailedin Sect. 5. The nominal background estimate in each bin iscalculated using the nominal fitting functions, which havebeen fitted in the sideband regions. The shape uncertainty ofthe background is estimated by employing the same nominalfitting functions, but fitting them in a sideband region whosewidth is varied by 5 GeV, corresponding to a 25% to 100%change in the fit range, depending on the category, allowingfor a large variability of the background shape. The spuri-ous signal bias or background model bias is assessed as anadditional uncertainty on the total number of signal events ineach category. This bias is estimated by generating pseudo-123Eur. Phys. J. C (2024) 84:742 Page 11 of 31 742 data using a modified background model and performing thefull signal-plus-background fit (see Sect. 7) on these pseudo-data [62]. The alternative background model for the spurioussignal bias estimate is based on a second-order polynomialfor the 2M, 1M1S, 3S, and 4S categories, while the functionfsys = N0 exp(p · x) + N1 + a · x2 + b · x is used for the 2Scategory. The estimated signal-strength in these pseudo-datais considered as an additional systematic uncertainty in thefinal signal-strength estimation. The largest impact is foundin the 4S category shifting the branching ratio limit by 10−6.6.3 Impact of theory uncertaintiesTo estimate the effects of scale uncertainties arising frommissing higher-order corrections in the theoretical calcula-tions, the factorisation and renormalisation scales are variedup and down by a factor of two from their nominal values.The cross-section is then recalculated for each case, and thelargest deviation from the nominal cross-section is taken asthe uncertainty. The uncertainties on the SM Higgs ggF pro-duction cross-section due to the choice of renormalisationscheme and top-quark mass, as well as their combinationwith those from factorisation and renormalisation scale vari-ations, are based on Ref. [63]. The uncertainties in the cross-sections, which include the effects of uncertainties on thePDF and the strong coupling constant αs , and the uncertain-ties in the H → γ γ branching fractions, are taken from Ref.[46] to be 5.7%. It is found that further uncertainties on theHiggs boson signal prediction are negligible.The uncertainties on the Higgs boson production cross-section enter when calculating the limit on the branchingratio of the signal process on all Higgs boson decays. Thevalues for the uncertainties are taken from Ref. [46].7 ResultsThe statistical analysis is carried out using the PyHF frame-work [64,65]. In the long-lived ALP searches, the analysisresults are obtained by performing a simultaneous maximum-likelihood fit to the mrecoinv distribution over the range 100 GeVto 150 GeV for the two most sensitive categories for eachALP mass and coupling parameter. The 2M and 1S1M cate-gories are most sensitive for low ALP masses (ma < 5 GeV),while for larger ALP masses, the 4S category dominates overthe 3S category. Including more than two categories in the fitdoes not significantly improve the sensitivity for any modelparameter. In the prompt ALP search, only the number ofevents in the signal region of the 4Sp category is used. Theanalysis sensitivity is limited by the available data statisticsfor the 4S and 4Sp categories, while the systematic uncer-tainties dominate in other categories. The likelihood functionis defined as follows:L =∏c⎛⎝Pois(nc|Nc(θ )) ·ncbins∏i=1fc(ni , mreco,iinv , θ )⎞⎠ · G(θ ).(1)Here, ncbins is the number of bins in the mrecoinv distribu-tion, nc is the observed number of events, and Nc is theexpected number of events for each category c. For eachbin i in the mrecoinv distribution of category c, fc is the valueof the probability density function (pdf) which is estimatedfrom simulation, ni is the number of observed events inbin i , θ represents the nuisance parameters (NP) used toparametrize the effect of systematic uncertainties, and G(θ )represents constraint pdfs for the nuisance parameters. Allconstraints correspond to Gaussian pdfs. The expected num-ber of events Nc is defined as the sum of the expected yieldsfrom H → aa → 4γ production processes (NH→aa), singleHiggs-boson production (N H→γ γbkg ), the non-resonant back-ground (N nonresbkg,c ), and the spurious signal uncertainty (NSS,c).It is defined as:Nc(θ ) = μ · NH→aa(θ yieldH→aa) + N H→γ γbkg (θ yieldH→γ γ )+N nonresbkg,c (θ yieldnonres) + NSS,c. (2)Here, μ is the signal strength, andθ yield represents the NPsaffecting the event yield, as described in Sect. 6. Correlationof the nuisance parameters across different signal and back-ground components, and categories, is taken into account.The normalisation parameter for the H → γ γ productionrate, θ yieldH→γ γ , is set to 1 and corresponds to the SM predictionfor the H → γ γ cross-section. It is allowed to vary withinits theoretical and experimental uncertainties.The signal-plus-background hypothesis for the productionof a Higgs boson that decays into ALPs is tested using theprofile-likelihood-ratio test statistic derived from Eq. 1, andis parameterized with the signal-strength parameter μ. Thisparameter is defined as the ratio of the extracted signal eventsto the total number of signal events in the MC simulation.3Figure 5 shows the distribution of the number of estimatedand observed events in the signal region of the most sensitivecategory for various ALP masses and coupling parameters forthe prompt and long-lived ALP searches. Good agreement isobserved between the estimated backgrounds and the data.No significant pulls of the NP are observed after the fits. TheNP θ yieldH→γ γ is found to be consistent with 1, correspondingto the expected SM Higgs boson production cross-section onthe 2S category.Upper limits, derived using the CLs technique [66], areset on B(H → aa → 4γ ). The branching ratio is obtained3 Only H → aa → 4γ events are simulated in the signal samples, i.e.,the branching ratio for this process is unity in the simulation.123 742 Page 12 of 31 Eur. Phys. J. C (2024) 84:742 Fig. 5 The number of data and estimated background events in thesignal region of the most sensitive categories. The uncertainty in thebackground estimate is shown as shaded band. The left side shows thedifferent categories of the long-lived ALP search, while the right sidedisplays the 4Sp category of the prompt search for increasing masshypotheses. The numbers in parentheses in the x-axis labels correspondto the probed ALP mass hypothesis in GeV. The SM H → γ γ back-ground is only sizeable in the first three bins, corresponding to thetwo-photon categoriesFig. 6 Upper limits on B(H → aa → 4γ ) at 95% CL as a function of the axion mass and for different ALP-photon couplings, from a Caγ γ = 1to d Caγ γ = 10−5123Eur. Phys. J. C (2024) 84:742 Page 13 of 31 742 Fig. 7 Zoomed in version of Fig. 6 showing upper limits on B(H → aa → 4γ ) at 95% CL as a function of the signal mass hypothesis and fordifferent ALP-photon couplings. a ma < 5.0 GeV, Caγ γ = 1; b ma < 5.0 GeV, Caγ γ = 0.01; c ma > 5.0 GeV, Caγ γ = 1; d ma > 5.0 GeV,Caγ γ = 0.01by dividing the fitted signal cross-section by the total Higgs-boson production cross-section of 55.6 pb [46]. The expectedand observed limits as a function of ma from the search opti-mized for long-lived ALPs, i.e., Caγ γ < 0.1, are shownin Fig. 6 along with the performance on prompt decays forCaγ γ = 1. For low masses and low couplings, the lifetime ofthe ALP gets significantly larger and most of the ALPs decayoutside the active detector area. Therefore there are no limitsavailable for Caγ γ ≤ 5 × 10−4 and ma < 10 GeV. Limitsfor prompt decays with Caγ γ = 1 are also shown. A rela-tively uniform sensitivity is achieved for larger ALP masses,above 10 GeV for Caγ γ ≥ 5 × 10−4 and above 25 GeV forCaγ γ = 10−5. The sensitivity for low ALP masses decreaseswith smaller coupling values, as more ALP decays happenoutside the sensitive detector volume. The largest differencesbetween expected and observed limits are found in long-lived ALP searches for masses between 10 and 25 GeV at1.5 σ . It should be noted that the background estimation isthe same for all couplings in this mass region. Hence cor-related behaviour is expected for all relevant couplings. Thelimits for the couplings Caγ γ = 1 and Caγ γ = 0.01 as afunction of ma are shown in Fig. 7, separated for low ALPmasses (ma < 5 GeV) and higher ALP masses. The upperlimits at 95% CL on B(H → aa → 4γ ) range from 10−4to 3 × 10−2 for low ALP masses and from 2 × 10−5 to2 × 10−4 for higher ALP masses. The observed limits arecompatible with the expected limits. The loss in sensitivityaround 3 GeV is due to the transition between the mergedand resolved photon categories, where the former have sig-nificantly larger background contributions.The limits on B(H → aa → 4γ ) derived from the 4Spcategory assuming promptly decaying ALPs are shown inFig. 8. The derived limit is mostly flat at B < 2 × 10−5 inthe mass range 10 GeV < ma < 62 GeV. For the long-livedsearches it is necessary to loosen the selection criteria to allowfor displaced ALP decays. Therefore the background contri-butions are significantly larger and consequently the searchesare less sensitive than the prompt searches. The observed lim-its are consistent with the expected limits.The limits on ALP masses with ma > 15 GeV are aboutone order of magnitude more stringent than previous ATLASanalyses [26] using 8 TeV data, and reach similar to slightly123 742 Page 14 of 31 Eur. Phys. J. C (2024) 84:742 Fig. 8 Upper limits onB(H → aa → 4γ ) at 95% CL as a function ofthe signal mass hypothesis and for the assumption of promptly decayingALPsFig. 9 Limits on the ALP mass and coupling to photons at 95% CL,assuming B(a → γ γ ) = 1,  = 1 TeV with |CeffaH | = 1 (solid line) and|CeffaH | = 0.1 (dashed line) as predicted in Ref. [19]. The shaded blue arearepresents the excluded region. The nearly horizontal orange shadedarea indicates the region favoured by an ALP explanation for the (g−2)μdiscrepancy [19]. Also shown are exclusion limits from the respectiveATLAS [67] and CMS [68] Light-by-Light (LbyL) scattering analysis,and beam dump experiments, supernova SN1987a and cosmologicalobservations adapted from Ref. [69]better sensitivity than previous analyses from CMS [28]using 132 fb−1 of√s = 13 TeV data. These are the firstlimits on ALPs with masses below 10 GeV from the ATLASexperiment, and are up to 40% more stringent than previousresults from CMS [27] using 136 fb−1 of √s = 13 TeV data.The limits on long-lived ALPs in anomalous Higgs bosondecays are the first obtained by any experiment.The limit on the branching ratio can be converted intoa limit on the coupling of axion-like particles to photons,Caγ γ . The branching ratio, which depends on Caγ γ , can becalculated using the method described in Ref. [19]:Btheo = Haa f 2aa(Caγ γ )B(a → γ γ )H + Haa , (3)where it is assumed that all ALPs decay into photons andhence B(a → γ γ ) = 1. In the following ma and m H referto the masses of the ALP and Higgs boson, respectively, vis the vacuum expectation value, and the effective couplingof the ALP to the Higgs boson is assumed to be Ceffa H/2 =1 TeV−2. H is the total decay width of the Higgs boson.The Higgs boson to ALP decay width Haa is calculated asHaa = v2m3H32π∣∣Ceffa H∣∣24(1 − 2m2am2H)2 √1 − 4m2am2H. (4)Using the Higgs mass of m H = 125 GeV and assumingma = 10 GeV and Ceffa H/2 = 1 TeV−2 yields a branchingratio of the H → aa process of 30%. The factor f 2aa(Caγ γ )represents the fraction of ALPs detected inside the detectorvolume. It depends on the ALP decay length, and hence onCaγ γ , since the decay width is given byaγ γ = 4πα2m3a2|Caγ γ |2. (5)faa is determined from the signal simulation and interpolatedbetween the simulated Caγ γ values. The coupling is adjusteduntil the expected branching ratio matches the observed limiton the branching ratio, yielding the corresponding limit onCaγ γ .The resulting limits are shown in the two-dimensionalexclusion plot of Caγ γ vs. ma presented in Fig. 9. This searchsignificantly reduces the allowed parameter space for ALP-based models that could explain the (g − 2)μ discrepancy inthe H → aa → 4γ decay mode, as suggested in Ref. [19].8 ConclusionThis paper reports a search for a light pseudoscalar particle(a) produced in the decay H → aa, where H is the 125 GeVHiggs boson. The a boson, which can have a short or longlifetime, decays into two photons, resulting in a final statewith four photons with an invariant mass near 125 GeV. Theanalysis uses 140 fb−1 of pp collision data at a centre-of-mass energy of 13 TeV collected by the ATLAS detectorbetween 2015 and 2018. The search aims to identify a nar-row a → γ γ resonance with a mass in the range of 100 MeVto 62 GeV, where the resonance decay occurs within a dis-tance of 1970 mm from the collision vertex. Dedicated searchstrategies for long-lived a → γ γ decays are developed forthe first time. To enable the search for low resonance masses,neural network classifiers are trained to distinguish betweensingle and collimated photon signatures.No significant excess over the Standard Model back-grounds is observed in the data. The largest deviation from theexpected limit, 1.5σ , is observed in the range of 10 GeV <ma < 25 GeV. Upper limits at 95% CL are set for B(H →123Eur. Phys. J. C (2024) 84:742 Page 15 of 31 742 aa → 4γ ), which range from 2 × 10−5 to 3 × 10−2 depend-ing on ma for the prompt axion-like particle search. Forthe search for long-lived ALPs with significant displaceddecay vertices, upper limits at 95% CL are set, ranging from2×10−5 to 6×10−5 for 10 GeV < ma < 62 GeV and from10−4 to 3 × 10−2 for 0.1 GeV < ma < 10 GeV. These arethe most stringent limits to date.Acknowledgements We thank CERN for the very successful oper-ation of the LHC and its injectors, as well as the support staff atCERN and at our institutions worldwide without whom ATLAS couldnot be operated efficiently. The crucial computing support from allWLCG partners is acknowledged gratefully, in particular from CERN,the ATLAS Tier-1 facilities at TRIUMF/SFU (Canada), NDGF (Den-mark, Norway, Sweden), CC-IN2P3 (France), KIT/GridKA (Germany),INFN-CNAF (Italy), NL-T1 (Netherlands), PIC (Spain), RAL (UK)and BNL (USA), the Tier-2 facilities worldwide and large non-WLCGresource providers. Major contributors of computing resources are listedin Ref. [70]. We gratefully acknowledge the support of ANPCyT,Argentina; YerPhI, Armenia; ARC, Australia; BMWFW and FWF, Aus-tria; ANAS, Azerbaijan; CNPq and FAPESP, Brazil; NSERC, NRCand CFI, Canada; CERN; ANID, Chile; CAS, MOST and NSFC,China; Minciencias, Colombia; MEYS CR, Czech Republic; DNRFand DNSRC, Denmark; IN2P3-CNRS and CEA-DRF/IRFU, France;SRNSFG, Georgia; BMBF, HGF and MPG, Germany; GSRI, Greece;RGC and Hong Kong SAR, China; ISF and Benoziyo Center, Israel;INFN, Italy; MEXT and JSPS, Japan; CNRST, Morocco; NWO, Nether-lands; RCN, Norway; MEiN, Poland; FCT, Portugal; MNE/IFA, Roma-nia; MESTD, Serbia; MSSR, Slovakia; ARRS and MIZŠ, Slove-nia; DSI/NRF, South Africa; MICINN, Spain; SRC and WallenbergFoundation, Sweden; SERI, SNSF and Cantons of Bern and Geneva,Switzerland; MOST, Taipei; TENMAK, Türkiye; STFC, United King-dom; DOE and NSF, United States of America. Individual groupsand members have received support from BCKDF, CANARIE, CRCand DRAC, Canada; CERN-CZ, PRIMUS 21/SCI/017 and UNCESCI/013, Czech Republic; COST, ERC, ERDF, Horizon 2020, ICSC-NextGenerationEU and Marie Skłodowska-Curie Actions, EuropeanUnion; Investissements d’Avenir Labex, Investissements d’Avenir Idexand ANR, France; DFG and AvH Foundation, Germany; Herakleitos,Thales and Aristeia programmes co-financed by EU-ESF and the GreekNSRF, Greece; BSF-NSF and MINERVA, Israel; Norwegian FinancialMechanism 2014-2021, Norway; NCN and NAWA, Poland; La CaixaBanking Foundation, CERCA Programme Generalitat de Catalunya andPROMETEO and GenT Programmes Generalitat Valenciana, Spain;Göran Gustafssons Stiftelse, Sweden; The Royal Society and Lever-hulme Trust, United Kingdom. In addition, individual members wishto acknowledge support from Chile: Agencia Nacional de Investi-gación y Desarrollo (FONDECYT 1190886, FONDECYT 1210400,FONDECYT 1230987); China: National Natural Science Foundationof China (NSFC-12175119, NSFC 12275265, NSFC-12075060); Euro-pean Union: European Research Council (ERC - 948254), Horizon2020 Framework Programme (MUCCA - CHIST-ERA-19-XAI-00),Italian Center for High Performance Computing, Big Data and Quan-tum Computing (ICSC, NextGenerationEU), Marie Sklodowska-CurieActions (EU H2020 MSC IF GRANT NO 101033496); France: AgenceNationale de la Recherche (ANR-20-CE31-0013, ANR-21-CE31-0013, ANR-21-CE31-0022), Investissements d’Avenir Idex (ANR-11-LABX-0012), Investissements d’Avenir Labex (ANR-11-LABX-0012); Germany: Baden-Württemberg Stiftung (BW Stiftung-PostdocEliteprogramme), Deutsche Forschungsgemeinschaft (DFG-CR 312/5-1); Italy: Istituto Nazionale di Fisica Nucleare (FELLINI G.A. n.754496, ICSC, NextGenerationEU); Japan: Japan Society for thePromotion of Science (JSPS KAKENHI JP21H05085, JSPS KAK-ENHI JP22H01227, JSPS KAKENHI JP22H04944); Netherlands:Netherlands Organisation for Scientific Research (NWO Veni 2020- VI.Veni.202.179); Norway: Research Council of Norway (RCN-314472); Poland: Polish National Agency for Academic Exchange(PPN/PPO/2020/1/00002/U/00001), Polish National Science Centre(NCN 2021/42/E/ST2/00350, NCN UMO-2019/34/E/ST2/00393, UMO-2020/37/B/ST2/01043, UMO-2021/40/C/ST2/00187); Slovenia: Slove-nian Research Agency (ARIS grant J1-3010); Spain: BBVA Foun-dation (LEO22-1-603), Generalitat Valenciana (Artemisa, FEDER,IDIFEDER/2018/048), La Caixa Banking Foundation (LCF/BQ/PI20/11760025), Ministry of Science and Innovation (MCIN and NextGenEU -PCI2022-135018-2, MICIN and FEDER -PID2021-125273NB, RYC2019-028510-I, RYC2020-030254-I), PROMETEO and GenT ProgrammesGeneralitat Valenciana (CIDEGENT/2019/023, CIDEGENT/2019/027);Sweden: Swedish Research Council (VR 2018-00482, VR 2022-03845,VR 2022-04683, VR grant 2021-03651), Knut and Alice WallenbergFoundation (KAW 2017.0100, KAW 2018.0157, KAW 2018.0458,KAW 2019.0447); Switzerland: Swiss National Science Foundation(SNSF-PCEFP2_194658); United Kingdom: Leverhulme Trust (Lev-erhulme Trust RPG-2020-004); United States of America: NeubauerFamily Foundation.Data Availability Statement This manuscript has no associated data.[Authors’ comment: Data sharing not applicable to this article as nodatasets were generated or analysed during the current study.]Code Availability Statement This manuscript has no associatedcode/software. 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Zwalinski361 Department of Physics, University of Adelaide, Adelaide, Australia2 Department of Physics, University of Alberta, Edmonton, AB, Canada3 (a)Department of Physics, Ankara University, Ankara, Türkiye; (b)Division of Physics, TOBB University of Economicsand Technology, Ankara, Türkiye4 LAPP, Université Savoie Mont Blanc, CNRS/IN2P3, Annecy, France5 APC, Université Paris Cité, CNRS/IN2P3, Paris, France6 High Energy Physics Division, Argonne National Laboratory, Argonne, IL, USA7 Department of Physics, University of Arizona, Tucson, AZ, USA8 Department of Physics, University of Texas at Arlington, Arlington, TX, USA9 Physics Department, National and Kapodistrian University of Athens, Athens, Greece10 Physics Department, National Technical University of Athens, Zografou, Greece11 Department of Physics, University of Texas at Austin, Austin, TX, USA12 Institute of Physics, Azerbaijan Academy of Sciences, Baku, Azerbaijan13 Institut de Física d’Altes Energies (IFAE), Barcelona Institute of Science and Technology, Barcelona, Spain14 (a)Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China; (b)Physics Department, TsinghuaUniversity, Beijing, China; (c)Department of Physics, Nanjing University, Nanjing, China; (d)School of Science,Shenzhen Campus of Sun Yat-sen University, China; (e)University of Chinese Academy of Science (UCAS), Beijing,China15 Institute of Physics, University of Belgrade, Belgrade, Serbia16 Department for Physics and Technology, University of Bergen, Bergen, Norway17 (a)Physics Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA; (b)University of California, Berkeley,CA, USA18 Institut für Physik, Humboldt Universität zu Berlin, Berlin, Germany19 Albert Einstein Center for Fundamental Physics and Laboratory for High Energy Physics, University of Bern, Bern,Switzerland20 School of Physics and Astronomy, University of Birmingham, Birmingham, UK21 (a)Department of Physics, Bogazici University, Istanbul, Türkiye; (b)Department of Physics Engineering, GaziantepUniversity, Gaziantep, Türkiye; (c)Department of Physics, Istanbul University, Istanbul, Türkiye22 (a)Facultad de Ciencias y Centro de Investigaciónes, Universidad Antonio Nariño, Bogotá, Colombia; (b)Departamentode Física, Universidad Nacional de Colombia, Bogotá, Colombia23 (a)Dipartimento di Fisica e Astronomia A. Righi, Università di Bologna, Bologna, Italy; (b)INFN Sezione di Bologna,Bologna, Italy123Eur. Phys. J. C (2024) 84:742 Page 27 of 31 742 24 Physikalisches Institut, Universität Bonn, Bonn, Germany25 Department of Physics, Boston University, Boston, MA, USA26 Department of Physics, Brandeis University, Waltham, MA, USA27 (a)Transilvania University of Brasov, Brasov, Romania; (b)Horia Hulubei National Institute of Physics and NuclearEngineering, Bucharest, Romania; (c)Department of Physics, Alexandru Ioan Cuza University of Iasi, Iasi, Romania; (d)National Institute for Research and Development of Isotopic and Molecular Technologies, Physics Department,Cluj-Napoca, Romania; (e)National University of Science and Technology Politechnica, Bucharest, Romania; (f)WestUniversity in Timisoara, Timisoara, Romania; (g)Faculty of Physics, University of Bucharest, Bucharest, Romania28 (a)Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovak Republic; (b)Department ofSubnuclear Physics, Institute of Experimental Physics of the Slovak Academy of Sciences, Kosice, Slovak Republic29 Physics Department, Brookhaven National Laboratory, Upton, NY, USA30 Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de Física, y CONICET, Institutode Física de Buenos Aires (IFIBA), Buenos Aires, Argentina31 California State University, CA, USA32 Cavendish Laboratory, University of Cambridge, Cambridge, UK33 (a)Department of Physics, University of Cape Town, Cape Town, South Africa; (b)iThemba Labs, Western Cape, SouthAfrica; (c)Department of Mechanical Engineering Science, University of Johannesburg, Johannesburg, South Africa; (d)National Institute of Physics, University of the Philippines Diliman (Philippines), Quezon City, South Africa; (e)University of South Africa, Department of Physics, Pretoria, South Africa; (f)University of Zululand, KwaDlangezwa,South Africa; (g)School of Physics, University of the Witwatersrand, Johannesburg, South Africa34 Department of Physics, Carleton University, Ottawa, ON, Canada35 (a)Faculté des Sciences Ain Chock, Réseau Universitaire de Physique des Hautes Energies - Université Hassan II,Casablanca, Morocco; (b)Faculté des Sciences, Université Ibn-Tofail, Kénitra, Morocco; (c)Faculté des SciencesSemlalia, Université Cadi Ayyad, LPHEA-Marrakech, Morocco; (d)LPMR, Faculté des Sciences, Université MohamedPremier, Oujda, Morocco; (e)Faculté des sciences, Université Mohammed V, Rabat, Morocco; (f)Institute of AppliedPhysics, Mohammed VI Polytechnic University, Ben Guerir, Morocco36 CERN, Geneva, Switzerland37 Affiliated with an institute covered by a cooperation agreement with CERN, Geneva, Switzerland38 Affiliated with an international laboratory covered by a cooperation agreement with CERN, Geneva, Switzerland39 Enrico Fermi Institute, University of Chicago, Chicago, IL, USA40 LPC, Université Clermont Auvergne, CNRS/IN2P3, Clermont-Ferrand, France41 Nevis Laboratory, Columbia University, Irvington, NY, USA42 Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark43 (a)Dipartimento di Fisica, Università della Calabria, Rende, Italy; (b)INFN Gruppo Collegato di Cosenza, LaboratoriNazionali di Frascati, Italy44 Physics Department, Southern Methodist University, Dallas, TX, USA45 Physics Department, University of Texas at Dallas, Richardson, TX, USA46 National Centre for Scientific Research “Demokritos”, Agia Paraskevi, Greece47 (a)Department of Physics, Stockholm University, Stockholm, Sweden; (b)Oskar Klein Centre, Stockholm, Sweden48 Deutsches Elektronen-Synchrotron DESY, Hamburg and Zeuthen, Germany49 Fakultät Physik , Technische Universität Dortmund, Dortmund, Germany50 Institut für Kern- und Teilchenphysik, Technische Universität Dresden, Dresden, Germany51 Department of Physics, Duke University, Durham, NC, USA52 SUPA-School of Physics and Astronomy, University of Edinburgh, Edinburgh, UK53 INFN e Laboratori Nazionali di Frascati, Frascati, Italy54 Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Freiburg, Germany55 II. Physikalisches Institut, Georg-August-Universität Göttingen, Göttingen, Germany56 Département de Physique Nucléaire et Corpusculaire, Université de Genève, Genève, Switzerland57 (a)Dipartimento di Fisica, Università di Genova, Genova, Italy; (b)INFN Sezione di Genova, Genoa, Italy58 II. Physikalisches Institut, Justus-Liebig-Universität Giessen, Giessen, Germany59 SUPA-School of Physics and Astronomy, University of Glasgow, Glasgow, UK60 LPSC, Université Grenoble Alpes, CNRS/IN2P3, Grenoble INP, Grenoble, France61 Laboratory for Particle Physics and Cosmology, Harvard University, Cambridge, MA, USA123 742 Page 28 of 31 Eur. Phys. J. C (2024) 84:742 62 (a)Department of Modern Physics and State Key Laboratory of Particle Detection and Electronics, University of Scienceand Technology of China, Hefei, China; (b)Institute of Frontier and Interdisciplinary Science and Key Laboratory ofParticle Physics and Particle Irradiation (MOE), Shandong University, Qingdao, China; (c)School of Physics andAstronomy, Shanghai Jiao Tong University, Key Laboratory for Particle Astrophysics and Cosmology (MOE), SKLPPC,Shanghai, China; (d)Tsung-Dao Lee Institute, Shanghai, China63 (a)Kirchhoff-Institut für Physik, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany; (b)Physikalisches Institut,Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany64 (a)Department of Physics, Chinese University of Hong Kong, Shatin, N.T., Hong Kong, China; (b)Department of Physics,University of Hong Kong, Hong Kong, China; (c)Department of Physics and Institute for Advanced Study, Hong KongUniversity of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China65 Department of Physics, National Tsing Hua University, Hsinchu, Taiwan66 IJCLab, Université Paris-Saclay, CNRS/IN2P3, 91405 Orsay, France67 Centro Nacional de Microelectrónica (IMB-CNM-CSIC), Barcelona, Spain68 Department of Physics, Indiana University, Bloomington, IN, USA69 (a)INFN Gruppo Collegato di Udine, Sezione di Trieste, Udine, Italy; (b)ICTP, Trieste, Italy; (c)Dipartimento Politecnicodi Ingegneria e Architettura, Università di Udine, Udine, Italy70 (a)INFN Sezione di Lecce, Lecce, Italy; (b)Dipartimento di Matematica e Fisica, Università del Salento, Lecce, Italy71 (a)INFN Sezione di Milano, Milan, Italy; (b)Dipartimento di Fisica, Università di Milano, Milan, Italy72 (a)INFN Sezione di Napoli, Naples, Italy; (b)Dipartimento di Fisica, Università di Napoli, Naples, Italy73 (a)INFN Sezione di Pavia, Pavia, Italy; (b)Dipartimento di Fisica, Università di Pavia, Pavia, Italy74 (a)INFN Sezione di Pisa, Pisa, Italy; (b)Dipartimento di Fisica E. Fermi, Università di Pisa, Pisa, Italy75 (a)INFN Sezione di Roma, Rome, Italy; (b)Dipartimento di Fisica, Sapienza Università di Roma, Rome, Italy76 (a)INFN Sezione di Roma Tor Vergata, Rome, Italy; (b)Dipartimento di Fisica, Università di Roma Tor Vergata, Rome,Italy77 (a)INFN Sezione di Roma Tre, Rome, Italy; (b)Dipartimento di Matematica e Fisica, Università Roma Tre, Rome, Italy78 (a)INFN-TIFPA, Rome, Italy; (b)Università degli Studi di Trento, Trento, Italy79 Universität Innsbruck, Department of Astro and Particle Physics, Innsbruck, Austria80 University of Iowa, Iowa City, IA, USA81 Department of Physics and Astronomy, Iowa State University, Ames, IA, USA82 Istinye University, Sariyer, Istanbul, Türkiye83 (a)Departamento de Engenharia Elétrica, Universidade Federal de Juiz de Fora (UFJF), Juiz de Fora, Brazil; (b)Universidade Federal do Rio De Janeiro COPPE/EE/IF, Rio de Janeiro, Brazil; (c)Instituto de Física, Universidade deSão Paulo, São Paulo, Brazil; (d)Rio de Janeiro State University, Rio de Janeiro, Brazil84 KEK, High Energy Accelerator Research Organization, Tsukuba, Japan85 Graduate School of Science, Kobe University, Kobe, Japan86 (a)AGH University of Krakow, Faculty of Physics and Applied Computer Science, Krakow, Poland; (b)MarianSmoluchowski Institute of Physics, Jagiellonian University, Krakow, Poland87 Institute of Nuclear Physics Polish Academy of Sciences, Krakow, Poland88 Faculty of Science, Kyoto University, Kyoto, Japan89 Research Center for Advanced Particle Physics and Department of Physics, Kyushu University, Fukuoka , Japan90 Instituto de Física La Plata, Universidad Nacional de La Plata and CONICET, La Plata, Argentina91 Physics Department, Lancaster University, Lancaster, UK92 Oliver Lodge Laboratory, University of Liverpool, Liverpool, UK93 Department of Experimental Particle Physics, Jožef Stefan Institute and Department of Physics, University of Ljubljana,Ljubljana, Slovenia94 School of Physics and Astronomy, Queen Mary University of London, London, UK95 Department of Physics, Royal Holloway University of London, Egham, UK96 Department of Physics and Astronomy, University College London, London, UK97 Louisiana Tech University, Ruston, LA, USA98 Fysiska institutionen, Lunds universitet, Lund, Sweden99 Departamento de Física Teorica C-15 and CIAFF, Universidad Autónoma de Madrid, Madrid, Spain100 Institut für Physik, Universität Mainz, Mainz, Germany101 School of Physics and Astronomy, University of Manchester, Manchester, UK123Eur. Phys. J. C (2024) 84:742 Page 29 of 31 742 102 CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France103 Department of Physics, University of Massachusetts, Amherst, MA, USA104 Department of Physics, McGill University, Montreal, QC, Canada105 School of Physics, University of Melbourne, Victoria, Australia106 Department of Physics, University of Michigan, Ann Arbor, MI, USA107 Department of Physics and Astronomy, Michigan State University, East Lansing, MI, USA108 Group of Particle Physics, University of Montreal, Montreal, QC, Canada109 Fakultät für Physik, Ludwig-Maximilians-Universität München, Munich, Germany110 Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), Munich, Germany111 Graduate School of Science and Kobayashi-Maskawa Institute, Nagoya University, Nagoya, Japan112 Department of Physics and Astronomy, University of New Mexico, Albuquerque, NM, USA113 Institute for Mathematics, Astrophysics and Particle Physics, Radboud University/Nikhef, Nijmegen, Netherlands114 Nikhef National Institute for Subatomic Physics and University of Amsterdam, Amsterdam, Netherlands115 Department of Physics, Northern Illinois University, DeKalb, IL, USA116 (a)New York University Abu Dhabi, Abu Dhabi, United Arab Emirates; (b)University of Sharjah, Sharjah, United ArabEmirates117 Department of Physics, New York University, New York, NY, USA118 Ochanomizu University, Otsuka, Bunkyo-ku, Tokyo, Japan119 Ohio State University, Columbus, OH, USA120 Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma, Norman, OK, USA121 Department of Physics, Oklahoma State University, Stillwater, OK, USA122 Palacký University, Joint Laboratory of Optics, Olomouc, Czech Republic123 Institute for Fundamental Science, University of Oregon, Eugene, OR, USA124 Graduate School of Science, Osaka University, Osaka, Japan125 Department of Physics, University of Oslo, Oslo, Norway126 Department of Physics, Oxford University, Oxford, UK127 LPNHE, Sorbonne Université, Université Paris Cité, CNRS/IN2P3, Paris, France128 Department of Physics, University of Pennsylvania, Philadelphia, PA, USA129 Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA, USA130 (a)Laboratório de Instrumentação e Física Experimental de Partículas - LIP, Lisbon, Portugal; (b)Departamento de Física,Faculdade de Ciências, Universidade de Lisboa, Lisbon, Portugal; (c)Departamento de Física, Universidade de Coimbra,Coimbra, Portugal; (d)Centro de Física Nuclear da Universidade de Lisboa, Lisbon, Portugal; (e)Departamento de Física,Universidade do Minho, Braga, Portugal; (f)Departamento de Física Teórica y del Cosmos, Universidad de Granada,Granada, Spain; (g)Departamento de Física, Instituto Superior Técnico, Universidade de Lisboa, Lisbon, Portugal131 Institute of Physics of the Czech Academy of Sciences, Prague, Czech Republic132 Czech Technical University in Prague, Prague, Czech Republic133 Charles University, Faculty of Mathematics and Physics, Prague, Czech Republic134 Particle Physics Department, Rutherford Appleton Laboratory, Didcot, UK135 IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette, France136 Santa Cruz Institute for Particle Physics, University of California Santa Cruz, Santa Cruz, CA, USA137 (a)Departamento de Física, Pontificia Universidad Católica de Chile, Santiago, Chile; (b)Millennium Institute forSubatomic physics at high energy frontier (SAPHIR), Santiago, Chile; (c)Instituto de Investigación Multidisciplinario enCiencia y Tecnología, y Departamento de Física, Universidad de La Serena, Chile; (d)Universidad Andres Bello,Department of Physics, Santiago, Chile; (e)Instituto de Alta Investigación, Universidad de Tarapacá, Arica, Chile; (f)Departamento de Física, Universidad Técnica Federico Santa María, Valparaíso, Chile138 Department of Physics, University of Washington, Seattle, WA, USA139 Department of Physics and Astronomy, University of Sheffield, Sheffield, UK140 Department of Physics, Shinshu University, Nagano, Japan141 Department Physik, Universität Siegen, Siegen, Germany142 Department of Physics, Simon Fraser University, Burnaby, BC, Canada143 SLAC National Accelerator Laboratory, Stanford, CA, USA144 Department of Physics, Royal Institute of Technology, Stockholm, Sweden145 Departments of Physics and Astronomy, Stony Brook University, Stony Brook, NY, USA123 742 Page 30 of 31 Eur. Phys. J. C (2024) 84:742 146 Department of Physics and Astronomy, University of Sussex, Brighton, UK147 School of Physics, University of Sydney, Sydney, Australia148 Institute of Physics, Academia Sinica, Taipei, Taiwan149 (a)E. Andronikashvili Institute of Physics, Iv. Javakhishvili Tbilisi State University, Tbilisi, Georgia; (b)High EnergyPhysics Institute, Tbilisi State University, Tbilisi, Georgia; (c)University of Georgia, Tbilisi, Georgia150 Department of Physics, Technion, Israel Institute of Technology, Haifa, Israel151 Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv, Israel152 Department of Physics, Aristotle University of Thessaloniki, Thessaloniki, Greece153 International Center for Elementary Particle Physics and Department of Physics, University of Tokyo, Tokyo, Japan154 Department of Physics, Tokyo Institute of Technology, Tokyo, Japan155 Department of Physics, University of Toronto, Toronto, ON, Canada156 (a)TRIUMF, Vancouver, BC, Canada; (b)Department of Physics and Astronomy, York University, Toronto, ON, Canada157 Division of Physics and Tomonaga Center for the History of the Universe, Faculty of Pure and Applied Sciences,University of Tsukuba, Tsukuba, Japan158 Department of Physics and Astronomy, Tufts University, Medford, MA, USA159 United Arab Emirates University, Al Ain, United Arab Emirates160 Department of Physics and Astronomy, University of California Irvine, Irvine, CA, USA161 Department of Physics and Astronomy, University of Uppsala, Uppsala, Sweden162 Department of Physics, University of Illinois, Urbana, IL, USA163 Instituto de Física Corpuscular (IFIC), Centro Mixto Universidad de Valencia-CSIC, Valencia, Spain164 Department of Physics, University of British Columbia, Vancouver, BC, Canada165 Department of Physics and Astronomy, University of Victoria, Victoria, BC, Canada166 Fakultät für Physik und Astronomie, Julius-Maximilians-Universität Würzburg, Würzburg, Germany167 Department of Physics, University of Warwick, Coventry, UK168 Waseda University, Tokyo, Japan169 Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot, Israel170 Department of Physics, University of Wisconsin, Madison, WI, USA171 Fakultät für Mathematik und Naturwissenschaften, Fachgruppe Physik, Bergische Universität Wuppertal, Wuppertal,Germany172 Department of Physics, Yale University, New Haven, CT, USAa Also Affiliated with an institute covered by a cooperation agreement with CERN, Geneva, Switzerlandb Also at An-Najah National University, Nablus, Palestinec Also at Borough of Manhattan Community College, City University of New York, New York, NY, USAd Also at Center for High Energy Physics, Peking University, Chinae Also at Center for Interdisciplinary Research and Innovation (CIRI-AUTH), Thessaloniki, Greecef Also at Centro Studi e Ricerche Enrico Fermi, Rome, Italyg Also at CERN, Geneva, Switzerlandh Also at Département de Physique Nucléaire et Corpusculaire, Université de Genève, Genève, Switzerlandi Also at Departament de Fisica de la Universitat Autonoma de Barcelona, Barcelona, Spainj Also at Department of Financial and Management Engineering, University of the Aegean, Chios, Greecek Also at Department of Physics, Ben Gurion University of the Negev, Beer Sheva, Israell Also at Department of Physics, California State University, Sacramento, USAm Also at Department of Physics, King’s College London, London, UKn Also at Department of Physics, Stanford University, Stanford, CA, USAo Also at Department of Physics, University of Fribourg, Fribourg, Switzerlandp Also at Department of Physics, University of Thessaly, Thessaly, Greeceq Also at Department of Physics, Westmont College, Santa Barbara, USAr Also at Hellenic Open University, Patras, Greeces Also at Institucio Catalana de Recerca i Estudis Avancats, ICREA, Barcelona, Spaint Also at Institut für Experimentalphysik, Universität Hamburg, Hamburg, Germanyu Also at Institute for Nuclear Research and Nuclear Energy (INRNE) of the Bulgarian Academy of Sciences, Sofia,Bulgaria123Eur. Phys. J. C (2024) 84:742 Page 31 of 31 742 v Also at Institute of Applied Physics, Mohammed VI Polytechnic University, Ben Guerir, Moroccow Also at Institute of Particle Physics (IPP), Toronto, Canadax Also at Institute of Physics and Technology, Mongolian Academy of Sciences, Ulaanbaatar, Mongoliay Also at Institute of Physics, Azerbaijan Academy of Sciences, Baku, Azerbaijanz Also at Institute of Theoretical Physics, Ilia State University, Tbilisi, Georgiaaa Also at L2IT, Université de Toulouse, CNRS/IN2P3, UPS, Toulouse, Franceab Also at Lawrence Livermore National Laboratory, Livermore, USAac Also at National Institute of Physics, University of the Philippines Diliman (Philippines), Quezon City, Philippinesad Also at Technical University of Munich, Munich, Germanyae Also at The Collaborative Innovation Center of Quantum Matter (CICQM), Beijing, Chinaaf Also at TRIUMF, Vancouver, BC, Canadaag Also at Università di Napoli Parthenope, Naples, Italyah Also at University of Chinese Academy of Sciences (UCAS), Beijing, Chinaai Also at Department of Physics, University of Colorado Boulder, Colorado, USAaj Also at Washington College, Chestertown, MD, USAak Also at Physics Department, Yeditepe University, Istanbul, Türkiye∗ Deceased123
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Search for short- and long-lived axion-like particles in H → aa → 4γ decays with the ATLAS experiment at the LHC
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