Observation of electroweak production of two jets in association with an isolated photon and missing transverse momentum, and search for a Higgs boson decaying into invisible particles at 13 TeV with the ATLAS detector

Eur. Phys. J. C (2022) 82:105 https://doi.org/10.1140/epjc/s10052-021-09878-z Regular Article - Experimental Physics Observation of electroweak production of two jets in association with an isolated photon and missing transverse momentum, and search for a Higgs boson decaying into invisible particles at 13 TeV with the ATLAS detector ATLAS Collaboration CERN, 1211 Geneva 23, Switzerland Received: 7 September 2021 / Accepted: 24 November 2021 / Published online: 3 February 2022 © CERN for the benefit of the ATLAS collaboration 2022 Abstract This paper presents a measurement of the electroweak production of two jets in association with a Zγpair, withthe Zbosondecayingintotwoneutrinos.Italsopresents a search for invisible or partially invisible decays of a Higgs boson with a mass of 125 GeV produced through vectorbosonfusionwithaphotoninthefinalstate.Theseresults use data from LHC proton–proton collisions at √s= 13 TeV collectedwiththeATLASdetectorandcorrespondingtoanintegrated luminosity of 139 fb−1. The event signature, shared by all benchmark processes considered for the measurements and searches, is characterized by a significant amount of unbalanced transverse momentum and a photon in the final state, in addition to a pair of forward jets. Electroweak Zγ production in association with two jets is observed in this final state with a significance of 5.2 (5.1 expected) standard deviations. The measured fiducial cross-section for this process is 1.31 ±0.29 fb. An observed (expected) upper limit of 0.37 (0.34+0.15 −0.10) at 95% confidence level is set on the branching ratio of a 125 GeV Higgs boson to invisible particles, assuming the Standard Model production cross-section. The signature is also interpreted in the context of decays of a Higgs boson into a photon and a dark photon. An observed (expected) 95% CL upper limit on the branching ratio for this decay is set at 0.018 (0.017+0.007 −0.005), assuming the Standard Model production cross-section for a 125 GeV Higgs boson. Contents 1 Introduction ..................... 1 2 ATLAS detector ................... 3 3 Data samples ..................... 4 4 Simulated event samples ............... 4 4.1 Vγ+jets processes .............. 4 e-mail: [email protected] 4.2 V+jets processes ............... 6 4.3 Top-quark processes ............... 6 4.4 Additional background samples ......... 7 4.5 Higgs boson processes ............. 7 5 Object reconstruction ................ 7 6 Event selection .................... 8 6.1 Baseline event selection ............. 9 6.2 Event classification and fiducial-volume definition for EW Zγ+jets measurement ......10 6.3 Event classification for H→inv.search ....11 6.4 Event classification for H→γγ dsearch ....12 6.5 Control region definitions ............12 6.6 Validation region for γ+jet background ...13 7 Data analysis .....................13 7.1 Background contribution estimation ......13 7.2 Systematic uncertainties .............15 8 Fit models and results ................16 8.1 Fit model and results for the EW Zγ+jets cross-section measurement ...........17 8.2 Fit model and results for H→inv.search ...19 8.3 Fit model and results for H→γγ dsearch ...20 9 Conclusion ......................21 References ........................24 1 Introduction Studying the self-couplings of the Standard Model (SM) vector bosons, precisely predicted through the SU(2)L×U(1)Y gauge symmetry, provides a unique opportunity to better understand the electroweak sector of the SM and gain insight into possible anomalies due to new phenomena. Vectorboson scattering (VBS), VV→VVwith V,V=W/Z/ γ, is an interesting process to study, being sensitive to both the triple and quartic gauge-boson couplings, which are particularly sensitive to the presence of physics effects beyond 123 105 Page 2 of 41 Eur. Phys. J. C (2022) 82 :105 (a) (b) (c) Fig. 1 Representative Feynman diagrams for the dominant SM processes contributing to the considered signature: ais an example of the order α2 sα3diagrams referred to as “strong”; b,care examples of the order α5diagrams, which are collectively referred to as “electroweak” (EW) the Standard Model (BSM) [1–3]. In hadron collisions, such as those produced at the Large Hadron Collider (LHC), VBS events occur whenever two vector bosons, radiated from the initial-state quarks, interact with each other [4], producing a final-state signature characterized by the two vector bosons and a pair of forward hadronic jets in opposite hemispheres. The two vector bosons can similarly annihilate and produce a SM Higgs boson in the so-called vector-boson fusion (VBF) mechanism. Depending on the subsequent decay of the SM Higgs boson, different final-state signatures can be exploited to investigate its properties. Precise knowledge of the various Higgs boson decay branching ratios is a fundamental aspect of understanding whether the 125 GeV scalar boson behaves according to the SM predictions or whether new physics phenomena modify the Higgs sector. This paper presents a set of SM measurements and searches for new phenomena in a final-state signature characterized by two forward hadronic jets, a photon, and a significant amount of unbalanced momentum in the plane transverse to the beam direction (Emiss T) due to undetected particles. In the SM this can result from Vγ+jets production, where Vis either a Zboson decaying into an undetected neutrino–antineutrino pair or a Wboson decaying leptonically, where the charged lepton is not reconstructed in the detector. The latter is a background to the measurements and searches in this paper. The Vγ+jets events are produced in the SM through a combination of ‘strong’ and ‘electroweak’ (EW) contributions: the former are produced through diagrams of order α2 sα3at the Born level as shown in Fig. 1a, where αsis the strong coupling constant and αis the electromagnetic coupling constant, while the latter are produced more rarely through diagrams of order α5at the Born level1 as shown in Fig. 1b, c. The Zγ+jets cross-sections have been computed at next-to-leading order (NLO) in αsfor both thestrong[5]and EW [6] production modes. It is not possible 1One order of αis included for the decay of the vector boson. to study VBS diagrams, as shown in Fig. 1b, independently of other electroweak processes (e.g. triboson production as shown in Fig. 1c) as only the ensemble is gauge invariant [7]. There is also interference between the SM electroweak and strong processes, which is accounted for in the measurement. In Run 1 the Zγ+jets EW production cross-section has been measured in the dielectron and dimuon final states of the Zboson by the ATLAS and CMS experiments [8,9] with observed significances of 4.1 and 3.0 standard deviations, respectively. The CMS Collaboration measured EW Z(→ )γ jj after observing the process with a significance of 9.4 standard deviations in 137 fb−1of 13 TeV proton–proton (pp) collisions [10]. Profiting from the full 139 fb−1dataset collected with the ATLAS detector during Run 2 of the LHC, the analysis presented in this paper reports the observation of EW Z(→ νν)γjj production at the LHC. The observation of EW production of Z(→νν)γjj lays the groundwork for further investigation of this signature in looking for possible hints of BSM physics, based on interesting and well-motivated benchmark scenarios involving new dark matter (DM) candidate particles or a hidden sector of new particles coupling with the SM Higgs boson. The existence of DM is evident from astrophysical observations [11], although its connection with the SM is still unknown because it has only been observed through gravitational interactions. In this paper, the connection of DM with SM particles is explored by introducing a coupling with the 125 GeV Higgs boson. A class of BSM scenarios, referred to as Higgs-portal models [12], feature a DM candidate behaving as a singlet under the SM gauge symmetries, with the Higgs boson playing the role of a mediator between the DM candidate and SM particles. Two main benchmark models are chosen when searching for new phenomena in the considered final-state signature, probing the invisible decay of the Higgs boson or its semivisible decay into one invisible particle and one photon. The 123 Eur. Phys. J. C (2022) 82 :105 Page 3 of 41 105 Fig. 2 Representative Feynman diagrams corresponding to the dominant BSM signal processes: athe signal due to the invisible Higgs boson decay produced through VBF in association with an emitted photon. The incoming quarks appearing on the left hand side of the diagram are different from each other. bThe signal due to the decay of the Higgs boson to a photon–dark-photon pair, produced through VBF (a) (b) decay of the Higgs boson into invisible particles (H→inv.) when produced through the SM-predicted VBF process in association with an emitted photon [13,14] is probed in this paper for the first time. The Feynman diagram for this signature is shown in Fig. 2a. Compared to a similar signature without the photon, this one benefits from better background rejection and a higher signal reconstruction efficiency; however, it has a lower production cross-section. No direct constraints on the H→inv.decays in this experimental signature currently exist. Constraints on the invisible Higgs boson branching ratio (Binv) were set by the ATLAS Collaboration using the full Run 1 dataset at 7 and 8TeV[15–17] and the full Run 2 dataset at 13 TeV[18,19]. Similar searches were carried out by the CMS Collaboration [20–22] using both the Run 1 and Run 2 datasets. The most stringent limits are from the statistical combination of the search results, for which ATLAS reports an observed (expected)upperlimitonBinv of0.26(0.17)andCMSreports an upper limit of 0.19 (0.15), all at 95% confidence level (CL). In these combinations, the VBF production channel is the single channel with the highest expected sensitivity, for which ATLAS and CMS reported observed (expected) 95% CL limits on Binv of 0.37 (0.28) and 0.33 (0.25), respectively, using36fb −1of Run 2 data. In addition to the H→inv.benchmark, this analysis probes a dark-photon model [23–25] which predicts a light or massless2dark photon (γd) coupled with the Higgs boson through a U(1) unbroken dark sector. The Feynman diagram for this signature is shown in Fig. 2b, and BSM extensions to other resonance masses are possible [26]. In this model, a Higgs boson decays into a photon and an invisible dark photon with a branching ratio B(H→γγ d). CMS has probed thisbenchmarkmodelbyconsideringassociated ZHproduction and VBF Higgs boson production [27,28], and reported observed (expected) 95% CL upper limits of 0.046 (0.036) and 0.035 (0.028) on B(H→γγ d)in their respective signa2For the results in this paper, the signal acceptance changes by less than 1% for dark-photon masses up to 10 GeV. tures. These two results were combined to yield an observed (expected) 95% CL upper limit of 0.029 (0.021). The SM processes resulting in the same final-state signature as described before, mainly Z(→νν)γ +jets and W(→ν)γ +jets, represent background contributions in the searches for new phenomena. These processes were simulated, for both the Zγ+jets EW cross-section measurement and the searches for new phenomena, through dedicated Monte Carlo samples, detailed in Sect. 4. Minor and reducible background contributions arise due to the misreconstruction of objects in the detector, including hadronic jets reconstructed as photons. These background processes are estimated using simulation and data-driven techniques and are validated using dedicated data samples. The SM H→Z(→νν)γ process produces the same signature as the investigated H→inv.+γsignal, but the small contribution of such events satisfying the criteria defined in Sect. 6is neglected in the searches for new phenomena. A brief description of the ATLAS detector is provided in Sect. 2. The dataset, simulated samples, and physics object selection are covered in Sects. 3,4, and 5, respectively. The analysis strategies and the event selection for the EW Z(→νν)γjj measurement and searches based on different signal hypotheses, H→inv.and H→γγ d, are discussed in Sect. 6. The modelling of the different processes contributing to the considered signature is presented in Sect. 7, and the fit models and extracted results for the different signal hypotheses are described in Sect. 8. 2 ATLAS detector The ATLAS experiment [29–31] at the LHC is a multipurpose particle detector with a forward–backward symmetric cylindrical geometry and near 4πcoverage in solid angle.3 3ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the centre of the detector and the z123 105 Page 4 of 41 Eur. Phys. J. C (2022) 82 :105 It consists of an inner tracking detector surrounded by a thin superconducting solenoid providing a 2 T axial magnetic field, electromagnetic and hadron calorimeters, and a muon spectrometer. The inner tracking detector (ID) covers the pseudorapidity range |η|<2.5. It consists of silicon pixel, silicon microstrip, and transition radiation tracking detectors. Lead/liquid-argon (LAr) sampling calorimeters provide electromagnetic (EM) energy measurements with high granularity. A steel/scintillator-tile hadron calorimeter covers the centralpseudorapidity range(|η|<1.7).TheendcapandforwardregionsareinstrumentedwithLArcalorimetersforboth the EM and hadronic energy measurements up to |η|=4.9. The muon spectrometer (MS) surrounds the calorimeters and is based on three large superconducting air-core toroidal magnetswitheightcoilseach. The fieldintegralof the toroids ranges between 2.0 and 6.0 T m across most of the detector. The muon spectrometer includes a system of precision tracking chambers and fast detectors for triggering. A two-level trigger system is used to select events. The first-level (L1) trigger is implemented in hardware and uses a subset of the detector information to accept events at a rate below 100 kHz. This is followed by a software-based high-level trigger (HLT) [32,33] which reduces the accepted event rate to 1 kHz on average depending on the data-taking conditions. An extensive software suite [34] is used in the reconstruction and analysis of real and simulated data, in detector operations, and in the trigger and data acquisition systems of the experiment. 3 Data samples This analysis relies on the data collected by the ATLAS experiment from LHC pp collisions at √s= 13 TeV during 2015–2018 stable beam conditions when all subdetectors were operational [35], corresponding to a total integrated luminosity of 139fb−1[36,37]. The data used in this analysis were recorded mainly using trigger algorithms based on the presence of missing transverse momentum, Emiss T(described in Sect. 5)[38]. The trigger thresholds for the Emiss Twere determined by the data-taking conditions during the different periods, especially by the average number of multiple pp interactions in the same or neighbouring bunch crossings, referred to as pile-up. The first-level trigger threshold was 50–55 GeV, depending on the data-taking period, and the lowest-transverse-momentum (pT) unprescaled HLT threshFootnote3 continued axis along the beam pipe. The x-axis points from the IP to the centre of the LHC ring, and the y-axis points upwards. Cylindrical coordinates (r,φ) are used in the transverse plane, φbeing the azimuthal angle around the z-axis. The pseudorapidity is defined in terms of the polar angle θas η=−ln tan(θ/2). Angular distance is measured in units of R≡(η)2+(φ)2. old for the Emiss Ttrigger algorithm was 70 GeV in 2015, 90GeVin2016and110GeVin2017–2018.Thiscorresponds to a trigger operating on its maximum-efficiency plateau for events with offline Emiss Tof ∼180 GeV, depending on the trigger thresholds, in this final state. Independent data samples exploited to study W(→ν)γ +jets background were collected using the lowest-pTunprescaled single-lepton triggers, with pTthresholds ranging from 20 to 26 GeV for the triggers with the tightest lepton identification criteria [39,40]. The Emiss Ttriggers complemented the muon triggers to increase the number of accepted single-muon events by 28%, as discussed in Sect. 6.5. 4 Simulated event samples Monte Carlo (MC) simulated samples are used to model both the SM and BSM processes. The full set of simulated samples is summarized in Table 1. The generated events were processed through a simulation [41] of the ATLAS detector geometry and response using Geant4 [42], and through the same reconstruction software as the collected data. For BSM signal samples with a Higgs boson mass different from 125 GeV, the detector response was simulated using a fast parameterized simulation of the ATLAS calorimeters [43] and the full Geant4 simulation for the other subdetectors. The pile-up effects in the same and neighbouring protonbunch crossings were modelled by adding detector signals from simulated inelastic pp events to the original hard-scattering (HS) event. These were generated with Pythia 8.186 [44]usingtheNNPDF2.3lo set of parton distribution functions (PDFs) [45] and the A3 set of tuned parameters (tune) [46]. The energy scale and resolution for leptons and jets, their reconstruction and identification efficiencies, and the trigger efficiencies in the simulation are corrected to match those measured in data. 4.1 Vγ+jets processes The W(→ν)γ +jets and Zγ+jets (together labelled Vγ+jets)processescontributingtothesignatureconsidered in this analysis contain a charged lepton (=e,μor τ) and a neutrino, a pair of neutrinos (νν) or a pair of charged leptons ()togetherwithaphotonandassociatedjets.The Vγ+jets processes are split into two components based on the order in the electroweak coupling constant α. At tree level, the strong component is of order α2 sα3and the EW component is of order α5; example Feynman diagrams are shown in Fig. 1for these different contributions. The strong component of each Vγ+jets contribution was simulated for photon pTgreater than 7 GeV using the Sherpa 2.2.8 [47] event generator at NLO precision in αsfor up to one additional parton and at LO precision in αsfor up to three additional partons. These cal123 Eur. Phys. J. C (2022) 82 :105 Page 5 of 41 105 Table 1 Summary of generators used for simulation. The details and the corresponding references are provided in the body of the text. The Vin V+jets represents either a Wor a Zboson. The calculation precision indicates the αsorder of the expansion Process Generator ME Order PDF Parton shower Tune SM process samples Strong Vγ+jets Sherpa2.2.8 NLO(upto1-jet), LO (up to 3-jets) NNPDF3.0nnlo Sherpa MEPS@NLO Sherpa EW Vγ+jets [email protected] LO NNPDF3.1lo Pythia8.240 A14 EW VV +jets Sherpa2.2.1 or Sherpa v2.2.2 LO NNPDF3.0nnlo Sherpa MEPS@NLO Sherpa VV +jets Sherpa2.2.1 or Sherpa 2.2.2 NLO (up to 1-jet), LO(upto3-jets) NNPDF3.0nnlo Sherpa MEPS@NLO Sherpa EW V+jets Herwig 7.1.3 or Herwig 7.2.0 NLO MMHT2014 2014nlo68cl Herwig 7.1.3 Herwig 7 Strong W(→ μν) +jets/ W(→τν)+jets Sherpa2.2.7 NLO (up to 2-jets), LO (up to 4-jets) NNPDF3.0nnlo Sherpa MEPS@NLO Sherpa t¯ tγ[email protected] NLO NNPDF2.3lo Pythia8.186 A14 t¯ t/Wt Powheg Box v2 NLO NNPDF3.0nlo Pythia 8.230 A14 Vγγ Sherpa2.2.2 (at 0-jet), LO (up to 2-jets) NLO NNPDF3.0nnlo Sherpa MEPS@NLO Sherpa γ+jet Sherpa2.2.2 NLO (up to 2-jets), LO (up to 4-jets) NNPDF3.0nnlo Sherpa MEPS@NLO Sherpa Higgs-related samples ggF Higgs Powheg v2 NNLOPS NNLO PDF4LHC15 Pythia8.230 AZNLO Higgs+γ[email protected] NLO PDF4LHC15 Herwig 7.1.3p1 A14 ggF Higgs→γγ dPowheg v2 NNLOPS NNLO PDF4LHC15 Pythia 8.244p3 AZNLO VBF Higgs→γγ dPowheg v2 NLO CTEQ6L1 Pythia8.244p3 AZNLO Systematic variation samples Vγ+jets α4interference [email protected] LO NNPDF3.1lo Pythia8.240 AZNLO 123 105 Page 6 of 41 Eur. Phys. J. C (2022) 82 :105 culationsusetheComix[48] andOpenLoops[49]matrixelement generators, and the parton-shower matching [50]was performed using the MEPS@LO [51]orMEPS@NLO [51– 54] prescription. The NNPDF3.0nnlo setofPDFs[55]was used, along with dedicated parton shower tuning developed by the Sherpa authors. Electroweak radiative corrections to strong Vγ+jets production have been computed at NLO [56–58] as weights in Sherpa, and these are roughly −2% to −4% relative corrections in the chosen signal region. A second sample of Z(→νν)γ +jets was generated using MadGraph5_aMC@NLO [59] with the FxFx merging scheme [60] at NLO precision in αsfor up to one additional parton, filtered for photon pT>10 GeV, and showered using Pythia 8[61]. The difference between the Sherpa and MadGraph5_aMC@NLO Z(→νν)γ +jets predictions is symmetrized around the Sherpa prediction and is taken as a source of modelling systematic uncertainty. Matrix elements for the EW contribution were calculated at LO in αsusing MadGraph5_aMC@NLO 2.6.5, and the photon pTwas required to be larger than 10 GeV. Generated events were showered using Pythia 8[61] with the dipole recoil option enabled along with the CKKW-L [62,63] merging scheme. These EW samples are normalized to NLO QCD predictions obtained from VBFNLO [64] through a correction which depends on the dijet invariant mass (mjj). The effect of the QCD factorization and renormalization scale choices is evaluated from the same NLO QCD process calculation in VBFNLO.TheMadGraph5_aMC@NLO 2.6.5 EW samples include VBS contributions (shown in Fig. 1b) and triboson contributions (shown in Fig. 2c) which can depend on trilinear and quartic gauge couplings. The triboson processes contribute as much as 15% of the EW samples for low mjj values, 250 <mjj <500 GeV, but less than 3% in the more signal-like high-mjj region. The interference between the EW and strong-production diagrams, which is of order αsα4, was simulated at LO in αsin MadGraph5_aMC@NLO 2.6.5 and the corresponding events were showered using Pythia 8 with the dipole recoil shower enabled. This simulated sample is not included in the background predictions but is used to calculate an uncertainty in the EW Vγ+jets contribution, which is 5% or less in the mjj >500 GeV kinematic region. Similarly, the EW production of a Wor Zboson in association with two photons was found to be less than 2% of the EW Vγ+jets samples calculated with MadGraph5_aMC@NLO 2.6.5, so it is not included. The whole Vγ+jets simulation (i.e. both EW and strong production) applies smooth-cone isolation [65] with a cone size of 0.1 and parameters n=2 and =0.10 to remove the collinear singularity between photons and charged partons which would otherwise appear in the process amplitude calculations. 4.2 V+jets processes Simulation is used to model V+jets processes when the vector boson decays into neutrinos, muons or τ-leptons, and most of these simulated events are removed by the lepton vetoes, object overlap removal described in Sect. 5, and the removal of overlaps with Vγ+jets, which is described later in this section. Therefore, their contribution is very small. However, Vdecays into electrons enter the selection mostly through the electrons being misidentified as photons, and this is modelled using the fully data-driven method described in Sect. 7.1. The strong-production V+jets sample was simulated with the Sherpa 2.2.7 event generator with the NNPDF3.0nnlo set of PDFs [55]. Parton-shower matching [50] was performed using either the MEPS@LO or MEPS@NLO prescription with associated parameters tuned by the Sherpa authors. The strong production of V+jets uses NLO matrix elements for up to two partons and LO matrix elements for up to four partons calculated with the Comix and OpenLoops libraries and the MEPS@NLO prescription. The samples are normalized to a next-to-next-toleading-order (NNLO) prediction for V+jets [66]. The EW V+jets sample was generated at NLO in αs,usingHerwig 7 [67] to perform the parton shower and hadronization with the MMHT2014 2014nlo68cl PDF set [68]. Herwig 7 uses its Matchbox module [69] to assemble calculations with dipole shower algorithms [70] and interfaces with matrix element plug-ins from VBFNLO to compute NLO αscorrections in the VBF approximation. After generating events for both the strong and EW Vγ+ jets processes as in Sect. 4.1, the samples may overlap with V+jets events in which an ISR/FSR photon is radiated. To avoidthisoverlap, Vγ+jetseventsareremovedifthephoton passes the smooth-cone isolation and lies within R=0.1 of an electron, muon, or τ-lepton that has pT>10 GeV. In V+jets samples, events are accepted only if they satisfy the same criteria. 4.3 Top-quark processes Minor background contributions originating from top-quarkrelated processes and associated production of top quarks witha Wboson,wereallmodelledusingthe Powheg Box v2 [71–73] generator at NLO with the NNPDF3.0nlo PDF set. The events were interfaced with Pythia 8.230 for the parton shower and hadronization modelling with the A14 tune [74] and the NNPDF3.0nlo set of PDFs. The production of t¯ tγwasmodelled using the MadGraph5_aMC@NLO 2.2.3 generatoratNLO.TheeventswereinterfacedwithPythia 8.186 for the parton shower and hadronization modelling with the A14 tune and the NNPDF2.3lo set of PDFs. The decays of bottom and charm hadrons were performed by EvtGen 1.6.0 [75] in all top-quark processes. 123 Eur. Phys. J. C (2022) 82 :105 Page 7 of 41 105 4.4 Additional background samples The γ+jet background is simulated using Sherpa 2.2.2 at NLO in αs, similarly to the Sherpa V+jets samples in Sect. 4.1 except for the use of a dynamical merging scale to capture the fragmentation contribution [76]. Due to the large cross-section for this process, a partially data-driven ‘jetsmearing’ technique was used to increase the sample size as discussed in Sect. 7.1. Other processes listed in Table 1but not described in the previous subsections result in a negligible contribution to the analysis signature. Therefore, no further description is given. 4.5 Higgs boson processes In the searches for H→inv.carried out in this paper the target is VBF Higgs boson production, although the small contribution from gluon–gluon fusion (ggF) Higgs boson production processes satisfying the selection criteria is also considered as a contributing signal. For both of these processes, corresponding MC samples were generated according to the details described in the following. The invisible Higgs boson decay was simulated using the SM H→ZZ∗→4νdecay with a 100% branching ratio. The difference in the relevant kinematic distributions between the H→4νprocess and Higgs boson decays into new undetected particles is negligible. The VBF Higgs boson production process with an additional photon, as shown in Fig. 2a, was simulated for a Higgs boson mass of 125 GeV, requiring the presence of only electroweak vertices at LO and photon pTlarger than 10 GeV. This process was computed to NLO accuracy in αsusing MadGraph5_aMC@NLO interfaced with Herwig 7[67,77] for parton shower and non-perturbative hadronization effects, using the PDF4LHC15 PDF set [78]. Parton shower uncertainties are computed from the relative difference between the process generated by MadGraph5_aMC@NLO at LO in αswith showering by Herwig 7 and the same process with showering by Pythia 8[79] with the dipole recoil shower variable [80] turned on. The parton shower comparison is not made at NLO because the dipole recoil option in Pythia 8 is available only at LO, and without it there is a larger prediction of central emissions.4 The same smooth-cone isolation as described in Sect. 4.1 is used to remove the collinear singularity between photons and charged partons. 4The option gives an alternative approach to local recoils, where only one final-state parton takes the recoil of an emission. The dipole recoil option has been shown to better model the CMS data in VBF Z→  processes [81,82]. When it is used, it improves the modelling of radiative emissions from non-colour-connected partons (the VBF jets), which are poorly modelled by Pythia 8 when it is turned off. The ggF Higgs boson production process was simulated at NNLO accuracy in αsusing Powheg NNLOPS [71–73,83,84], which achieves NNLO accuracy for arbitrary inclusive gg →Hobservables by reweighting the Higgs boson rapidity spectrum in MJ-MiNLO [85–87]to that in HNNLO [88]. The PDF4LHC15 PDF set [78] and the AZNLO tune of Pythia 8 were used. This simulation was interfaced with Pythia 8 for parton shower and nonperturbative hadronization effects. The ggF prediction from the MC samples is normalized to the next-to-NNLO crosssection in QCD plus electroweak corrections at NLO [89– 99]. Photons present in these samples were generated using Photos [100,101] since no complete matrix element computation of ggF Higgs boson with a photon is available.5 The simulation of ggF production of a 125 GeV Higgs boson described above is also used to model its decay into a photon and an invisible massless dark photon (γd)again normalized to a 100% branching ratio. The VBF production process was simulated to NLO precision in αswith the Powheg generator interfaced with Pythia 8 for hadronization and showering and the same γγ ddecay, as shown in Fig. 2b. The NLO electroweak corrections for VBF Higgs boson production were computed using HAWK [102] and were applied as a function of the Higgs boson’s pT.The VBF samples were generated not only for a 125 GeV Higgs boson, but also for lighter and heavier Higgs bosons, for the interpretationofthesearchinthecontextofotherscalarmediators. Throughout this paper, the samples with a Higgs boson assume SM couplings and use the narrow width approximation [89] for the various Higgs boson masses, ranging from 60GeVto2TeV. 5 Object reconstruction Objects are reconstructed from detector signatures by using identification algorithms widely deployed in ATLAS analyses. Candidate events are required to have a reconstructed vertex with at least two associated tracks, each with pT> 0.5 GeV and originating from the beam collision region in the x–yplane. The primary vertex in the event is selected as the vertex with the highest scalar sum of the squared pTof associated tracks [103]. Electrons are reconstructed by matching clustered energy deposits in the EM calorimeters to tracks in the ID [104], including the transition regions between the barrel and endcap EM calorimeters at 1.37 <|η|<1.52. Electron candidates must have pT>4.5 GeV and |η|<2.47, and fulfill loose identification criteria. Depending on the pTand |η| range, muons are reconstructed by matching ID tracks to MS 5The Powheg sample does not include photon radiation from charged particles running in the Higgs boson production loop. 123 105 Page 8 of 41 Eur. Phys. J. C (2022) 82 :105 tracksortracksegments,bymatchingIDtrackstoacalorimeter energy deposit compatible with a minimum-ionizing particle,orbyidentifyingMStracks passing a loose requirement andcompatiblewithoriginatingfromtheIP[105].Muoncandidates must have pT>4 GeV and |η|<2.7, and fulfill a very loose identification criterion. No isolation requirement is placed on electron or muon candidates used as a lepton veto. In events with one or more leptons associated with the primary vertex, i.e. in control regions described in Sect. 6, muons(electrons)arerequiredtosatisfymedium(tight)identificationcriteria inordertoimprovethepurityofbackground processes. Photoncandidatesarereconstructedfromclusteredenergy deposits in the EM calorimeter [104]. They must have pT>15 GeV, fulfill tight identification and isolation criteria [104], and lie within |η|<2.37 but not in the transition region (1.37 <|η|<1.52) between barrel and endcap EM calorimeters. Particle flow (PFlow) jets are reconstructed using the antiktalgorithm [106,107] with a radius parameter of R=0.4, using charged constituents associated with the primary vertex and neutral PFlow constituents as inputs [108]. The jet energy is calibrated with the effect of pile-up removed [109]. Jets are required to have pT>20 GeV and |η|<4.5. For jets with pT<60 GeV and |η|<2.5 the jet vertex tagger (JVT) discriminant [110] is used to identify jets originating from the HS interaction through the use of tracking and vertexing. The chosen JVT working point corresponds to a selection efficiency for HS jets of about 97%, evaluated on an inclusive Z(→μμ) + jets sample. For |η|>2.5, the two leading jets must pass a forward jet vertex tagger algorithm (fJVT) [111,112] that accepts 93% of jets from the HS interaction and rejects about 58% of pile-up jets with pT>50 GeV, evaluated on an inclusive Z(→μμ) + jets sample. Jets containing b-hadrons (b-jets) are identified using a multivariate discriminant (MV2c10) output distribution [113]. The working point is chosen to provide a 77% b-jet efficiency on an inclusive t¯ tsample, with rejection factors of 6 and 134 for charm-hadron jets and light-flavour quarkor gluon-initiated jets, respectively. To avoid double counting of energy deposits, the reconstructed objects are required to be separated according to the procedure detailed in Table 2. The overlap of photons with electrons, muons and jets is resolved by a Rcriterion. For leptons in the vicinity of jets, the Rthreshold for sufficient separation depends on the pTof the lepton to account for the collimation of boosted objects. The unbalanced momentum in the transverse plane, referred to as missing transverse momentum or  Emiss T,is defined as the negative vectorial sum of the transverse momenta of all selected electrons, muons, photons, and jets, as well as tracks compatible with the primary vertex but not matched to any of those objects, this last contribution Table 2 Overview of the overlap removal between objects and the corresponding matching criteria, listed according to decreasing priority Remove Keep Matching criteria Electron Electron Shared inner-detector track, electron with lower pTremoved Muon Electron Muon with calorimeter deposits and shared inner-detector track Electron Muon Shared inner-detector track Photon Electron R<0.4 Photon Muon R<0.4 Jet Electron R<0.2 Electron Jet R<min(0.4,0.04 +10 GeV/pe T) Jet Muon Number of tracks <3andR<0.2 Muon Jet R<min(0.4,0.04 +10 GeV/pμ T) Jet Photon R<0.4 being called the soft term [114,115]. To define an estimate of the boson pTin decays with charged leptons, events containing one or more selected leptons have the  Emiss Tevaluation modified by treating such leptons as invisible particles. Each prompt lepton pTis vectorially added to the  Emiss Tto define the quantity  Emiss,lep-rm T, as described in Ref. [115]. The magnitude of the  Emiss T( Emiss,lep-rm T) is denoted by Emiss T (Emiss,lep-rm T). A related event property Ejets,no-jvt Tis the magnitudeofthenegativevectorialsumofalljetsintheeventwith pT>20 GeV before the JVT requirement. This is a powerful variable for rejecting events where the Emiss Tis generated by inefficiencies of the JVT requirement for HS jets. Several cleaning requirements are applied to suppress non-collision backgrounds [116]. Misreconstructed jets can be caused by electronic noise, and jets from collisions are identified by requiring a good fit to the expected pulse shape for each constituent calorimeter cell. Beam-halo interactions with the LHC collimators are another source of misreconstructed jets. Those jets are identified by requirements on their energy distribution in the calorimeter and the fraction oftheir constituent tracks that originate from the primary vertex. The event is rejected if any selected jet is identified as a misreconstructed jet. Residual contributions of non-collision jets are absorbed into the normalization for the γ+jet background as described in Sect. 7.1. 6 Event selection Based on the reconstructed objects in each event final state, the collected data are assigned to disjoint samples identified with specific phase-space regions, used in this analysis for different purposes. The signal regions (SRs) have the highest purity of signal process events, with mostly irreducible back123 Eur. Phys. J. C (2022) 82 :105 Page 9 of 41 105 ground contributions. The control regions (CR) are enriched in background processes and are used to constrain estimates of such contributions. The validation regions (VR), similar in background process content to the CRs, are used to quantify the level of agreement between data and background predicted yields but are not included in the fit. A baseline set of requirements is applied to select events with a photon, high Emiss T, and the VBF jet signature considered in this paper, as described in Sect. 6.1.FortheEW Zγ+jets cross-section measurement, events satisfying the baseline SR requirements are categorized according to their dijet invariant mass mjj, as described in Sect. 6.2.Inthe same section the fiducial volume considered for the crosssection measurement is defined. The SR-selected events for the H→inv.search are split into categories of different signal purities based on a multivariate analysis discriminant, which is described in Sect. 6.3. The SR selection and fitted discriminant are modified for the resonant kinematics of the H→γγ dsearch, which are described in Sect. 6.4. In the statistical analysis of the data, described in Sect. 8, CR events are classified according to the same strategy described for the signal regions in the aforementioned measurement and searches. 6.1 Baseline event selection Stringent background discrimination is made possible by the characteristic features of the VBF process, such as the presence of two highly energetic jets, typically in opposite η hemispheres of the detector, more forward than jets from non-VBF processes at comparable momentum transfer of the initial-state partons. These features lead, for example, to large values of the pseudorapidity separation ηjj and invariant mass mjj of the jet pair. Multijet production predicted by QCD is instead characterized by two back-to-back leading jets in the transverse plane (φjj ∼π); therefore, to reduce that background contribution, the azimuthal separation of the leading jets, φjj, is required to be smaller than 2.5 for all SRs. The requirements defining the different regions considered in the analysis are summarized in Table 3. The following section describes the selection criteria. The photon produced in association with either the Higgs boson (for the H→inv.search) or the Zboson (for the EW Zγ+jets cross-section measurement) is usually radiated from the scattering Wbosons, and it is produced within the large rapidity gap between the two leading jets. For this reason the photon centrality Cγ[117] is defined as Cγ=exp−4 (η1−η2)2ηγ−η1+η2 22,(1) wherethesubscripts1and2indicate the highestand secondhighest pTjets in the event. The value of Cγis 1 when the photon is centred between the two jets characterizing the VBF signature,1/ewhen it is aligned with one of the two jets, and tends to zero when the photon is farther forward in |η|than the jets. EventsareassignedtotheSRiftheysatisfyasetofrequirements that have been optimized to maximize the sensitivity of the analysis to the EW Zγ+jets and VBF H→inv.signals. These requirements are summarized in the following. As discussed in Sect. 3, events are selected with the Emiss Ttrigger algorithm. To ensure a trigger efficiency exceeding 97%inthistopology,theoffline Emiss T,afterfullofflinereconstruction and calibration of all the objects in the events, is required to be larger than 150 GeV. Corrections and uncertainties in those corrections to the simulation modelling of the Emiss Ttrigger are discussed in Sect. 7.2. The leading and subleading jets are required to have pT>60 GeV and 50 GeV, respectively, both satisfying the fJVT requirements mentioned in Sect. 5. These same two leading jets must be located in opposite ηhemispheres (η(j1)×η( j2)<0), to be well separated in pseudorapidity (|ηjj|>3.0) and not back-to-back in the plane transverse to the beamline (φjj <2.5), and must have large invariant mass (mjj >0.25 TeV). Another characteristic of the EW processes in the VBF topology is reduced hadronic activity in the large rapidity gap between the two leading jets, caused by the absence of colour connection between the two quarks. To suppress the contribution from strong Vγ+jets production with additionaljetsfromQCDradiation in comparison withthebenchmark signals, the equivalent centrality C3is defined for the third-leading jet in the event, if any, replacing ηγin Eq. (1) with the third-leading jet’s pseudorapidity η3. A third jet with pT>25 GeV can be present in the events, and additional jets are allowed only if they have pT<25 GeV. The thirdleading jet is required to be in one of the two forward regions, corresponding to a small centrality value, C3<0.7. All jets must be well separated in azimuth from the  Emiss T direction, satisfying φ( ji, Emiss T)>1 for each jet jiwith pT>25 GeV. At most one b-jet identified using the algorithm defined in Sect. 5is allowed to be present, and the Ejets,no-jvt Tvariablemustbelarger than130GeVineachevent. Therequirementon themaximumnumber ofb-jetshasanegligible effect (<0.1%) on the signal selection efficiencies, while it ensures that the dataset considered in the search for H→inv.produced through VBF presented in this paper is orthogonaltothedatasetconsideredinthesearchforinvisible decaysofHiggsbosonsproducedinassociationwitht¯ t[118]. Each event must contain a single reconstructed photon with 15 <pT<110 GeV, φ(  Emiss T,γ) > 1.8, and Cγ> 0.4. The upper bound on the photon pTreduces contributions 123 105 Page 16 of 41 Eur. Phys. J. C (2022) 82 :105 Several experimental uncertainties impact the sensitivity of the analyses presented in this paper. They are grouped into categories: uncertainties in the luminosity, uncertainties in the trigger efficiencies, and uncertainties related to the reconstruction of physics objects such as electrons, muons, jets, and the Emiss T. A summary of the systematic impact on the measured signal strength or limits set by this search is reported in Table 7. Theuncertaintyintheluminosity is 1.7% [36] and impacts the signal yield and the simulated background yield. The Emiss Trequirement of 150 GeV in the SR is key to maximizing the sensitivity of the analysis. The Emiss Ttriggers are not fully efficient, so systematic uncertainties are used to account for possible trigger efficiency differences between data and simulation. This is done by comparing the combined L1+HLT trigger efficiency as a function of Emiss,lep-rm Tfor simulated W(→μν) +jets events and data events, both selected with single-muon triggers. Neither the Emiss Ttrigger nor the offline Emiss Treconstruction includes muon momenta in their calculations. The Emiss Ttrigger has an efficiencyofroughly81%at Emiss T=150GeV and>99%for Emiss T>200 GeV in simulation. The Emiss T-trigger efficiencies for simulated W(→μν) +jets, W(→μν)γ +jets, and Z(→νν)γ +jetsarefoundtobestatisticallyconsistentinall the considered regions, so the same correction for differences betweenthedataandsimulationtriggerefficienciesisapplied to all simulated events passing the Emiss Ttrigger. The correction as a function of Emiss Tvaries from around (3–6)% ±4% at Emiss T=150 GeV to less than 0.4% ±1% for Emiss T> 200 GeV depending on the specific Emiss T-trigger algorithm used in a given data-taking period. The uncertainty in the correction comes from the data statistical uncertainties used to derivethe correction.Forthe Wγ ν CR scalefactorsand uncertainties in events passing lepton triggers, the corresponding single-lepton triggers corrections are applied [39,40]. Systematic uncertainties are calculated for lepton reconstruction and isolation efficiencies [104,105] and for the energy scale and resolution [104]. For the electron (muon) veto, an uncertainty in the electron (muon) reconstruction inefficiency is taken into account. For jets, uncertainties are derived in the energy scale and resolution [109] and for the pile-up tagging efficiencies [39,110]. For the photon, uncertainties in the reconstruction, isolation, energy scale and resolution [104,126] are considered. The above uncertainties associated with the reconstructed objects are propagated to the calculation of Emiss T, as is the uncertainty in the scale and resolution of the Emiss Tsoft term [115]. 8 Fit models and results The statistical analysis carried out has two objectives: first measuring the EW Zγ+jets production cross-section, and then searching for evidence of BSM physics in specific models involving invisible or semi-visible decays of the Higgs boson. The different processes of interest are compared to data using a profile-likelihood-ratio test statistic in a frequentist approach. A maximum-likelihood fit to the observed data in each bin of the event classification described in Sects. 6.2, 6.3, and 6.4 is used to set constraints on the signal strength μfor each model considered, all using asymptotic formulae [127]: a two-sided confidence level (CL) interval with the CLsdefinition [128] is extracted for the EW Zγ+jets cross-section measurement, while one-sided confidence levels calculated with the same approach are considered to set upper limits on new physics contributions. Each bin iof the SR is assumed to include a number of events Niwhere the total expected background yield is Bi and the signal contribution is Si. A likelihood function Lis defined as L= i∈bins P(Ni|Bi(−→ θ)+μSi(−→ θ)) · j∈syst. G(0|θj)Bi(−→ θ)= k∈bkg.comp. βi,k·Bi,k(−→ θ) (2) where P(x|ν) is the Poisson probability density function, G(x|θ)is the probability density function of a Gaussian with unit width, and θjrepresents the nuisance parameters corresponding to each considered uncertainty. The expected background yield in a given bin, Bi, is given by the sum of several contributions, where a normalization factor βfor each background component is included. The βfactors represent the overall normalization of a given background contribution estimate. In the maximum-likelihood fit such normalization factors can be either fixed to 1 or left floating in the maximization.Thetreatmentof these factorsinthe statistical analysis framework is detailed in the following for each scenario considered. In the framework of the EW Zγ+jets crosssection measurement, this process is considered as the signal and its corresponding βfactor is replaced by the parameter of interest μZγEW . In the framework of the searches for invisible or semi-visible decays of the Higgs boson, expected signal yields are evaluated with the assumption Binv =1or B(H→γγ d)=1, which allows the parameter of interest μ to directly determine the actual Higgs boson decay branching fraction to the considered invisible or semi-visible particles.6 The signal considered in this framework is normalized to the SM cross-section for Higgs boson production. The expected yields depend not only on Biand Sibut also on the nuisance parameters, although these parameters are constrained in the likelihood function by the G(0|θj)factors. Some of 6When small signal contaminations are expected in a CR, these are correctly accounted for in the statistical analysis. 123 Eur. Phys. J. C (2022) 82 :105 Page 17 of 41 105 the systematic uncertainties affecting background and signal predictions vary the final observable by less than 0.1% and these are ignored to improve the stability of the fit with no loss of accuracy. Each experimental uncertainty source is taken to be fully correlated across all signal and control regions. The applied correlation of theory systematic uncertainties depends on the type of uncertainty. PDF uncertainties are treated as fully correlated across bins. The uncertainty in the interference between the EW and strong Z(→νν)γ +jets processes is treated as a fully correlated one-sided uncertainty in the EW Z(→νν)γjj process. The parton showering in each of the four Vγ+jets samples (EW and strong-production componentsof Wγ+jetsand Zγ+jets)iscorrelatedacrossallbins and similar for the scale variations in the strong-production Vγ+jets samples, except the scale uncertainties in the onelepton CRs which are not correlated with the other bins. A separate nuisance parameter for the latter is motivated by the less than 1% background contribution to the one-lepton CR, and the contribution due to missing one of the leptons. Scale uncertainties for EW Zγjj and EW Wγjj are treated as uncorrelated among regions and correlated in bins of the same region to avoid constraining this source of uncertainty. Within rounding, no change in the measured significance nor in the extracted limits was found compared with correlating these uncertainties across all analysis bins. 8.1 Fit model and results for the EW Zγ+jets cross-section measurement ThesignatureconsideredinthispaperhasasignificantcontributionfromEW Z(→νν)γjjproduction,whichhasnotbeen observed previously. A measurement of the cross-section for this process is an important first step, as a result complementary to the prior SM CMS observation of EW Z(→)γ jj [10]. No BSM signal contributions are considered in this subsection. For this measurement events are categorized into four mjj bins, as described in Sect. 6.2, to profit from differences between the kinematic distributions of EW Zγ+jets production and strong Zγ+jets production. The statistical analysis of data entering either the SR, Wγ μν CR, Wγ eνCR, Zγ Rev.Cen.CR, or Fake-eCR is performed according to their mjj bins, expanding the likelihood function defined in Eq. (2) as LμZγEW ,βZγstrong ,β Wγ,−→ θ = i∈SR bins PNi|μZγEW Si,ZγEW +βZγstrong Bi,Zγstrong +βWγBi,Wγ+Bi,others × k∈CR bins PNWγ eνCR k|βWγBWγ eνCR k,Wγ+BWγ eνCR k,others +βk,fake-eBFake-eCR k,fake−eRfake-e × k∈CR bins PNWγ μν CR k|βWγBWγ μν CR k,Wγ+BWγ μν CR k,others  × k∈CR bins P(NZγ Rev.Cen.CR k|μZγEW SZγ Rev.Cen.CR k,ZγEW +βZγstrong BZγ Rev.Cen.CR k,Zγstrong +βWγBZγ Rev.Cen.CR k,Wγ+BZγ Rev.Cen.CR k,others  × k∈CR bins PNFake-eCR k|βWγBFake-eCR k,Wγ +BFake-eCR k,others +βk,fake-eBFake-eCR k,fake-e × j∈syst. G(0|θj)(3) The EW Zγ+jets signal contribution entering the Zγ Rev.Cen.CR is taken into account in the statistical analysis. The fake-electron background in the CR bin at high Emiss T is determined by the product of Bfake-eand the transfer factor Rfake-e(see Sect. 7.1). The symbol BFake-eCR fake-erepresents the number of events with a fake electron in the corresponding bin of the Fake-eCR at low Emiss T. For this measurement, in addition to the parameter of interest μZγEW ,the normalization factors βZγstrong and βWγcorresponding to the strong-production Zγ+jets component and, inclusively, to the Wγ+jets component of the investigated distribution respectively, are allowed to float in the fit. The result of the maximum-likelihood fit to data in the 4 SR bins and 16 CR bins is shown in Fig. 3, with the bestfit model propagated in all the regions. The SR bin-by-bin yields and CR yields are shown in Table 5for the SM process contributions and data. The level of agreement between the data and the prediction from background simulation is good overall and is better after the fit, as shown in the lower panel of Fig. 3. The best-fit values of the three free-floating normalization factors appearing in Eq. (3) are reported in Table 6.In particular, the EW Zγ+jets normalization best-fit value is 1.03±0.16(stat)±0.19(syst)±0.02(lumi). The excess over the background-only hypothesis is quantified by a p-value using the profile likelihood ratio, evaluated at μZγEW =0, as a test statistic. EW Zγjj is observed with a significance of 5.2σwith respect to the other SM background processes, and the expected significance is 5.1σ. The statistical component of the uncertainty includes only the data statistical uncertainty with other sources such as the limited number of 123 105 Page 18 of 41 Eur. Phys. J. C (2022) 82 :105 Fig. 3 Post-fit results for all mjj SRandCRbinsintheEW Zγ+jets cross-section measurement as defined in Eq. (3)withtheμZγEW signal normalization floating. The post-fit uncertainties include statistical, experimental, and theory contributions. The lower panel shows the ratio of data to the sum of all the SM process predictions and also compares the pre-fit and post-fit predictions Table 5 Data yields and fitted predictions, after the fit to 139fb−1of data with the μZγEW signal normalization floating as defined in Eq. (3), for the four mjj bins of the SR and the inclusive CRs. The uncertainties in the SM processes are derived by the fit and include the effects of nuisance parameter constraints and the correlation of systematic uncertainties. The individual uncertainties are correlated and do not necessarily add in quadrature to equal the total background uncertainty. A dash ‘–’ indicates less than 0.01 events Process Fake-eCR Wγ eνCR Wγ μν CR Zγ Rev.Cen.CR SR – mjj [TeV] 0.25–0.5 0.5–1.0 1.0–1.5 ≥1.5 Strong Zγ+jets 8 ±80±13±250±12 20 ±654±12 13 ±55±2 EW Zγ+jets 0.6±0.20.3±0.20.4±0.27±24±130±725±536±7 Strong Wγ+jets 43 ±947±9 133 ±21 24 ±622±635±10 9 ±33±1 EW Wγ+jets 19 ±631±759±13 1.4±0.52±16±14±15±1 jet→γ1±12±23±22±21±12±21±10.4±0.3 jet→e34 ±17 5 ±3– – – – – – e→γ–2.7±0.42.9±0.413±16±111±12.6±0.41.4±0.3 γ+jet – – – 0.7±0.50.7±0.50.4±0.30.1±0.10.1±0.1 t¯ tγ/Vγγ 3±19±213±23±12±14±10.4±0.20.1±0.1 Fitted Yields 108 ±10 96 ±8 213 ±14 102 ±958±6 143 ±12 54 ±552±6 Data 108 95 216 100 52 153 50 52 Data/Fit 1.00 ±0.14 0.99 ±0.12 1.01 ±0.09 0.98 ±0.13 0.90 ±0.15 1.07 ±0.11 0.93 ±0.16 0.99 ±0.18 Table 6 Thebest-fitvalues and corresponding uncertainties of the three free-floating normalization factors derived from the statistical analysis described by Eq. (3) μZγEW βZγstrong βWγ 1.03 ±0.25 1.02 ±0.41 1.01 ±0.20 simulated events and the normalization of the backgrounds included in the systematic component of the uncertainty. The impact on the measurement of μZγEW from different groups of uncertainties is shown in Table 7. It is evaluated by repeating the fit procedure, after fixing the nuisance parameters corresponding to each group of systematic uncertainties, in turn, to their best-fit values, and subtracting the new variance(σ2)ofthebest-fitvalueofμZγEW fromtheoriginal variance.Thedatastatisticaluncertaintyhasthelargestimpacton the measured signal strength, followed by the signal acceptance uncertainties. A small correlation is observed among the different sources of uncertainty. The signal uncertainties are divided into acceptance uncertainties for the signal events entering the fiducial volume and the shape uncertainties, which are the uncertainties in the shape of signal distributions within the fiducial volume. The signal acceptance uncertainties are assigned to the theoretical cross-section and not to the fiducial cross-section. The measured fiducial cross-section is extracted by taking the product of the signal strength, μZγEW , and the predicted cross-section times branching ratio to neutrinos in the fiducial volume defined in Sect. 6.2. The measurement 123 Eur. Phys. J. C (2022) 82 :105 Page 19 of 41 105 Table 7 The contributions from different groups of systematic uncertainties to the ±1σuncertainty bands of the μZγEW best-fit value and on Binv and B(H→γγ d)95% CL limits. The evaluation is performed by fixing a given group of systematic uncertainties to their best-fit values and subtracting the new variance (σ2) of the best-fit value or the limit from the nominal variance including all systematic uncertainties. Due to residual correlations between categories, the sum in quadrature of the systematic uncertainties can differ from the actual value. The uncertainty due to the finite number of data events (‘Data stats.’) is obtained by fixing all systematic uncertainties to their best-fit values. The sum of all systematic uncertainties is estimated by subtracting the statistical variance component from the total variance. The experimental uncertainties and the uncertainty related to the size of MC simulated samples (‘MC stats.’) are treated as separate categories. The Vγ+jets theory entry includes the theoretical uncertainties in strong Zγ+jets, EW Wγ+jets and strong Wγ+jets production for μZγEW ;however,for Binv and B(H→γγ d), it also includes those from EW Zγ+jets. For the last two columns the impact of systematic uncertainties is computed from a fit to data with Binv =0orB(H→γγ d)=0 for each respective column Source 1σUncertainty on μZγEW 1σUncertainty on Binv 1σUncertainty on B(H→γγ d) Jet scale and resolution 0.076 0.045 0.0011 Vγ+jets theory 0.067 0.044 0.0018 pile-up 0.040 0.021 0.0004 Photon 0.035 0.031 0.0011 e→γ, jet→e,γ Bkg. 0.035 0.034 0.0028 Lepton 0.027 0.003 0.0008 Emiss T0.023 0.018 0.0003 Signal theory shape 0.020 – – Signal theory acceptance 0.12 – – Data stats. 0.16 0.11 0.0056 Wγ+ jets/Zγ+ jets Norm. 0.073 0.013 0.0004 MC stats. 0.063 0.046 0.0026 Total 0.25 0.15 0.0073 and SM prediction agree within the measurement uncertainties. The measured fiducial cross-section is σfid. Z(→νν)γEW = 1.31 ±0.20(stat) ±0.20(syst) fb, which includes the contribution from the interference term with the strong production of Zγ+jets. The interference computed through MadGraph is 2% in the fiducial volume and is treated as an uncertainty in the EW Zγ+jets cross-section. The theoretical MadGraph cross-section including the 0.3% NLO QCD K-factor correction from VBFNLO is 1.27 ± 0.01(stat)±0.17(LO QCD MadGraph scale)±0.03(pdf) fb =1.27±0.17 fb. The jet-veto is not part of the fiducial phasespace definition; the loss in efficiency in simulation for this veto is 5%. 8.2 Fit model and results for H→inv.search In the search for H→inv., events are categorized into four bins according to the DNN output score. These bins enter the likelihood function definition in Eq. (2). In addition to the SR bins, the correspondingly binned Wγ eνCR, Wγ μν CR, Zγ Rev.Cen.CR, and Fake-eCR are included in the likelihood function definition to provide constraints on the background contribution to the SR. The signal contribution in the Zγ Rev.Cen.CR is taken into account in the statistical analysis. In the likelihood function definition, all the normalization factors βfrom Eq. (3) are fixed to one except the ones corresponding to the Wγ+jets and fake-ebackground contributions. The μZγEW normalization factor is fixed to one because the shape of this contribution and the one of the H→inv.signal aresosimilar thatleavingtheformer unconstrained would largely affect the search sensitivity. The result of the EW Zγ+jets cross-section measurement described in Sect. 8.1 further supports this assumption. The βZγstrong normalization factor is fixed to one because the CR yields are not large enough to reduce the theoretical uncertainties. In addition, the observed normalization in the EW Zγ+jets cross-sectionmeasurementisconsistentwithunityinTable6. The likelihood is Lμ, βWγ,β fake-e,−→ θ = i∈SR bins PNi|βWγBi,Wγ +Bi,Zγ+Bi,γ +jet +Bi,others +μSi × k∈CR bins PNWγ eνCR k|βWγBWγ eνCR k,Wγ+BWγ eνCR k,non-W +βk,fake−eBFake-eCR k,fake-e Rfake-e × k∈CR bins PNWγ μν CR k|βWγBWγ μν CR k,Wγ+BWγ μν CR k,non-W × k∈CR bins−1 PNZγ Rev.Cen.CR k|BZγ Rev.Cen.CR k,TOT. +μSZγ Rev.Cen.CR k × k∈CR bins PNFake-eCR k|βWγBFake-eCR k,Wγ +BFake-eCR k,non-W+βk,fake-eBFake-eCR k,fake-e  × j∈syst. G(0|θj), (4) where BZγ Rev.Cen.CR k,TOT. is the sum of the expected background yields in the bin kof the Zγ Rev.Cen.CR, and Bk,Wγis the sum of the EW and strong Wγ+jets events with their ratios fixed from theoretical predictions. Because of a very small 123 105 Page 20 of 41 Eur. Phys. J. C (2022) 82 :105 Fig. 4 Post-fit results for all DNNSRandCRbinsinthe search for H→inv.as defined in Eq. (4)withtheBinv signal normalization set to zero. For the Zγ Rev.Cen.CR, the third bin contains all events with DNN output score values of 0.6–1.0. The H→inv.signal is scaled to a Binv of 37%. The post-fit uncertainties include statistical, experimental, and theoretical contributions. The lower panel showstheratioofdatatothe post-fit yields and also compares the pre-fit and post-fit background predictions Table 8 Data yields and background predictions, after the fit to 139fb−1of data with the Binv signal normalization set to zero, for the four DNN output score bins of the SR and the inclusive CRs. The uncertainties in the backgrounds are derived by the fit and include the effects of nuisance parameter constraints and the correlation of systematic uncertainties; as a result, the uncertainties in the total background can be smaller than the sum of those in the single contributions. The predicted signal yields, assuming a 37% branching ratio for H→inv. are shown with their associated uncertainties. A dash ‘–’ indicates less than 0.01 events Process Fake-eCR Wγ eνCR Wγ μν CR Zγ Rev.Cen.CR SR – DNN output score 0–0.25 0.25–0.6 0.6–0.8 0.8–1.0 Strong Zγ+jets 7 ±40.3±0.13±155±631±653±10 10 ±20.9±0.2 EW Zγ+jets 0.6±0.10.3±0.10.4±0.27±114±239±529±410±2 Strong Wγ+jets 44 ±746±6.1 127 ±13 20 ±229±631±98±20.1±0.2 EW Wγ+jets 21 ±335±466±71.5±0.25±18±15±11.2±0.3 jet→γ1±12±12±22±12±22±20.7±0.8– jet→e32 ±15 4 ±2–– –––– e→γ–2.6±0.22.9±0.213±19±19±11.9±0.20.3±0.1 γ+jet – – – 1.4±0.50.7±0.50.6±0.40.04 ±0.03 – t¯ tγ/Vγγ 3±18±112±23±14±12.4±0.40.9±0.20.01 ±0.01 Fitted Bkg 108 ±10 97 ±7 214 ±14 101 ±793±8 145 ±11 55 ±513±2 H(Binv =0.37) – – – 3.3±0.42.6±0.315±214±27±1 Data 108 95 216 100 94 146 51 16 Data/Fit 1.01 ±0.14 0.97 ±0.12 1.01 ±0.09 0.98 ±0.12 1.01 ±0.13 1.01 ±0.11 0.92 ±0.15 1.25 ±0.35 yield in the fourth bin of the Zγ Rev.Cen.CR for the Binv search, the third and fourth bins are merged into one bin covering 0.6–1.0 in DNN output score. The result of the maximumlikelihood fit to data in the 4 SR and 15 CR bins is shown in Fig. 4, with the best-fit model propagated in all the regions. The SR bin-by-bin yields and CR yields are shown in Table 8 for the background contribution, a benchmark H→inv.signal contribution, and recorded data. The fitted normalization of the sum of the EW and strong Wγ+jets events relative to the SM prediction is 1.07 ±0.18; the fake-electron normalization is not reported because no comparison with the SM predictions is possible. The level of agreement between the data and the prediction from background simulation is good overall, and is better after the fit, as shown in the lower panel of Fig. 4. No evidence of a new physics contribution is visible on top of the background prediction. The observed (expected) upper limit on Binv is 0.37 (0.34+0.15 −0.10) at 95% CL. The impact on the limit from different groups of uncertainties is shown in Table 7, and the results are evaluated in the same way as for observation of EW Zγ+jets, described in Sect. 8.1, except that Binv is fixed to zero. 8.3 Fit model and results for H→γγ dsearch In the search for a Higgs boson decaying into a γγ dpair, the most powerful discriminating observable is the photon– Emiss Ttransverse mass mT(γ, Emiss T), so this observable is used to search for this new physics signal. The events enter123 Eur. Phys. J. C (2022) 82 :105 Page 21 of 41 105 ing the dedicated SRγd(see Sect. 6) are separated into five mTbins, as described in Sect. 6.4. Because the relative contributions of H→γγ dsignal produced through ggF and VBF production vary with mjj, events are also separated into two mjj categories, those with mjj <1 TeV and those with mjj ≥1 TeV. A total of ten bins in the SR as well as ten bins in each CR enter the likelihood function definition, which is equivalent to the one in Eq. (4) other than having a different number of bins in the SR and CRs and a different signal benchmark model for the interpretation in the context of the H→γγ dsearch. The fixing of the βand μZγEW normalizationfactorsto unity inEq.(4)isrepeatedtobe consistent with Sect. 8.2, but allowing them to float in the fit does not change theresultswithinrounding.TheSRbin-by-binyieldsandCR yields are shown in Table 9for the background contribution and recorded data yields after a fit to the background-only contributions. Theresultofthemaximum-likelihoodfit withtheB(H→ γγ d)signal normalization set to zero in the ten SR bins and four inclusive CRs is shown in Fig. 5. The CRs are shown inclusively to reduce the number of bins presented, but the same binning as the SR is used in the fit model. The data and predictions from background simulation agree within the reported uncertainties, apart from a small deficit in the data in the bins corresponding to the highest mTvalues. The pre-fit background predictions in the highest mT bins are pulled down by the fit to data, and uncertainties describing these differences, which increase in this high mT range, come from the interference between EW and strong Z(→νν)γ +jets production as well as a comparison between MadGraph5_aMC@NLO and Sherpa simulation for the strong-production Z(→νν)γ +jets background contributions. Overall, the level of agreement is better after the fit, as shown in the lower panel of Fig. 5; no evidence of a new physics contribution is visible on top of the background prediction. Figure 6shows the distribution of mT(γ, Emiss T)in the inclusive SRγd(no mjj split), and also shows the shape of a H→γγ dsignal for two different mass hypotheses compared with same post-fit background predictions and data as for Fig. 5. Thus the reasons for the change in the pre-fit predictions for the highest mTvalues are the same as described for Fig. 5. Good agreement between data and the background expectationsinthemT(γ, Emiss T)distributionisobservedalso in the CRs considered in the statistical analysis. The statistical analysis sets an observed (expected) upper limit on B(H→γγ d)of 0.018 (0.017+0.007 −0.005) at 95% CL when considering both the VBF and ggF Higgs boson production mechanisms at a Higgs boson mass of 125 GeV. If considering a BSM scalar boson with a mass of 125 GeV produced through VBF, the observed (expected) upper limit on the cross-section times branching ratio is 0.064 pb (0.064+0.030 −0.019 pb) at 95%. For such a BSM scalar boson produced through ggF, the observed (expected) upper limit on the cross-section times branching ratiois 10.2 pb (7.3+3.4 −1.9pb) at 95%, which shows that the sensitivity is dominated by the VBF production mode. The 95% CL limit on σVBF ×B(H→γγ d)has also been calculated for a VBF-produced Higgs boson with different mass hypotheses in the narrow width approximation (NWA), ranging from 60 GeV to 2 TeV, as shown in Fig. 7. The crosssection for a VBF-produced Higgs boson decreases rapidly with increasing boson mass, leading to smaller signal yields in the SR. The signal corresponding to a high-mass scalar mediator peaks towards high values of mT(γ, Emiss T), where the smaller background leads to good sensitivity despite the small expected signal. The impact of various sources of uncertainty on the B(H→γγ d)upper limit is shown in Table 7, evaluated in the same way as for the H→inv.search, described in Sect. 8.2. The statistical uncertainty of the yields of data events in SRγdhas the largest impact on the limit determination. A negligible correlation is observed among the nuisance parameters corresponding to the different sources of uncertainty. 9 Conclusion Data collected from 139fb−1of 13 TeV proton–proton collisions by the ATLAS experiment during the Run 2 of the LHC are scrutinized in a VBF-favoured signature of two forward jets, Emiss T, and a photon, to provide constraints on several SM and BSM processes. The observation of SM EW Zγ+jetsproductionisreportedwithanobserved(expected) significance of 5.2σ(5.1σ). The fitted normalization for the EW Zγ+jets process relative to the SM prediction is μZγEW =1.03±0.25, corresponding to a measured crosssection of 1.31 ±0.29 fb in the considered fiducial volume. A search for Higgs bosons decaying solely into invisible particles is performed in the same final-state signature. Because no significant excess is observed, 95% CL upper limits of 0.37 (0.34+0.15 −0.10) are set on the observed (expected) branching ratio to invisible particles. A search for Higgs bosons decaying into a photon and a dark photon is also performed, and the results exclude at 95% CL cross-section times branching ratio values ranging from 0.15 pb for a scalar mediator with a mass of 60 GeV to 3 fb for a scalar mediator with a mass of 2 TeV. For a Higgs boson mass of 125 GeV, the observed (expected) 95% CL upper limit on the Higgs boson branching ratio to γγ dis 0.018 (0.017+0.007 −0.005), the most stringent to date. 123 105 Page 22 of 41 Eur. Phys. J. C (2022) 82 :105 Table 9 Event yields of data and background predictions, after the fit to 139fb−1of data with the B(H→γγ d)signal normalization set to 0, for the ten bins of the SRγdselection based on [mT,mjj] binning, and for the inclusive CRs. The uncertainties in the backgrounds are derived by the fit and include the effects of nuisance parameter constraints and the correlation of systematic uncertainties; as a result, the uncertainties in the total background can be smaller than the sum of those in the single contributions. The predicted signal yields, assuming the SM production cross-section for a 125 GeV Higgs boson and B(H→γγ d)=0.02, are shown with their associated uncertainties. A dash ‘–’ indicates less than 0.01 events Process Fake-eCR Wγ eνCR Wγ μν CR Zγ Rev.Cen.CR SR - mjj <1TeV mT[GeV] 0–90 90–130 130–200 200–350 ≥350 Strong Zγ+jets 38 ±63±28±273±12 29 ±730±729±722±55±1 EW Zγ+jets 7 ±10.9±0.20.8±0.213±210±29±114±212±24±1 Strong Wγ+jets 105 ±18 126 ±17 244 ±30 115 ±16 117 ±15 22 ±427±517±33±1 EW Wγ+jets 37 ±962±14 114 ±24 5 ±116±34±14±12.1±0.40.5±0.2 jet→γ4±35±46±55±410±83±21±11±10.1±0.1 jet→e46 ±21 6 ±2–– ––––– e→γ–5±16±1 160 ±14 179 ±15 20 ±25±12.8±0.30.5±0.1 γ+jet – – – 21 ±67±76±62±20.2±0.20.1±0.1 t¯ tγ/Vγγ 7±225 ±432±49±115±24±12.7±0.32.3±0.30.1±0.1 Fitted Bkg 245 ±16 233 ±11 411 ±18 398 ±19 363 ±15 97 ±884±759±512±2 VBF H125 (B(H→γγ d)=0.02) – – – 0.27 ±0.03 3.6±0.48.8±1.11.7±0.2– – ggF H125 (B(H→γγ d)=0.02) – – – 0.4±0.11.9±0.64.3±1.30.8±0.3– – Data 244 236 410 348 362 112 75 59 8 Data/Fit 1.00 ±0.09 1.01 ±0.08 1.00 ±0.07 0.88 ±0.12 1.00 ±0.07 1.15 ±0.14 0.89 ±0.13 1.00 ±0.16 0.65 ±0.25 Process SR – mjj ≥1TeV mT[GeV] 0–90 90–130 130–200 200–350 ≥350 Strong Zγ+jets 6 ±26±27±24±12±1 EW Zγ+jets 23 ±314±225±320±39±2 Strong Wγ+jets 34 ±58±15±22±12±1 EW Wγ+jets 31 ±53±14±13±11.5±0.3 jet→γ3±30.5±0.50.6±0.50.1±0.10.1±0.1 jet→e––––– e→γ76 ±66±11.4±0.10.8±0.10.2±0.1 γ+jet 2 ±11±10.4±0.40.1±0.10.03 ±0.02 t¯ tγ/Vγγ 9±10.8±0.30.1±0.10.04 ±0.09 0.03 ±0.01 Fitted Bkg 184 ±840±344±330±314±2 VBF H125 (B(H→γγ d)=0.02) 5.7±0.712.2±1.42.7±0.3– – ggF H125 (B(H→γγ d)=0.02) 0.7±0.31.2±0.40.2±0.1– – Data 188 31 56 35 9 Data/Fit 1.02 ±0.09 0.78 ±0.15 1.27 ±0.19 1.17 ±0.23 0.63 ±0.23 123 Eur. Phys. J. C (2022) 82 :105 Page 23 of 41 105 Fig. 5 Post-fit results for the ten [mjj,mT] bins constituting the SR defined for the dark-photon search, and the CRs as defined in Eq. (4)withthe B(H→γγ d)signal normalization set to zero. A H→γγ dsignal is shown for two different mass hypotheses (125 GeV, 500 GeV) and scaled to a branching ratio of 2% and 1%, respectively. The post-fit uncertainties include statistical, experimental, and theoretical contributions. The lower panel showstheratioofdatatothe sum of all the background contributions as well as a comparison of the pre-fit and post-fit background predictions Fig. 6 Post-fit mT(γ, Emiss T) distribution in the inclusive signal region for the dark-photon search with the 125 GeV mass B(H→γγ d) signal normalization set to zero. AH→γγ dsignal is shown for two different mass hypotheses, 125 GeV and 500 GeV, and scaled to a B(H→γγ d)of 2% and 1%, respectively. The lower panel shows the ratio of data to the sum of all the background contributions, a comparison with the pre-fit background prediction, and the signal-to-background ratio shiftedby1.0(tosharethesame vertical axis). Events with mT(γ, Emiss T)larger than the rightmost bin boundary are added to that bin Fig. 7 The 95% CL upper limit on the Higgs boson production cross-section times branching ratio to γγ dfor different VBF-produced scalar-mediator-mass hypotheses in the NWA. The theoretically predicted cross-section of a Higgs boson produced via VBF and with the B(H→γγ d)=5%is superimposed on the ±1σand ±2σNNLO QCD+NLO EW uncertainty bands of the expected production cross-section limit 123 105 Page 24 of 41 Eur. Phys. J. C (2022) 82 :105 Acknowledgements We thank CERN for the very successful operation of the LHC, as well as the support staff from our institutions without whom ATLAS could not be operated efficiently. We acknowledge the support of ANPCyT, Argentina; YerPhI, Armenia; ARC, Australia; BMWFWand FWF,Austria;ANAS,Azerbaijan;SSTC,Belarus;CNPq and FAPESP, Brazil; NSERC, NRC and CFI, Canada; CERN; ANID, Chile; CAS, MOST and NSFC, China; Minciencias, Colombia; MSMT CR, MPO CR and VSC CR, Czech Republic; DNRF and 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, Netherlands; RCN, Norway; MEiN,Poland;FCT,Portugal;MNE/IFA,Romania;JINR;MESofRussiaandNRCKI,RussianFederation;MESTD, Serbia;MSSR,Slovakia; ARRS and MIZŠ, Slovenia; DSI/NRF, South Africa; MICINN, Spain; SRC and Wallenberg Foundation, Sweden; SERI, SNSF and Cantons of Bern and Geneva, Switzerland; MOST, Taiwan; TAEK, Turkey; STFC, United Kingdom; DOE and NSF, United States of America. In addition, individual groups and members have received support from BCKDF, CANARIE, Compute Canada and CRC, Canada; COST, ERC, ERDF, Horizon 2020 and Marie Skłodowska-Curie Actions, European Union; Investissements d’Avenir Labex, Investissements d’Avenir Idex and ANR, France; DFG and AvH Foundation, Germany; Herakleitos, Thales and Aristeia programmes co-financed by EU-ESF and the Greek NSRF, Greece; BSF-NSF and GIF, Israel; Norwegian Financial Mechanism2014–2021,Norway;NCN and NAWA,Poland;LaCaixaBanking Foundation, CERCA Programme Generalitat de Catalunya and PROMETEO and GenT Programmes Generalitat Valenciana, Spain; Göran Gustafssons Stiftelse, Sweden; The Royal Society and Leverhulme Trust, United Kingdom. The crucial computing support from all WLCG partners is acknowledged gratefully, in particular from CERN, the ATLAS Tier-1 facilities at TRIUMF (Canada), NDGF (Denmark, Norway, Sweden), CCIN2P3 (France), KIT/GridKA (Germany), INFN-CNAF (Italy), NLT1 (Netherlands), PIC (Spain), ASGC (Taiwan), RAL (UK) and BNL (USA), the Tier-2 facilities worldwide and large non-WLCG resource providers. Major contributors of computing resources are listed in Ref. [ATL-SOFT-PUB-2021-003]. Data Availability Statement This manuscript has no associated data or the data will not be deposited. [Authors’ comment: All ATLAS scientific output is published in journals, and preliminary results are made available in Conference Notes. All are openly available, without restriction on use by external parties beyond copyright law and the standard conditions agreed by CERN. Data associated with journal publications are also made available: tables and data from plots (e.g. cross section values, likelihood profiles, selection efficiencies, cross section limits, ...) are stored in appropriate repositories such as HEPDATA (http://hepdata.cedar.ac.uk/). ATLAS also strives to make additional material related to the paper available that allows a reinterpretation of the data in the context of new theoretical models. For example, an extended encapsulation of the analysis is often provided for measurements in the framework of RIVET (http://rivet.hepforge. org/).] Open Access This article is licensed under a Creative Commons Attribution4.0InternationalLicense, whichpermitsuse,sharing,adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. 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Xiotidis152,D.Xu 13a ,H.Xu 58a,H.Xu 58a , L. Xu58a ,R.Xu 132 ,T.Xu 58a ,W.Xu 103 ,Y.Xu 13b ,Z.Xu 58b ,Z.Xu 149 , B. Yabsley153 , S. Yacoob31a , N. Yamaguchi85 , Y. Yamaguchi160 , M. Yamatani159, H. Yamauchi164 , T. Yamazaki16 , Y. Yamazaki80 ,J.Yan 58c, S. Yan130 ,Z.Yan 23 , H.J.Yang 58c,58d , H.T.Yang 16 , S. Yang58a , T. Yang60c , X. Yang58a , X. Yang13a , Y. Yang159 , Z. Yang58a,103 ,W-M.Yao 16 ,Y.C.Yap 44 ,H.Ye 13c ,J.Ye 40 ,S.Ye 27 , I. Yeletskikh77 , M. R. Yexley87 ,P.Yin 37 , K. Yorita174 , K. Yoshihara76 , C. J. S. Young50 , C. Young149 , R. Yuan58b,i, X. Yue59a , M. Zaazoua33e , B. Zabinski82 , G. Zacharis9,E.Zaid 48, A.M.Zaitsev 119,ae , T. Zakareishvili155b , N. Zakharchuk32 , S. Zambito34 , D. Zanzi50 , S. V. Zeißner45 , C. Zeitnitz177 ,J.C.Zeng 168 , D. T. Zenger Jr24 , O. Zenin119 , T. Ženiš26a , S. Zenz90 , S. Zerradi33a ,D.Zerwas 62 , B. Zhang13c , D. F. Zhang13b , G. Zhang13b , 123 105 Page 36 of 41 Eur. Phys. J. C (2022) 82 :105 J. Zhang5, K. Zhang13a , L. Zhang13c , M. Zhang168 , R. Zhang176 , S. Zhang103, X. Zhang58c , X. Zhang58b , Z. Zhang62 , P. Zhao47 , Y. Zhao141 , Z. Zhao58a , A. Zhemchugov77 , Z. Zheng149 , D. Zhong168 , B. Zhou103, C. Zhou176 , H. Zhou6, N. Zhou58c , Y. Zhou6, C.G.Zhu 58b ,C.Zhu 13a,13d , H.L.Zhu 58a , H. Zhu13a ,J.Zhu 103 ,Y.Zhu 58a , X. Zhuang13a , K. Zhukov108 , V. Zhulanov118a,118b , D. Zieminska63 , N. I. Zimine77 , S. Zimmermann50,*, J. Zinsser59b, M. Ziolkowski147 ,L.Živkovi´c14 , A. Zoccoli21a,21b , K. Zoch52 , T. G. Zorbas145 ,O.Zormpa 42 ,W.Zou 37 , L. Zwalinski34 1Department of Physics, University of Adelaide, Adelaide, Australia 2Department of Physics, University of Alberta, Edmonton, AB, Canada 3(a)Department of Physics, Ankara University, Ankara, Turkey; (b)Application and Research Center for Advanced Studies, Istanbul Aydin University, Istanbul, Turkey; (c)Division of Physics, TOBB University of Economics and Technology, Ankara, Turkey 4LAPP, Univ. Savoie Mont Blanc, CNRS/IN2P3, Annecy , France 5High Energy Physics Division, Argonne National Laboratory, Argonne, IL, USA 6Department of Physics, University of Arizona, Tucson, AZ, USA 7Department of Physics, University of Texas at Arlington, Arlington, TX, USA 8Physics Department, National and Kapodistrian University of Athens, Athens, Greece 9Physics Department, National Technical University of Athens, Zografou, Greece 10 Department of Physics, University of Texas at Austin, Austin, TX, USA 11 (a)Bahcesehir University, Faculty of Engineering and Natural Sciences, Istanbul, Turkey; (b)Istanbul Bilgi University, Faculty of Engineering and Natural Sciences, Istanbul, Turkey; (c)Department of Physics, Bogazici University, Istanbul, Turkey; (d)Department of Physics Engineering, Gaziantep University, Gaziantep, Turkey; (e)Department of Physics, Istanbul University, Istanbul, Turkey; (f)Istinye University, Sariyer, Istanbul, Turkey 12 Institut de Física d’Altes Energies (IFAE), Barcelona Institute of Science and Technology, Barcelona, Spain 13 (a)Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China; (b)Physics Department, Tsinghua University, Beijing, China; (c)Department of Physics, Nanjing University, Nanjing, China; (d)University of Chinese Academy of Science (UCAS), Beijing, China 14 Institute of Physics, University of Belgrade, Belgrade, Serbia 15 Department for Physics and Technology, University of Bergen, Bergen, Norway 16 Physics Division, Lawrence Berkeley National Laboratory and University of California, Berkeley, CA, USA 17 Institut für Physik, Humboldt Universität zu Berlin, Berlin, Germany 18 Albert Einstein Center for Fundamental Physics and Laboratory for High Energy Physics, University of Bern, Bern, Switzerland 19 School of Physics and Astronomy, University of Birmingham, Birmingham, UK 20 (a)Facultad de Ciencias y Centro de Investigaciónes, Universidad Antonio Nariño, Bogotá, Colombia; (b)Departamento de Física, Universidad Nacional de Colombia, Bogotá, Colombia 21 (a)Dipartimento di Fisica e Astronomia A. Righi, Università di Bologna, Bologna, Italy; (b)INFN Sezione di Bologna, Bologna, Italy 22 Physikalisches Institut, Universität Bonn, Bonn, Germany 23 Department of Physics, Boston University, Boston, MA, USA 24 Department of Physics, Brandeis University, Waltham, MA, USA 25 (a)Transilvania University of Brasov, Brasov, Romania; (b)Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest, Romania; (c)Department of Physics, Alexandru Ioan Cuza University of Iasi, Iasi, Romania; (d)Physics Department, National Institute for Research and Development of Isotopic and Molecular Technologies, Cluj-Napoca, Romania; (e)University Politehnica Bucharest, Bucharest, Romania; (f)West University in Timisoara, Timisoara, Romania 26 (a)Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovak Republic; (b)Department of Subnuclear Physics, Institute of Experimental Physics of the Slovak Academy of Sciences, Kosice, Slovak Republic 27 Physics Department, Brookhaven National Laboratory, Upton, NY, USA 28 Departamento de Física (FCEN) and IFIBA, Universidad de Buenos Aires and CONICET, Buenos Aires, Argentina 29 California State University, Long Beach, CA, USA 30 Cavendish Laboratory, University of Cambridge, Cambridge, UK 123 Eur. Phys. J. C (2022) 82 :105 Page 37 of 41 105 31 (a)Department of Physics, University of Cape Town, Cape Town, South Africa; (b)iThemba Labs, Western Cape, South Africa; (c)Department of Mechanical Engineering Science, University of Johannesburg, Johannesburg, South Africa; (d)National Institute of Physics, University of the Philippines, Diliman, Philippines; (e)Department of Physics, University of South Africa, Pretoria, South Africa; (f)University of Zululand, KwaDlangezwa, South Africa; (g)School of Physics, University of the Witwatersrand, Johannesburg, South Africa 32 Department of Physics, Carleton University, Ottawa, ON, Canada 33 (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 Sciences Semlalia, Université Cadi Ayyad, LPHEA-Marrakech, Marrakesh, Morocco; (d)LPMR, Faculté des Sciences, Université Mohamed Premier, Oujda, Morocco; (e)Faculté des sciences, Université Mohammed V, Rabat, Morocco; (f)Mohammed VI Polytechnic University, Ben Guerir, Morocco 34 CERN, Geneva, Switzerland 35 Enrico Fermi Institute, University of Chicago, Chicago, IL, USA 36 LPC, Université Clermont Auvergne, CNRS/IN2P3, Clermont-Ferrand, France 37 Nevis Laboratory, Columbia University, Irvington, NY, USA 38 Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark 39 (a)Dipartimento di Fisica, Università della Calabria, Rende, Italy; (b)INFN Gruppo Collegato di Cosenza, Laboratori Nazionali di Frascati, Frascati, Italy 40 Physics Department, Southern Methodist University, Dallas, TX, USA 41 Physics Department, University of Texas at Dallas, Richardson, TX, USA 42 National Centre for Scientific Research “Demokritos”, Agia Paraskevi, Greece 43 (a)Department of Physics, Stockholm University, Stockholm, Sweden; (b)Oskar Klein Centre, Stockholm, Sweden 44 Deutsches Elektronen-Synchrotron DESY, Hamburg and Zeuthen, Germany 45 Lehrstuhl für Experimentelle Physik IV, Technische Universität Dortmund, Dortmund, Germany 46 Institut für Kernund Teilchenphysik, Technische Universität Dresden, Dresden, Germany 47 Department of Physics, Duke University, Durham, NC, USA 48 SUPA-School of Physics and Astronomy, University of Edinburgh, Edinburgh, UK 49 INFN e Laboratori Nazionali di Frascati, Frascati, Italy 50 Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Freiburg, Germany 51 II. Physikalisches Institut, Georg-August-Universität Göttingen, Göttingen, Germany 52 Département de Physique Nucléaire et Corpusculaire, Université de Genève, Geneva, Switzerland 53 (a)Dipartimento di Fisica, Università di Genova, Genoa, Italy; (b)INFN Sezione di Genova, Genoa, Italy 54 II. Physikalisches Institut, Justus-Liebig-Universität Giessen, Giessen, Germany 55 SUPA-School of Physics and Astronomy, University of Glasgow, Glasgow, UK 56 LPSC, Université Grenoble Alpes, CNRS/IN2P3, Grenoble INP, Grenoble, France 57 Laboratory for Particle Physics and Cosmology, Harvard University, Cambridge, MA, USA 58 (a)Department of Modern Physics and State Key Laboratory of Particle Detection and Electronics, University of Science and Technology of China, Hefei, China; (b)Institute of Frontier and Interdisciplinary Science and Key Laboratory of Particle Physics and Particle Irradiation (MOE), Shandong University, Qingdao, China; (c)School of Physics and Astronomy, Shanghai Jiao Tong University, Key Laboratory for Particle Astrophysics and Cosmology (MOE), SKLPPC, Shanghai, China; (d)Tsung-Dao Lee Institute, Shanghai, China 59 (a)Kirchhoff-Institut für Physik, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany; (b)Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany 60 (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 Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China 61 Department of Physics, National Tsing Hua University, Hsinchu, Taiwan 62 IJCLab, Université Paris-Saclay, CNRS/IN2P3, 91405 Orsay, France 63 Department of Physics, Indiana University, Bloomington, IN, USA 64 (a)INFN Gruppo Collegato di Udine, Sezione di Trieste, Udine, Italy; (b)ICTP, Trieste, Italy; (c)Dipartimento Politecnico di Ingegneria e Architettura, Università di Udine, Udine, Italy 65 (a)INFN Sezione di Lecce, Lecce, Italy; (b)Dipartimento di Matematica e Fisica, Università del Salento, Lecce, Italy 66 (a)INFN Sezione di Milano, Milan, Italy; (b)Dipartimento di Fisica, Università di Milano, Milan, Italy 123 105 Page 38 of 41 Eur. Phys. J. C (2022) 82 :105 67 (a)INFN Sezione di Napoli, Naples, Italy; (b)Dipartimento di Fisica, Università di Napoli, Naples, Italy 68 (a)INFN Sezione di Pavia, Pavia, Italy; (b)Dipartimento di Fisica, Università di Pavia, Pavia, Italy 69 (a)INFN Sezione di Pisa, Pisa, Italy; (b)Dipartimento di Fisica E. Fermi, Università di Pisa, Pisa, Italy 70 (a)INFN Sezione di Roma, Rome, Italy; (b)Dipartimento di Fisica, Sapienza Università di Roma, Rome, Italy 71 (a)INFN Sezione di Roma Tor Vergata, Rome, Italy; (b)Dipartimento di Fisica, Università di Roma Tor Vergata, Rome, Italy 72 (a)INFN Sezione di Roma Tre, Rome, Italy; (b)Dipartimento di Matematica e Fisica, Università Roma Tre, Rome, Italy 73 (a)INFN-TIFPA, Povo, Italy; (b)Università degli Studi di Trento, Trento, Italy 74 Institut für Astround Teilchenphysik, Leopold-Franzens-Universität, Innsbruck, Austria 75 University of Iowa, Iowa City, IA, USA 76 Department of Physics and Astronomy, Iowa State University, Ames, IA, USA 77 Joint Institute for Nuclear Research, Dubna, Russia 78 (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 de São Paulo, São Paulo, Brazil; (d)Rio de Janeiro State University, Rio de Janeiro, Brazil 79 KEK, High Energy Accelerator Research Organization, Tsukuba, Japan 80 Graduate School of Science, Kobe University, Kobe, Japan 81 (a)AGH University of Science and Technology, Faculty of Physics and Applied Computer Science, Krakow, Poland; (b)Marian Smoluchowski Institute of Physics, Jagiellonian University, Krakow, Poland 82 Institute of Nuclear Physics Polish Academy of Sciences, Krakow, Poland 83 Faculty of Science, Kyoto University, Kyoto, Japan 84 Kyoto University of Education, Kyoto, Japan 85 Research Center for Advanced Particle Physics and Department of Physics, Kyushu University, Fukuoka , Japan 86 Instituto de Física La Plata, Universidad Nacional de La Plata and CONICET, La Plata, Argentina 87 Physics Department, Lancaster University, Lancaster, UK 88 Oliver Lodge Laboratory, University of Liverpool, Liverpool, UK 89 Department of Experimental Particle Physics, Jožef Stefan Institute and Department of Physics, University of Ljubljana, Ljubljana, Slovenia 90 School of Physics and Astronomy, Queen Mary University of London, London, UK 91 Department of Physics, Royal Holloway University of London, Egham, UK 92 Department of Physics and Astronomy, University College London, London, UK 93 Louisiana Tech University, Ruston, LA, USA 94 Lunds Universitet, Lund, Sweden 95 Centre de Calcul de l’Institut National de Physique Nucléaire et de Physique des Particules (IN2P3), Villeurbanne, France 96 Departamento de Física Teorica C-15 and CIAFF, Universidad Autónoma de Madrid, Madrid, Spain 97 Institut für Physik, Universität Mainz, Mainz, Germany 98 School of Physics and Astronomy, University of Manchester, Manchester, UK 99 CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France 100 Department of Physics, University of Massachusetts, Amherst, MA, USA 101 Department of Physics, McGill University, Montreal, QC, Canada 102 School of Physics, University of Melbourne, Melbourne, VIC, Australia 103 Department of Physics, University of Michigan, Ann Arbor, MI, USA 104 Department of Physics and Astronomy, Michigan State University, East Lansing, MI, USA 105 B.I. Stepanov Institute of Physics, National Academy of Sciences of Belarus, Minsk, Belarus 106 Research Institute for Nuclear Problems of Byelorussian State University, Minsk, Belarus 107 Group of Particle Physics, University of Montreal, Montreal, QC, Canada 108 P.N. Lebedev Physical Institute of the Russian Academy of Sciences, Moscow, Russia 109 National Research Nuclear University MEPhI, Moscow, Russia 110 D.V. Skobeltsyn Institute of Nuclear Physics, M.V. Lomonosov Moscow State University, Moscow, Russia 111 Fakultät für Physik, Ludwig-Maximilians-Universität München, Munich, Germany 112 Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), Munich, Germany 113 Graduate School of Science and Kobayashi-Maskawa Institute, Nagoya University, Nagoya, Japan 123 Eur. Phys. J. C (2022) 82 :105 Page 39 of 41 105 114 Department of Physics and Astronomy, University of New Mexico, Albuquerque, NM, USA 115 Institute for Mathematics, Astrophysics and Particle Physics, Radboud University/Nikhef, Nijmegen, The Netherlands 116 Nikhef National Institute for Subatomic Physics and University of Amsterdam, Amsterdam, The Netherlands 117 Department of Physics, Northern Illinois University, DeKalb, IL, USA 118 (a)Budker Institute of Nuclear Physics and NSU, SB RAS, Novosibirsk, Russia; (b)Novosibirsk State University, Novosibirsk, Russia 119 Institute for High Energy Physics of the National Research Centre Kurchatov Institute, Protvino, Russia 120 Institute for Theoretical and Experimental Physics named by A.I. Alikhanov of National Research Centre “Kurchatov Institute”, Moscow, Russia 121 Department of Physics, New York University, New York, NY, USA 122 Ochanomizu University, Otsuka, Bunkyo-ku, Tokyo, Japan 123 Ohio State University, Columbus, OH, USA 124 Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma, Norman, OK, USA 125 Department of Physics, Oklahoma State University, Stillwater, OK, USA 126 Palacký University, Joint Laboratory of Optics, Olomouc, Czech Republic 127 Institute for Fundamental Science, University of Oregon, Eugene, OR, USA 128 Graduate School of Science, Osaka University, Osaka, Japan 129 Department of Physics, University of Oslo, Oslo, Norway 130 Department of Physics, Oxford University, Oxford, UK 131 LPNHE, Sorbonne Université, Université de Paris, CNRS/IN2P3, Paris, France 132 Department of Physics, University of Pennsylvania, Philadelphia, PA, USA 133 Konstantinov Nuclear Physics Institute of National Research Centre “Kurchatov Institute”, PNPI, St. Petersburg, Russia 134 Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA, USA 135 (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)Dep Física and CEFITEC of Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Caparica, Portugal; (h)Instituto Superior Técnico, Universidade de Lisboa, Lisbon, Portugal 136 Institute of Physics of the Czech Academy of Sciences, Prague, Czech Republic 137 Czech Technical University in Prague, Prague, Czech Republic 138 Charles University, Faculty of Mathematics and Physics, Prague, Czech Republic 139 Particle Physics Department, Rutherford Appleton Laboratory, Didcot, UK 140 IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette, France 141 Santa Cruz Institute for Particle Physics, University of California Santa Cruz, Santa Cruz, CA, USA 142 (a)Departamento de Física, Pontificia Universidad Católica de Chile, Santiago, Chile; (b)Millennium Institute for Subatomic Physics at High Energy Frontier (SAPHIR), Santiago, Chile; (c)Universidad de la Serena, La Serena, Chile ;(d)Department of Physics, Universidad Andres Bello, Santiago, Chile; (e)Instituto de Alta Investigación, Universidad de Tarapacá, Arica, Chile; (f)Departamento de Física, Universidad Técnica Federico Santa María, Valparaíso, Chile 143 Universidade Federal de São João del Rei (UFSJ), São João del Rei, Brazil 144 Department of Physics, University of Washington, Seattle, WA, USA 145 Department of Physics and Astronomy, University of Sheffield, Sheffield, UK 146 Department of Physics, Shinshu University, Nagano, Japan 147 Department Physik, Universität Siegen, Siegen, Germany 148 Department of Physics, Simon Fraser University, Burnaby, BC, Canada 149 SLAC National Accelerator Laboratory, Stanford, CA, USA 150 Department of Physics, Royal Institute of Technology, Stockholm, Sweden 151 Departments of Physics and Astronomy, Stony Brook University, Stony Brook, NY, USA 152 Department of Physics and Astronomy, University of Sussex, Brighton, UK 153 School of Physics, University of Sydney, Sydney, Australia 154 Institute of Physics, Academia Sinica, Taipei, Taiwan 155 (a)E. Andronikashvili Institute of Physics, Iv. Javakhishvili Tbilisi State University, Tbilisi, Georgia; (b)High Energy Physics Institute, Tbilisi State University, Tbilisi, Georgia 123 105 Page 40 of 41 Eur. Phys. J. C (2022) 82 :105 156 Department of Physics, Technion, Israel Institute of Technology, Haifa, Israel 157 Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv, Israel 158 Department of Physics, Aristotle University of Thessaloniki, Thessaloniki, Greece 159 International Center for Elementary Particle Physics and Department of Physics, University of Tokyo, Tokyo, Japan 160 Department of Physics, Tokyo Institute of Technology, Tokyo, Japan 161 Tomsk State University, Tomsk, Russia 162 Department of Physics, University of Toronto, Toronto, ON, Canada 163 (a)TRIUMF, Vancouver, BC, Canada; (b)Department of Physics and Astronomy, York University, Toronto, ON, Canada 164 Division of Physics and Tomonaga Center for the History of the Universe, Faculty of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Japan 165 Department of Physics and Astronomy, Tufts University, Medford, MA, USA 166 Department of Physics and Astronomy, University of California Irvine, Irvine, CA, USA 167 Department of Physics and Astronomy, University of Uppsala, Uppsala, Sweden 168 Department of Physics, University of Illinois, Urbana, IL, USA 169 Instituto de Física Corpuscular (IFIC), Centro Mixto Universidad de Valencia-CSIC, Valencia, Spain 170 Department of Physics, University of British Columbia, Vancouver, BC, Canada 171 Department of Physics and Astronomy, University of Victoria, Victoria, BC, Canada 172 Fakultät für Physik und Astronomie, Julius-Maximilians-Universität Würzburg, Würzburg, Germany 173 Department of Physics, University of Warwick, Coventry, UK 174 Waseda University, Tokyo, Japan 175 Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot, Israel 176 Department of Physics, University of Wisconsin, Madison, WI, USA 177 Fakultät für Mathematik und Naturwissenschaften, Fachgruppe Physik, Bergische Universität Wuppertal, Wuppertal, Germany 178 Department of Physics, Yale University, New Haven, CT, USA aAlso at Borough of Manhattan Community College, City University of New York, New York, NY, USA bAlso at Bruno Kessler Foundation, Trento, Italy cAlso at Center for High Energy Physics, Peking University, Beijing, China dAlso at Centro Studi e Ricerche Enrico Fermi, Rome, Italy eAlso at CERN, Geneva, Switzerland fAlso at Département de Physique Nucléaire et Corpusculaire, Université de Genève, Geneva, Switzerland gAlso at Departament de Fisica de la Universitat Autonoma de Barcelona, Barcelona, Spain hAlso at Department of Financial and Management Engineering, University of the Aegean, Chios, Greece iAlso at Department of Physics and Astronomy, Michigan State University, East Lansing, MI, USA jAlso at Department of Physics and Astronomy, University of Louisville, Louisville, KY, USA kAlso at Department of Physics, Ben Gurion University of the Negev, Beer Sheva, Israel lAlso at Department of Physics, California State University, East Bay, USA mAlso at Department of Physics, California State University, Fresno, USA nAlso at Department of Physics, California State University, Sacramento, USA oAlso at Department of Physics, King’s College London, London, UK pAlso at Department of Physics, St. Petersburg State Polytechnical University, St. Petersburg, Russia qAlso at Department of Physics, University of Fribourg, Fribourg, Switzerland rAlso at Faculty of Physics, M.V. Lomonosov Moscow State University, Moscow, Russia sAlso at Faculty of Physics, Sofia University, St. Kliment Ohridski, Sofia, Bulgaria tAlso at Graduate School of Science, Osaka University, Osaka, Japan uAlso at Hellenic Open University, Patras, Greece vAlso at Institucio Catalana de Recerca i Estudis Avancats, ICREA, Barcelona, Spain wAlso at Institut für Experimentalphysik, Universität Hamburg, Hamburg, Germany xAlso at Institute for Particle and Nuclear Physics, Wigner Research Centre for Physics, Budapest, Hungary yAlso at Institute of Particle Physics (IPP), Toronto, Canada zAlso at Institute of Physics, Azerbaijan Academy of Sciences, Baku, Azerbaijan aa Also at Institute of Theoretical Physics, Ilia State University, Tbilisi, Georgia 123 Eur. Phys. J. C (2022) 82 :105 Page 41 of 41 105 ab Also at Instituto de Fisica Teorica, IFT-UAM/CSIC, Madrid, Spain ac Also at Department of Physics, Istanbul University, Istanbul, Turkey ad Also at Joint Institute for Nuclear Research, Dubna, Russia ae Also at Moscow Institute of Physics and Technology, State University, Dolgoprudny, Russia af Also at National Research Nuclear University MEPhI, Moscow, Russia ag Also at Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Freiburg, Germany ah Also at The City College of New York, New York, NY, USA ai Also at TRIUMF, Vancouver, BC, Canada aj Also at Universita di Napoli Parthenope, Naples, Italy ak Also at University of Chinese Academy of Sciences (UCAS), Beijing, China al Also at Physics Department, Yeditepe University, Istanbul, Turkey ∗Deceased 123