PHYSICAL REVIEW D 99, 012008 (2019) pffiffi of highly collimated photon-jets in pp collisions Search for pairs at s = 13 TeV with the ATLAS detector M. Aaboud et al.* (ATLAS Collaboration) (Received 3 September 2018; published 18 January 2019) Results of a search for the pair production of photon-jets—collimated groupings of photons—in the ATLAS detector at the Large Hadron Collider are reported. Highly collimated photon-jets can arise from the decay of new, highly boosted particles that can decay to multiple photons collimated enough to be identified in the electromagnetic calorimeter as a single, photonlike energy cluster. Data from proton-proton collisions at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 36.7 fb−1 , were collected in 2015 and 2016. Candidate photon-jet pair production events are selected from those containing two reconstructed photons using a set of identification criteria much less stringent than that typically used for the selection of photons, with additional criteria applied to provide improved sensitivity to photon-jets. Narrow excesses in the reconstructed diphoton mass spectra are searched for. The observed mass spectra are consistent with the Standard Model background expectation. The results are interpreted in the context of a model containing a new, high-mass scalar particle with narrow width, X, that decays into pairs of photon-jets via new, light particles, a. Upper limits are placed on the cross section times the product of branching ratios σ × BðX → aaÞ × Bða → γγÞ2 for 200 GeV < mX < 2 TeV and for ranges of ma from a lower mass of 100 MeV up to between 2 and 10 GeV, depending upon mX . Upper limits are also placed on σ × BðX → aaÞ × Bða → 3π 0 Þ2 for the same range of mX and for ranges of ma from a lower mass of 500 MeV up to between 2 and 10 GeV. DOI: 10.1103/PhysRevD.99.012008 I. INTRODUCTION photon signatures, rather than specific signal models. In many beyond the Standard Model (BSM) theories [5–13], The quest for new particles at the Large Hadron Collider new scalar, pseudoscalar, or vector gauge bosons can (LHC) at CERN has been greatly rewarded by closely decay into photon-only final states that lead to collimated examining collision events that contain photons in the final groupings of photons (“photon-jets” [14,15]). In some state. Despite the relatively small branching ratio predicted cases, the Lorentz boost of the new particles is large for the process in the Standard Model (SM), the decay of the Higgs boson into two photons is readily identifiable enough to lead to an opening angle between the trajectories due to the good energy resolution of the electromagnetic of the final-state photons that is smaller than or comparable (EM) calorimeters of the ATLAS [1] and CMS [2] to the angular size of an energy cluster in the EM detectors and the relatively small backgrounds in final calorimeter corresponding to a single photon, resulting states with only photons. The search for this process was in highly collimated photon-jets. Such boosted particles one of the main methods by which the Higgs boson was arise, for example, when a high-mass particle produced in observed [3,4]. Moreover, the establishment of a wide the proton-proton collision decays into intermediate par- range of results that so far are consistent with the SM at the ticles, with much lower masses, that subsequently decay LHC at a center-of-mass energy of 13 TeV motivates a into photons. Thus, events selected to contain two, well- renewed focus on searches for new physics that target separated, reconstructed photons can be used to search for general experimental signatures, including nonstandard pairs of highly collimated photon-jets resulting from BSM particle decays. A search for highly collimated photon-jets using * Full author list given at the end of the article. 36.7 fb−1 of LHC proton-proton collision data collected by the ATLAS detector in 2015 and 2016 at a center-of- Published by the American Physical Society under the terms of mass energy of 13 TeV is presented. Candidate photon-jet the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to pair production events are selected from those containing the author(s) and the published article’s title, journal citation, two reconstructed photons (denoted “γ R ”), using a set of and DOI. Funded by SCOAP3. identification criteria much less stringent than that typically 2470-0010=2019=99(1)=012008(29) 012008-1 © 2019 CERN, for the ATLAS Collaboration M. AABOUD et al. PHYS. REV. D 99, 012008 (2019) FIG. 1. Diagrams for BSM scenarios that result in events with pairs of photon-jets in the final state. used for the selection of photons, and with additional silicon microstrip tracker that normally provides four two- criteria applied to provide improved sensitivity to photon- dimensional measurement points per track. These silicon jets. Narrow excesses are searched for in the spectra of the detectors are complemented by the transition radiation reconstructed diphoton mass mγR γR . tracker, which enables radially extended track reconstruction The results of the search are interpreted in the context of up to jηj ¼ 2.0. The transition radiation tracker also provides a benchmark BSM scenario involving a high-mass, narrow- electron identification information based on the fraction of width scalar particle, X, with mass mX > 200 GeV, origi- hits (typically 30 in total) above a higher energy-deposit nating from the gluon-gluon fusion process and that can threshold corresponding to transition radiation. decay into a pair of intermediate particles with spin 0, a, as The calorimeter system covers the pseudorapidity range shown in Fig. 1. The a particle can in general decay to jηj < 4.9. Within the region jηj < 3.2, EM calorimetry is several final states, but here is restricted to decay either into provided by a high-granularity lead/liquid-argon (LAr) EM a pair of photons, via X → aa → 4γ, or into three neutral calorimeter. The EM calorimeter is divided into a barrel pions, via X → aa → 6π 0 → 12γ, yielding events contain- section covering jηj < 1.475 and two end cap sections ing a pair of photon-jets of either low or high multiplicity; covering 1.375 < jηj < 3.2. For jηj < 2.5, the EM calorim- the result is interpreted for both cases. Because the search is eter is composed of three sampling layers in the longitudinal performed using events that contain two calorimeter direction of shower depth. The first layer is segmented into deposits that are initially loosely identified as individual high-granularity strips in the η direction, with a typical cell photons, the search is sensitive to the parameter region in size of Δη × Δϕ ¼ 0.003 × 0.1 for the ranges jηj < 1.4 and which the a particle is highly boosted, ma < 0.01 × mX . 1.5 < jηj < 2.4, and a coarser cell size of Δη × Δϕ ¼ 0.025 × 0.1 for other regions. This fine granularity in the II. ATLAS DETECTOR η direction allows identification of events with two over- The ATLAS detector [1] is a multipurpose detector with lapping showers originating from the decays of neutral a forward-backward symmetric cylindrical geometry.1 The hadrons in hadronic jets, mostly π 0 → γγ decays. The detector covers nearly the entire solid angle around the second layer has a cell size of Δη × Δϕ ¼ 0.025 × 0.025. collision point. It consists of an inner tracking detector This layer collects most of the energy deposited in the surrounded by a thin superconducting solenoid, EM and calorimeter by photon and electron showers. The third layer hadronic calorimeters, and a muon spectrometer incorpo- is used to correct for energy leakage beyond the EM rating three large superconducting toroid magnets. calorimeter from high-energy showers. The thicknesses of The inner-detector system is immersed in a 2 T axial the first, second, and third layers at η ¼ 0 are 4.3 radiation magnetic field and provides charged-particle tracking in the lengths (X0 ), 16X0 , and 2X0 , respectively, and they vary range jηj < 2.5. The high-granularity silicon pixel detector with the pseudorapidity range [1]. Placed in front of these covers the vertex region. The innermost layer of the pixel layers, an additional thin LAr presampler layer covering detector, the insertable B-layer [16], was installed between jηj < 1.8 is used to correct for energy loss in material Run 1 and Run 2 of the LHC. The pixel detector typically upstream of the calorimeters. Hadronic calorimetry is provides four measurements per track. It is followed by the provided by the steel/scintillator-tile calorimeter, segmented into three barrel structures within jηj < 1.7, and two copper/ 1 ATLAS uses a right-handed coordinate system with its origin LAr hadronic endcap calorimeters. The solid angle coverage at the nominal interaction point in the center of the detector and is completed with forward copper/LAr and tungsten/LAr the z axis along the beam pipe. The x axis points from the calorimeter modules optimized for EM and hadronic mea- interaction point to the center of the LHC ring, and the y axis surements respectively. points upwards. Cylindrical coordinates ðr; ϕÞ are used in the transverse plane, ϕ being the azimuthal angle around the z axis. A two-level trigger system, the first level implemented in The pseudorapidity is defined in terms of the polar angle θ as custom hardware followed by a software-based level, is η ¼ − ln ptanðθ=2Þ. Angular ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi distance is measured in units of used to reduce the event rate to about 1 kHz for offline ΔR ≡ ðΔηÞ2 þ ðΔϕÞ2 . storage. 012008-2 SEARCH FOR PAIRS OF HIGHLY COLLIMATED PHOTON … PHYS. REV. D 99, 012008 (2019) III. PHOTON-JET SIGNAL CHARACTERISTICS 0.25 ATLAS Simulation X → aa → 4γ photon-jets, defined as collimated groupings of photons, mX = 800 GeV can arise from decays of particles that are highly boosted as a 0.2 ma = 0.5 GeV Fraction of events ma = 1 GeV result of themselves being the decay products of higher- ma = 2 GeV mass particles. For the benchmark BSM scenario considered 0.15 ma = 5 GeV here, the extent to which photons from decays of a particles are collimated depends on the ratio of the masses of the X 0.1 and a, particularly in the case where the X particle is produced with a momentum significantly less than its mass. 0.05 For large values of the ratio ma =mX , the boost of the a is small enough to yield more than two individual photons, 0 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 well separated and isolated, that can be identified in the ΔRγ γ , generator level detector. In this regime, a general search for new phenom- ena in events with at least three isolated photons, using a FIG. 2. The distribution of ΔRγγ , the angular separation three-photon trigger, was performed by ATLAS at 8 TeV between two photons that are reconstructed as a single photon [17]. This search was sensitive to cases where the angular jet in the ATLAS detector, for the benchmark signal scenario for separation between photons was large, for ΔRγγ ≳ 0.3, the process X → aa → 4γ, using simulated signal samples at generator level. The distribution has a peak at ∼4 × ma =mX and a which corresponds to ma =mX ≳ 0.08 for the benchmark long tail on the right side. For the values of mX and ma presented signal scenario. For slightly smaller values of the ratio in the figure, ΔRγγ is smaller than or comparable in size to an ma =mX , the individual final-state photons appear too close EM cluster. together in the detector and fail isolation criteria, limiting the sensitivity of the 8 TeV ATLAS search in this regime. For very small values of the ratio ma =mX , the boost of For values of the ratio ma =mX greater than 0.01, the the a is large enough to lead to angular separations between final-state photons are separated enough to lead to a the final-state photons of ΔRγγ ≲ 0.04, which is approx- relatively large cluster of energy in the calorimeter, and imately the same size as a standard single-photon energy such events do not satisfy the isolation criteria or the cluster in the ATLAS EM calorimeter. In this case, existing initial loose identification of photons at the trigger level. triggers cannot distinguish a calorimeter energy deposit The signal selection efficiency for the present analysis in resulting from highly collimated photons from that of a this ma =mX > 0.01 region is lower than 4%, and so no single photon. Thus, diphotonlike events can be used as a attempt is made to search in this regime. There is therefore starting point for a search for highly collimated photon-jets, an intermediate region, 0.01 < ma =mX ≲ 0.08, which is and the sensitivity to this region of the photon-jet parameter covered by neither this search nor the previous search for space can be increased by placing criteria on the shape of three-photon final states at 8 TeV. the shower in the EM calorimeter in addition to those applied in the trigger. This analysis presents a search for IV. EVENT SAMPLES highly collimated photon-jets that is sensitive to a wide The data sample used for this search corresponds to an mass range for the parent X particle, mX > 200 GeV, and integrated luminosity of 36.7 fb−1 (after applying data- for ma =mX < 0.01 in the benchmark signal scenario. quality requirements), collected under normal data-taking For this benchmark scenario, for the process X → conditions for pp collisions aa → 4γ, the distribution of ΔRγγ is shown in Fig. 2. pffiffiffiduring 2015 and 2016 at a center-of-mass energy of s ¼ 13 TeV. The data were Due to the kinematics of boosted particles, ΔRγγ has a selected using an unprescaled trigger that filters events with maximum at a value of 2=γ, where γ is the Lorentz factor of two energy deposits in the EM calorimeter that satisfy the a particle, γ ¼ Ea =ma . When the X particle is produced trigger-level loose photon identification criteria with trans- nearly at rest, since the energy of the a particle has a median verse energy values of ET;1 > 35 GeV and ET;2 > 25 GeV. value of Ea ∼ mX =2, the distribution of ΔRγγ has a maxi- Samples of the benchmark signal scenario with two mum at ∼4 × ma =mX . The approximate proportionality of different final states, X → aa → 4γ and X → aa → 6π 0 , the angular spread of photons within the photon-jet to were simulated. For the production of the X via gluon- ma =mX holds for photon-jets in general, including those gluon fusion, MADGRAPH5_AMC@NLO [18] Version 2.3.3, with larger photon multiplicity resulting from processes at next-to-leading order (NLO) in quantum chromodynam- such as X → aa → 6π 0 . Since the two different final states ics (QCD) with the NNPDF30NLO parton distribution of the benchmark scenario are similar, some parts of the function (PDF) set [19], was used. For the subsequent descriptions in the following sections are only mentioned decay of the X into aa and into the photon-jet final states, for the X → aa → 4γ decay to avoid repetition, although PYTHIA 8 [20] Version 8.210, with the A14 set of tuned they apply to the X → aa → 6π 0 decay as well. parameters [21], was used, as well as for the parton-shower 012008-3 M. AABOUD et al. PHYS. REV. D 99, 012008 (2019) and hadronization simulation of initial state radiation jets. of Δη × Δϕ ¼ 0.125 × 0.125). Reconstructed photons are The samples were produced using a narrow-width approxi- required to match photon objects calculated at the trigger mation (NWA) approach with the resonance widths of the X level, within the separation of ΔR < 0.07, and may have and a set to 4 and 1 MeV, respectively. Samples were associated tracks and conversion vertices reconstructed in simulated for mass ranges of 200 GeV < mX < 2000 GeV the inner detector. and 0.1 GeV < ma < 0.01 × mX . The two leading reconstructed photons are required to be The nonresonant production of diphoton events in the SM within the fiducial calorimeter region of jηj < 2.37, exclud- is the dominant background source for this analysis, and ing the transition region at 1.37 < jηj < 1.52 between these events were simulated with SHERPA 2.1.1 [22]. Matrix the barrel and end cap calorimeters. The criterion ET;1 > elements were calculated with up to two additional partons at 0.4 × mγR γR is applied to the leading reconstructed photon, leading order (LO) in QCD and merged with the SHERPA and ET;2 > 0.3 × mγR γR to the subleading reconstructed parton-shower simulation [23] using the ME+PS@LO pre- photon. These criteria increase the sensitivity to photon- scription [24]. The CT10 PDF set [25] was used in con- jet pairs from a scalar resonance, since such candidate junction with a dedicated parton-shower tune of SHERPA. signal events tend to contain photons with larger ET =mγR γR These samples are used to validate the background modeling ratios compared with those from background events domi- based on analytic functions (described in Sec. VI B). nated by t-channel processes [31]. Only events with Simulated samples of the reducible SM background con- mγR γR > 175 GeV are selected for further analysis. sisting of one photon and one hadronic jet from the hard The two leading reconstructed photons are required to be process were also generated with SHERPA 2.1.1—using the isolated from other calorimeter energy deposits and from same PDF set, parton-shower tune, and merging prescription nearby tracks not associated with the photon. The calo- as for the diphoton sample—with matrix elements calculated rimeter isolation variable Eiso T is defined as the sum of at LO with up to four additional partons. These samples are energy deposits in the calorimeter in a cone of size ΔR ¼ used for optimizing the search strategy described in Sec. V. 0.4 around the barycenter of the photon cluster (excluding Additional interactions in the same or nearby bunch the energy associated with the photon cluster) minus crossings (pileup) were simulated using Pythia 8.186 [20] 0.022 × ET . This cone energy is corrected for the leakage using the A2 set of tuned parameters [26] and the of the photon energy from the photon cluster and for the MSTW2008LO PDF [27] set and overlayed on the simu- effects of pileup [32]. The calorimeter isolation variable is lated signal and SM background events. All simulated required to satisfy EisoT < 2.45 GeV. The track isolation event samples were produced using the ATLAS simulation infrastructure [28], using the full GEANT 4 [29] simulation variable pT is defined as the scalar sum of the transverse iso of the ATLAS detector. Simulated events were then momenta of tracks not associated with the photon in a cone reconstructed with the same software as used for the data. of size ΔR ¼ 0.2 around the barycenter of the photon cluster. It is required to satisfy piso T < 0.05 × ET. V. OBJECT AND EVENT SELECTION B. Optimized photon selection for photon-jet signatures This analysis selects events containing at least two Photon identification in ATLAS [30] is based on a set of reconstructed photons, obtained from a diphoton trigger, requirements placed on several discriminating variables and then searches for pair-produced photon-jets. This is that characterize the shower development in the calorimeter accomplished by applying additional selection criteria and (“shower shapes”), defined to reject the background from scanning for deviations from the expected background in the hadronic jets misidentified as photons. Nine discriminating mγR γR spectrum, defined as the distribution of the mass values variables are defined, and they are described in detail in of the two reconstructed photons, which would correspond to Table 1 of Ref. [30]. One variable quantifies the shower the mass of the high-mass particle mX in the case of a signal leakage fraction in the hadronic calorimeter, and three event. No attempt is made to reconstruct the mass of the a in variables quantify the lateral shower development in the the process X → aa → photon-jets (although specifics of the EM calorimeter second layer. The other five variables a are taken into account in several parameters of the signal quantify the lateral shower development in the finely modeling, which is detailed in Sec. VI A). segmented strips of the first layer, and two of them are utilized to identify photon candidates with two separate A. Initial event selection with two loose photons local energy maxima in the fine strips, which are character- Reconstructed photons are obtained from clusters of istic of neutral hadron decays in hadronic jets, primarily energy deposited in the EM calorimeter [30]. In the barrel from π 0 → γγ. section a cluster size of 3 × 7 cells in the middle layer is Several reference selections are defined, including those used (equivalent to an area of size Δη × Δϕ ¼ 0.075 × referred to as “loose” and “tight.” The loose selection is 0.175), while a cluster of 5 × 5 cells in the middle layer based only on shower shapes in the second layer of the EM is used in the end cap sections (equivalent to an area calorimeter and on the leakage in the hadronic calorimeter, 012008-4 SEARCH FOR PAIRS OF HIGHLY COLLIMATED PHOTON … PHYS. REV. D 99, 012008 (2019) and is used by the photon triggers, including the diphoton identification criteria described in the previous sections, the trigger used for the collection of the data sample for this final signal region is defined by dividing the events search. The tight selection is based on all nine variables and into two orthogonal categories based on the value of the is used for the standard photon identification in ATLAS, calorimeter variable ΔE for the reconstructed photons. The but is not used in this search. The criteria for the tight quantity ΔE corresponds to a shower shape variable based selection change as a function of the η values of the on information in the first layer of the EM calorimeter, and reconstructed photons, to account for the calorimeter quantifies the relative size of multiple, individual energy geometry and effects from the material upstream of the deposits that may be contained within a single energy calorimeter, and are separately optimized for reconstructed cluster. photons with and without an associated conversion vertex It is defined as to increase the photon identification efficiency. In this search, both reconstructed photons are required to fulfill the “loose0 ” selection. This selection is defined by ΔE ¼ ES1 S1 2nd max − Emin removing requirements on all five variables quantifying the shower development in the finely segmented strip layer of where ES1 2nd max is the energy of the strip cell with the the calorimeter (ws3 ; wstot ; Fside ; ΔE, and Eratio , defined in second-largest energy, and ES1 min is the energy in the strip Table 1 of Ref. [30]), with respect to the standard Tight cell with the lowest energy located between the strips with selection. The requirements on the other four variables (Rhad , the largest and the second-largest energy. If the strip cells Rη , wη2 , and Rϕ ) remain the same as for the standard tight with the largest and the second-largest energy are located selection. By definition, the loose0 is an intermediate selec- next to each other, or if there is no second-largest energy tion between loose and tight. Based on simulated samples of strip, then ΔE ¼ 0. This variable is useful for identifying signal and SM background processes, this loose0 selection the π 0 → γγ process, prevalent in hadronic jets, which provides good sensitivity to photon-jet signals. This is leaves a characteristic signature in the first layer of the EM explained by the fact that energy clusters of photon-jets calorimeter that often yields two peaks in the η direction, exhibit multiple local energy maxima in the fine strip layer, resulting in large ΔE values. When the photon-jet signals since the angular separation of photons constituting the from decays such as a → γγ and a → 3π 0 → 6γ have photon-jet can be larger than the segmentation of the strips, angular separation of photons larger than the segmentation depending on the mass parameters mX and ma of the of the first layer of the EM calorimeter, they leave benchmark signal scenario, as seen in Fig. 2. For signal signatures in the calorimeter similar to π 0 → γγ events. mass values 0.003 < ma =mX < 0.006 and mX > 200 GeV, Thus, the variable ΔE is used to effectively select photon- the total selection efficiency is less than 5% when the jet signals. standard tight selection is applied, in addition to the selection The categorization by ΔE is as follows: criteria described in Sec. VA, and this increases to 20%–50% (i) Low-ΔE category: both reconstructed photons are with the loose0 selection. Comparing the two selection required to have values of ΔE below given thresh- criteria, an increase in the overall event yield of roughly olds. This requirement corresponds to reconstructed 30% is observed with the loose0 selection. Thus, the analysis photons with a signature in the fine strip layer sensitivity to photon-jet signals is increased by the use of the similar to that of single photons. loose0 selection, rather than the standard tight selection. (ii) High-ΔE category: at least one of the two leading Additionally, the choice of loose0 allows the definition of reconstructed photons is required to have a value of a set of “not loose0 ” criteria (i.e., where at least one of the ΔE above a given threshold. This requirement two reconstructed photons fails the loose0 selection) that is corresponds to events containing reconstructed used to define the control regions for the evaluation of the photons which have a π 0 -like signature. background composition, as described in Sec. VI B. The thresholds for the value of ΔE used to determine whether an event appears in either the low- or high-ΔE C. Categorization of events by the shower category are the same as those used in the standard tight shape variable ΔE photon selection. These thresholds range from 100 to After the preselection of events with two leading 500 MeV, depending on the photon η and whether there reconstructed photons satisfying the isolation and loose0 are associated tracks or conversion vertices. TABLE I. Number of events observed in the two categories for different mγR γ R ranges. mγR γ R range 175–400 GeV 400–600 GeV 600–800 GeV >800 GeV 4 3 2 Low-ΔE category 5.3 × 10 2.5 × 10 5.2 × 10 2.3 × 102 High-ΔE category 9.8 × 103 3.5 × 102 5.2 × 101 2.1 × 101 012008-5 M. AABOUD et al. PHYS. REV. D 99, 012008 (2019) ATLAS Simulation X → aa → 4γ , s = 13 TeV ATLAS Simulation X → aa → 4γ , s = 13 TeV Fraction in the low-ΔE category [%] 50 10.0 1.1 0.4 0.5 1.1 2.8 19.1 37.3 10.0 96.6 77.7 56.8 33.8 17.5 10.0 8.9 90 80 Selection Efficiency [%] 5.0 0.7 1.5 7.1 21.3 34.7 48.6 51.4 40 5.0 82.8 35.8 15.1 10.5 9.3 10.1 14.0 70 2.0 3.3 28.5 42.9 47.1 48.6 50.6 50.6 2.0 30.1 11.1 11.5 15.8 22.8 50.9 77.1 ma [GeV] 60 ma [GeV] 30 1.0 21.3 40.8 45.0 47.7 49.1 50.2 51.6 1.0 13.8 18.3 37.2 63.0 81.4 95.2 97.3 50 20 40 0.7 29.9 41.3 45.7 47.7 49.1 50.3 50.8 0.7 15.3 37.2 71.7 90.1 95.5 97.8 98.3 30 0.5 31.8 41.1 45.4 47.4 48.5 50.5 51.4 10 0.5 24.4 69.5 92.5 96.7 97.8 98.1 98.4 20 10 0.1 33.2 41.8 46.0 47.5 48.9 50.3 51.2 0.1 97.5 97.9 98.0 98.3 98.3 98.5 98.4 0 0 200 400 600 800 1000 1500 2000 200 400 600 800 1000 1500 2000 mX [GeV] mX [GeV] (a) (b) FIG. 3. (a) Total selection efficiency ε (including kinematic acceptance and excluding categorization by ΔE) as a function of ma and mX for the decay X → aa → 4γ. (b) The fraction f of events in the low-ΔE category. The high-ΔE category is found to have a significantly for different ranges of mγR γR is shown in Table I. Although better signal-to-background ratio compared with the low- overall the ratio of signal-to-background is lower for the ΔE category, since reconstructed photons with large ΔE low-ΔE category, it still provides increased sensitivity to values typically correspond to photon-jets with a larger photon-jet signals with smaller angular separation, and so angular spread among the constituent photons. The high- both categories are used in this search. ΔE criterion also effectively reduces the contribution of single photons, which tend to have small ΔE values. D. Summary of the selection Hadronic jets from SM processes containing π 0 → γγ The overall efficiency, ε, of selecting signal events after decays are likely to fall into the high-ΔE category, but applying all criteria, including kinematic acceptance and the contribution of these events is small due to the isolation excluding the categorization by ΔE, is shown in Fig. 3(a), requirements. This leads to lower expected background and the fraction, f, of signal events that appear in the low- event yields in the high-ΔE category, resulting in better ΔE category is shown in Fig. 3(b), both as a function of ma signal-to-background ratios compared with the low-ΔE and mX for the decay X → aa → 4γ. The selection effi- category. The number of events observed in each category ciency is low for small values of mX and large values of ma , and almost all events are in the low-ΔE category for large TABLE II. Number of events in collision data that satisfy the successive selection criteria, as well as the cumulative and relative values of mX and small values of ma . For smaller ma and fraction of events remaining after applying each criterion. The larger mX , f increases because of the small angular spread values in the last two lines of the “Relative” column are of photons inside the photon-jet, which leads to a calo- the fraction of events relative to the “mγ R γ R > 175 GeV” line. rimeter signature similar to that of a single photon. The values in the “Preselection” line include the offline loose Additionally, for larger ma and smaller mX , f also increases photon selection, ET > 25 GeV, jηj < 2.37, excluding the tran- because individual photons are reconstructed separately sition region between the barrel and endcap calorimeters, and the due to the large angular separation, resulting in events matching of the reconstructed photon to the photon trigger object containing more than two reconstructed photons, each applied to the two leading reconstructed photons. The label of which more resembles a single photon. The results “Relative ET ” denotes the requirements on ET =mγR γ R for the for the decay X → aa → 6π 0 are similar to those of the reconstructed photons, described in Sec. VA. decay X → aa → 4γ. Fraction of events Table II displays the number of events in data that satisfy each selection criterion. The fraction of events with both of N observed Cumulative Relative the two leading reconstructed photons found in jηj < 1.37 9   All triggered events 6.4 × 10 (i.e. the barrel section) is 59% (63%) for the low-ΔE (high- Preselection 3.1 × 107 4.8 × 10−3 4.8 × 10−3 ΔE) category. Loose0 photon selection 1.7 × 107 2.6 × 10−3 5.3 × 10−1 Photon isolation 2.2 × 106 3.4 × 10−4 1.3 × 10−1 VI. SIGNAL AND BACKGROUND MODELING Relative ET 1.7 × 106 2.6 × 10−4 7.7 × 10−1 mγ R γR > 175 GeV 6.7 × 104 1.0 × 10−5 4.0 × 10−2 The reconstructed signal mass shape is modeled with a double-sided Crystal Ball (DSCB) function. The back- Low-ΔE category 5.6 × 104 8.8 × 10−6 8.5 × 10−1 grounds are determined by fitting functions to the observed High-ΔE category 1.0 × 104 1.6 × 10−6 1.5 × 10−1 mass spectra of two reconstructed photons, mγR γR . 012008-6 SEARCH FOR PAIRS OF HIGHLY COLLIMATED PHOTON … PHYS. REV. D 99, 012008 (2019) A. Signal modeling difference between these two numbers is taken as a The DSCB function has been shown to be effective in systematic uncertainty in the signal mass shape modeling. modeling new-particle resonances expected to have a The fraction, f, of signal events that appear in the low- Gaussian core surrounded by asymmetric and non- ΔE category is parametrized as a function of the mass Gaussian low- and high-mass tails, and is described in parameters mX and ma of the benchmark signal scenario, to detail elsewhere [31]. In this analysis the DSCB is a have a continuous model for all the masses considered in function of the mass of two reconstructed photons the results. The values of f are taken from simulation and a (photon-jets in simulated signal samples), with parameters third-order spline interpolation is performed as a function to account for the peak position and width of the Gaussian of ma =mX . part, as well as for the upper and lower tails where the Similarly, the total signal selection efficiency, ε, is calculated from the individual signal mass points gener- resonance shape meets the smoothly falling two-photon ated, and is parameterized as a function of mX and ma . This mass background. For the benchmark signal scenario serves as an input to the calculation of the cross-section investigated here, since the reconstructed photons are times branching ratios for the benchmark signal scenario. photon-jets (e.g., a → γγ and a → 3π 0 → 6γ), the recon- The modeling of signal mass shape, f, and ε as functions structed mγR γR corresponds to the mass of two a particles, of ðmX ; ma Þ is performed separately for the two different i.e., the mass of the parent particle, X. final states of the benchmark signal scenario, X → aa → For the benchmark signal scenario, for very small values 4γ and X → aa → 6π 0 . In general, the results are similar of ma =mX , the behavior of the DSCB as a function of for the two decay scenarios. The main distinction is in the the mass of two photon-jets is nearly identical to that of the different trend in f with respect to mX and ma , especially BSM process X → 2γ. The position of the fitted peak of the the threshold in ma =mX at which the values of f transition DSCB is slightly lower than the mass input to the generator. from f > 0.5 to f < 0.5. This threshold is found to be at With the NWA approach, the width of the Gaussian core ma =mX ≃ 0.0015 for X → aa → 4γ, and at ma =mX ≃ σ CB is dominated by detector resolution, and it increases 0.0020 for X → aa → 6π 0. linearly with mX , from 2 GeV for mX ¼ 200 GeV to 14 GeV for mX ¼ 2 TeV. For larger values of ma =mX , the wider opening angle between the photons inside a B. Background modeling photon-jet leads to a greater fraction of the energy of the The backgrounds in this search mainly consist of the SM shower leaking out of the window defined by the cells of production of events containing either two prompt photons; the EM calorimeter to collect energy for the reconstruction one prompt photon and one hadronic jet; or two hadronic of photons, leading to a further increase in the mass shift jets. Prompt photons are defined as photons not originating and width of the DSCB. For instance, for mX ¼ 600 GeV from hadron decays. Hadronic jets can be misreconstructed and ma ¼ 5 GeV, the width is σ CB ¼ 8 GeV for the as a photon. The three background components are denoted process X → aa → 4γ, and σ CB ¼ 9 GeV for the process γγ, γj or jγ, and jj, respectively, with the first symbol X → aa → 6π 0 . For a given mX and ma , the same signal indicating the one with a higher value of ET . The mγR γR mass shape modeling results are used for the analysis of the distribution of the sum of these background components is two orthogonal event categories (the low-ΔE category and described by an analytic function, separately for each of the the high-ΔE category), since only a small dependence of two ΔE categories. The parameters of the two analytic the signal mass distributions on ΔE is observed. functions are determined from fits to the mγR γR distributions To validate the mass shape modeling results, injection in the analysis signal region of collision data from a lower tests are performed, where a fixed number of signal events edge of mγR γR ¼ 175 GeV. are inserted into a pseudo-dataset reproducing a back- Based on simulated samples, the contribution from ground-only mγR γR spectrum of one of the two event Drell–Yan processes, where the two isolated electrons categories, and the number of events inserted is then are misreconstructed as photons, is expected to be at the compared with the number determined by fitting the sub-percent level in the analysis signal region. The shape of DSCB. The pseudo-datasets are generated from back- the mγR γR distribution of the Drell-Yan contribution in the ground probability density functions [represented by mass range mγR γR > 175 GeV is expected to be similar to Eq. (1), described in Sec. VI B] with the parameters that of the γγ component, and it is therefore absorbed into determined from a fit to the observed mγR γR spectra in the analytic function fit for the continuum background collision data. For each simulated sample of the benchmark components. scenario, with different values of ma and mX , separate tests The choice of the functional form describing the back- are performed for an increasing number of injected signal ground distribution is based on studies of background events. The average of the number of events determined templates. A variety of functional forms are considered for from the fit to multiple pseudo-datasets and the number the background parameterization to achieve a good com- inserted should be identical in an ideal case, and the promise between limiting the size of a potential bias toward 012008-7 M. AABOUD et al. PHYS. REV. D 99, 012008 (2019) the identification of a signal when none is present (the of the isolation selection criteria by 1 GeV, determining spurious signal) and retaining good statistical power. The the resulting change in the calculated fake rates, and size of the spurious signal for a given functional form is assigning the difference as a systematic uncertainty in estimated by performing a maximum-likelihood fit to the these values. background templates using the sum of signal and back- An additional uncertainty is assessed by altering the ground parametrizations. definition of the control regions. To accomplish this, a To determine the overall shape of the background mass looser photon selection, with respect to the loose0 selection, spectra, background templates are determined using both is defined by removing the requirement on one shower the simulation and collision data, separately for each of the shape variable (wη2 ) instead of two and comparing the two ΔE categories. A simulated sample of prompt diphoton difference between the resulting fake rates. events is used to model the shape of the contribution from The resulting background compositions are shown in γγ events. Subsets of collision data that are similar but Table III. Good agreement is seen between the observed orthogonal to the signal region are used to determine the isolation spectrum and the expected spectrum based on the shapes of the γj, jγ and jj components, where the matrix method results, within uncertainties, as shown subleading reconstructed photon, leading reconstructed in Fig. 4. photon, or both reconstructed photons, respectively, are The background templates are derived with the summa- required to fail the default isolation criterion but satisfy a tion of the γγ; γj; jγ and jj components scaled by the looser one. This looser criterion is defined by loosening the background composition fractions, separately for each of requirement for the calorimeter isolation variable to the two ΔE categories, as described above. The resulting Eiso T < 7 GeV. The resulting samples of γγ; γj; jγ, and jj background templates are presented in Fig. 5. are summed to derive the background templates, scaled To evaluate the size of the spurious signal, a test is with the background composition fractions determined performed using these background templates and the signal from the matrix method described below. modeling described in Sec. VI A. The background tem- The background composition of a given mass spectrum plates are normalized to the integrated luminosity for this of two reconstructed photons is estimated using a matrix search, 36.7 fb−1 . A family of functions, adapted from method [33], where events are categorized into four subsets those used by searches for new physics signatures in dijet by whether both, only the leading, only the subleading, or final states [34], is chosen to describe the shape of the mγR γR neither of the two leading reconstructed photons satisfy the distribution: calorimeter isolation requirement. The method relies on Pk b ðlog xÞj gðkÞ ðx; a; fbj gj¼0;k Þ ¼ Nð1 − x2 Þa x j¼0 j external estimates of the efficiency for prompt photons 1 : ð1Þ satisfying calorimeter isolation and the rate at which hadronic jets can mimic a photon satisfying calorimeter pffiffiffi The variable x is defined as x ¼ mγR γR = s. The parameters isolation (the “fake rate”). Photon isolation efficiency is a and bj are free parameters and N is the normalization estimated with simulated samples of prompt photons. The isolation variables of photons in simulated samples are factor. The spurious signal tests are then performed using a adjusted by applying correction factors obtained from small maximum-likelihood fit of the sum of the signal and differences observed between photon-enriched control background parametrizations to each of the two back- samples of collision data and simulation. An uncertainty ground templates. The spurious signal is allowed to be is assessed for the photon isolation efficiency by comparing negative as well as positive. The final functional form used the nominal efficiencies with those derived without apply- to model the background when performing the search for resonances is one where the estimated spurious signal is ing the corrections to the isolation variable in simulated required to be smaller than 30% of the statistical uncer- samples. Fake rates are determined using subsets of tainty in the fitted signal yield across the full mass collision data with selection criteria imposed so that they spectrum. The cutoff of 30% is chosen to ensure that the are similar but orthogonal to the analysis signal region contribution of this systematic uncertainty to the total (“control regions”). These control regions are defined by requiring reconstructed photons to fail the baseline loose0 photon selection but satisfy another, looser photon selec- TABLE III. Summary of the measured background composi- tion. This looser photon selection, with respect to the loose0 tions for the two categories. selection, is defined by removing requirements on two Low-ΔE category High-ΔE category additional shower shape variables that quantify the lateral shower development in the EM calorimeter second layer γγ 0.930þ0.027 −0.031 0.48  0.16 (wη2 and Rϕ , described in Table 1 of Ref. [30]). γj 0.051þ0.021 −0.018 0.32þ0.08 −0.09 A difference of approximately 1 GeV is found between jγ 0.014þ0.004 0.108þ0.001 −0.005 −0.016 the isolation energy spectra in the signal and control jj 0.005þ0.006 −0.003 0.09þ0.09 −0.05 regions. This is accounted for by shifting the threshold 012008-8 SEARCH FOR PAIRS OF HIGHLY COLLIMATED PHOTON … PHYS. REV. D 99, 012008 (2019) 0.45 0.5 ATLAS ATLAS 1/N dN/dET [1/4.0 GeV] 0.4 T [1/4.0 GeV] s =13 TeV, 36.7 fb-1 s =13 TeV, 36.7 fb-1 0.4 0.35 low-ΔE category low-ΔE category leading γ 0.3 subleading γ R R iso 0.3 Data 0.25 Data 1/N dN/dEiso Matrix Method Results (total) Matrix Method Results (total) Real-Real component 0.2 Real-Real component 0.2 Real-Fake component Real-Fake component 0.15 Fake-Real component Fake-Real component 0.1 Fake-Fake component 0.1 Fake-Fake component 0.05 0 0 −40 −20 0 20 40 60 80 −40 −20 0 20 40 60 80 iso iso ET [GeV] ET [GeV] (a) (b) 0.3 0.2 ATLAS ATLAS 1/N dN/dET [1/4.0 GeV] 0.18 T [1/4.0 GeV] -1 -1 0.25 s =13 TeV, 36.7 fb s =13 TeV, 36.7 fb 0.16 high-ΔE category high-ΔE category 0.2 leading γ R 0.14 subleading γ R 0.12 iso Data Data 1/N dN/dEiso 0.15 Matrix Method Results (total) 0.1 Matrix Method Results (total) Real-Real component Real-Real component Real-Fake component 0.08 Real-Fake component 0.1 Fake-Real component 0.06 Fake-Real component Fake-Fake component Fake-Fake component 0.05 0.04 0.02 0 0 −40 −20 0 20 40 60 80 −40 −20 0 20 40 60 80 iso iso ET [GeV] ET [GeV] (c) (d) FIG. 4. Comparison of the observed Eiso T spectra and the expected spectra based on the background composition measurement results. The modeled spectra of γγ (dashed), γj (dotted), jγ (dot-dashed), and jj (long-dashed) components are added using the background composition measured with the matrix method. The results are compared for each of the two ΔE categories where (a) shows the leading reconstructed photon in the low-ΔE category, (b) the subleading reconstructed photon in the low-ΔE category, (c) the leading reconstructed photon in the high-ΔE category, and (d) the subleading reconstructed photon in the high-ΔE category. 1 1 ATLAS ATLAS 10−1 s=13 TeV, 36.7 fb-1 Fit 10−1 s=13 TeV, 36.7 fb-1 Fit low-ΔE category Background template: high-ΔE category Background template: 10−2 Sum 10−2 Sum [GeV-1] [GeV-1] γ γ Fraction: 93% γ γ Fraction: 48% 10−3 10−3 γj 5% γj 32% −4 10−4 R R 10 jγ jγ R R 1% 11% γ γ 1/N dN/dmγ 1/N dN/dmγ jj 1% jj 9% 10−5 10−5 −6 10 10−6 10−7 10−7 10−8 10−8 −9 10 10−9 500 1000 1500 2000 2500 500 1000 1500 2000 2500 mγ γ [GeV] mγ γ [GeV] R R R R FIG. 5. Background templates used for the spurious signal test. The sum of the background components for each of the two ΔE categories, and the breakdown into components (γγ, γj, jγ, and jj) are shown. The unbinned likelihood fit with the chosen functional form [shown in Eq. (1) with k ¼ 1] is superimposed. The expected background compositions, which are measured inclusively for events in mγ R γR > 175 GeV, are shown on the figures. 012008-9 M. AABOUD et al. PHYS. REV. D 99, 012008 (2019) uncertainty, including all statistical and systematic uncer- at around ma =mX ¼ 0.002, and decreasing to 6%–10% at tainties, is subdominant and smaller than 5%. 0.002 < ma =mX < 0.01. This is taken as the estimate of the The method is validated by checking that similar results systematic uncertainty in f. are obtained when the test is performed using variations of Other systematic uncertainties in the extracted signal the background templates, for which the background yield and the migration of signal events between the two compositions are shifted within the uncertainties presented orthogonal ΔE categories are evaluated by comparisons in Table III. When the fraction of the γγ component is between nominal and systematically varied versions of shifted up and those for γj, jγ, jj are shifted down, or vice various experimental uncertainty sources, such as the versa, the size of the resulting spurious signals are con- photon energy scale and resolution, isolation selection sistent within the statistical uncertainty of the background efficiency, shower shape modeling, and pileup. The sys- templates. tematic uncertainties due to the photon energy scale and The resulting functional form used for the background resolution are adapted from results determined during LHC mass spectrum evaluation of the two categories is shown in Run 1 [32], with minor updates derived from data-driven Eq. (1) with k ¼ 1. Figure 5 shows the level of agreement corrections determined using Run 2 data. Uncertainties between this functional form and the background tem- related to the loose0 photon identification scheme are plates. The resulting background model and its associated evaluated with the systematic variations for the shower systematic uncertainties are used when searching for shape modeling, without the correction factors applied to resonances in the mass spectra of the signal region. simulation derived from small differences observed between photon-enriched control samples of collision data VII. SYSTEMATIC UNCERTAINTIES and simulation [36]. The uncertainty in the photon calo- Several sources of systematic uncertainties that affect rimeter isolation efficiency is calculated from changes the determination of the signal yield are taken into account. due to applying and not applying corrections derived In most cases, systematic uncertainties are smaller than from small differences observed between photon-enriched statistical errors. control samples of collision data and simulation. The The uncertainty in the combined 2015 þ 2016 integrated uncertainties of the efficiency correction factors using luminosity is 2.1%. It is derived, following a methodology photon-enriched control samples of collision data are used similar to that detailed in Ref. [35], from a calibration of to derive the uncertainty in the photon track isolation the luminosity scale using x–y beam-separation scans efficiency. The pileup uncertainty is taken into account by performed in August 2015 and May 2016. propagating it through the event selection. The uncertainties The impact of the photon energy resolution on signal in ε and f due to these sources for the mass regions modeling is evaluated. It mainly affects the mass shape considered for the benchmark signal scenario are calculated. width, σ CB , of the Crystal Ball function used to model the The uncertainties are less than 1% in almost all cases, rising signal mass shape. The photon energy resolution is adjusted to ∼4% for some isolation and shower shape uncertainties for by one standard deviation from the nominal value in both larger values of ma =mX at the edge of the analysis sensitivity. positive and negative directions, and the resulting change in Additional systematic uncertainties in the loose diphoton the fitted signal width is determined. The relative difference trigger efficiency are not assessed. The ET requirements for in the fitted value of σ CB ranges from as small as a few reconstructed photons are much larger than the value at percent to as large as 37%, increasing with larger mX and which the diphoton trigger utilized becomes nearly 100% dependent slightly on ma , and is taken as a systematic efficient, and any additional uncertainties in signal effi- uncertainty. ciency due to mismodeling of the trigger-level shower Systematic uncertainties in the extracted signal yield due shape variables are accounted for when calculating uncer- to signal mass shape modeling are evaluated via injection tainties in offline loose0 identification, because the loose tests, described in Sec. VI A. The final fitted values of the photon identification definitions at the trigger and offline number of signal events deviate from the injected values by levels are strongly correlated. less than 1% almost everywhere, rising to a maximum of The uncertainty in the signal kinematic acceptance, 5% for some signal mass values at the edge of the analysis which is included in the definition of the total signal search region of ma ¼ 0.1 GeV for the high-ΔE category selection efficiency, is evaluated for the choice of PDF set and ma ¼ 0.01 × mX for the low-ΔE category. This is used for the simulation of the signal samples. It is less than taken as the estimate of the systematic uncertainty in the 1% in most cases, rising to ∼4% for large mX around signal yield. mX ∼ 2 TeV. Uncertainties in the modeling of the category fraction, f, The systematic uncertainties related to the evaluation of are evaluated by an envelope to cover the deviations of the the background mass spectrum are determined from the values of f from simulation and the parameterization. The spurious signal method, described in Sec. VI B. The absolute value of the change in f varies as a function of spurious signal as a function of mX and ma is parametrized ma =mX , from 3% at ma =mX ¼ 0, increasing to 12%–14% so that the modeling between mass points is continuous. 012008-10 SEARCH FOR PAIRS OF HIGHLY COLLIMATED PHOTON … PHYS. REV. D 99, 012008 (2019) TABLE IV. Breakdown of the relative contributions to the total uncertainty in the signal yield obtained from the fit. For each source of uncertainty σ source, the fraction σ source =σ total is presented, where σ total is the total uncertainty that includes the statistical uncertainty. The sum in quadrature of the individual components differs from 100% due to small correlations between the components. The values here are for the signal process X → aa → 4γ. The mass points ðmX ; ma Þ ¼ ð200 GeV; 0.3 GeVÞ; ð600 GeV; 0.9 GeVÞ correspond to those values for which the systematic uncertainty of the category fraction f is the highest. Similar results are found for the decay X → aa → 6π 0. mX ½GeV; ma ½GeV (200, 0.1) (200, 0.3) (200, 2) (600, 0.1) (600, 0.9) (600, 5) σ source =σ total Statistical 66% 72% 86% 99% 94% 98% Spurious signal (low-ΔE) 74% 37% 9% 13% 5% 3% Spurious signal (high-ΔE) 6% 67% 55% 2% 24% 22% Category fraction f 7% 19% 9% 3% 25% 7% Signal mass resolution 7% 2% 5% 13% 12% 1% Signal mass shape (low-ΔE) 3% 1%  5% 4% 3% Signal mass shape (high-ΔE)   1% 3% 3% 2% This parametrization is performed in such a way that it can Gaussian function (for spurious signal and uncertainties slightly overestimate the size of spurious signals, especially related to the migration of events between the ΔE catego- at the lower end of the mX range, mX ¼ 200 GeV. The size ries) or a log-normal function (for all other uncertainties). of the parametrized spurious signal decreases for larger mX Two nuisance parameters are introduced for the extracted and depends slightly on the ma value, ranging from 85 to signal yield due to signal mass shape modeling uncertain- 6 × 10−3 events for the low-ΔE category, and from 32 to ties, one for each ΔE category, and they are multiplied by 1 × 10−2 events for the high-ΔE category. the signal normalizations of each category. One nuisance The systematic uncertainties are generally smaller than parameter is introduced for the impact of the photon energy the statistical errors, with the systematic uncertainty in the resolution on the mass shape width, and it is multiplied by background evaluated from the spurious signal being the the signal mass shape width σ CB . One nuisance parameter is largest contribution. This is because the parametrization of introduced for the modeling of the category fraction, f, the size of spurious signals slightly overestimates the values which is added to f to shift its value. Several nuisance at the lower end of the mX range, as described above. The parameters are introduced for experimental uncertainty impact of the systematic uncertainties on the expected limit sources and PDF uncertainty that affect the extracted signal decreases with the resonance mass mX from 51% at most yield, total signal selection efficiency, ε, and category for mX ¼ 200 GeV to 5% at most for mX > 800 GeV. The fraction, f. Two nuisance parameters are introduced for impact of the systematic uncertainties on the signal yield the spurious signals, one for each ΔE category. For a given obtained from the fit is summarized in Table IV. signal mass ðmX ; ma Þ hypothesis, the spurious signals are given the same mγR γR shape as the signal component, and VIII. STATISTICAL PROCEDURE normalized by the size of the spurious signals. For a given fixed signal mass hypothesis, a mass The calculation of p-values for the background- spectrum fit including both the background and signal only hypothesis (p0 ) is performed for a narrow resonance components is performed to the full mass spectrum of from mX ¼ 200 GeV to mX ¼ 2.7 TeV, with a scan step mγR γR > 175 GeV, using an unbinned maximum-likeli- of 1 GeV. Since the samples for the benchmark signal hood approach, simultaneously for the two categories scenario were simulated for the mX values in the range (low-ΔE and high-ΔE categories). A constraint is placed 200 GeV < mX < 2 TeV, the results of signal mass shape on the ratio of the two separate normalization factors of the modeling, modeling of category fraction f, and systematic signal component for the two categories, evaluated from the uncertainties are extrapolated for the mX values in the category fraction f, which depends on the signal masses range 2 TeV < mX < 2.7 TeV. mX and ma . Deviations from the background-only hypoth- Expected and observed upper limits, at the 95% esis are searched for starting from mX ¼ 200 GeV, and the confidence level (C.L.), on the production cross section entire mγR γR range is used for the background component times the product of branching ratios are calculated as a for each hypothesis test. The p-values are calculated with function of the mass parameters of the benchmark signal the profile likelihood ratio as the basis for the test statistic scenario, mX and ma , following the CLs modified frequent- and utilizing an asymptotic approximation [37]. ist prescription [38]. Upper limits are determined separately Systematic uncertainties (described in Sec. VII) are for the two final states of the benchmark signal scenario treated as nuisance parameters in the likelihood function, where the a particle decays into either a pair of photons or where each is a floating parameter constrained by either a three neutral pions. 012008-11 M. AABOUD et al. PHYS. REV. D 99, 012008 (2019) The assumptions inherent in the use of the asymptotic category. The largest local deviation from the background- approximation are validated by sampling distributions of only hypothesis is found to be 2.7σ, corresponding to the test statistic using pseudoexperiments, for a few mX ¼ 729 GeV and ma ¼ 0.1 GeV for the decay X → signal mass points. The asymptotic approximation yields aa → 4γ. The width of the signal mass shape for mX ¼ median values of the expected upper limits within 5% of 729 GeV and ma ¼ 0.1 GeV is 6 GeV, and thus this those calculated with a large number of pseudoexperi- deviation appears as a small area in Fig. 7. A small excess ments for most of the values of mX and ma tested. Due to of events is also observed centered around mX ¼ 1.1 TeV the small number of events in data in the region mγR γR > and ma ¼ 7 GeV, which corresponds to a local deviation of 1 TeV in the high-ΔE category, larger deviations are 2.2σ. The observed maximum local deviation is less signifi- observed for mX > 1TeV and large ma . The deviation is cant than the median of the largest deviation obtained in smaller than 5% at ðmX ; ma Þ ¼ ð1 TeV; 10 GeVÞ, but the background-only pseudoexperiments, calculated in the expected upper limits obtained from the asymptotic search region defined by mX values from 200 GeV to approximation are smaller than those from pseudoexperi- 2.7 TeV and ma values from 0.1 GeV to 0.01 × mX . The ments by 20% for ðmX ; ma Þ ¼ ð1.5 TeV; 10 GeVÞ, and mγR γR mass distribution is found to be consistent with the 30% for ðmX ; ma Þ ¼ ð2 TeV; 10 GeVÞ. background-only hypothesis. The 95% C.L. observed and expected upper limits on the cross section for the production via gluon-gluon IX. RESULTS fusion of a high-mass scalar particle, X, with narrow The observed mγR γR spectra in the signal region are shown width times the branching ratios into a pair of a particles in Fig. 6. The results of the two-dimensional scan of p0 , and the subsequent decay of each a into a pair of photons, equivalently expressed in terms of the local significance—the σ X × BðX → aaÞ × Bða → γγÞ2 , are shown in Fig. 8, number of standard deviations away from the mean of a separately for different values of ma . The same result normal distribution—are shown in Fig. 7. Two different is presented in Fig. 9, with the ratio ma =mX shown on the regimes can be seen in this plot, above and below the horizontal axis. This plot illustrates the two features of threshold at ma ∼ 0.0015 × mX . These are a result of the this search. First, when the ratio ma =mX is larger than a categorization of events based on the ΔE variable. For threshold of roughly 0.0015, more signal events are ma ≲ 0.0015 × mX , a larger fraction of signal events is ex- expected in the high-ΔE category, which has a signifi- pected in the low-ΔE category, and for ma ≳ 0.0015 × mX , a cantly better signal-to-background ratio compared with larger fraction of signal events is expected in the high-ΔE the low-ΔE category, thus leading to stronger upper 105 105 ATLAS ATLAS 104 s=13 TeV, 36.7 fb-1 104 s=13 TeV, 36.7 fb-1 low-Δ E category high-Δ E category Events / 20 GeV Events / 20 GeV 103 Data 103 Data 2 Background-only fit ± 1σ 2 Background-only fit ± 1σ 10 10 10 10 1 1 −1 −1 10 10 10−2 10−2 500 1000 1500 2000 2500 500 1000 1500 2000 2500 mγ [GeV] mγ [GeV] Significance Significance γ γ 2 R R 2 R R 0 0 −2 −2 500 1000 1500 2000 2500 500 1000 1500 2000 2500 mγ γ [GeV] mγ γ [GeV] R R R R FIG. 6. Observed distributions of the mass of two reconstructed photons passing all analysis selections, mγR γ R , for the two signal region categories. The background-only fit result is superimposed. The 1σ uncertainty originating from the uncertainties in the fit function parameter values is shown as a shaded band around the fit. The lower panel of each plot displays the significance associated with the observed event yield in each bin, calculated before considering systematic uncertainties. The calculation assumes that the event yield in each bin is Poisson-distributed with a mean given by the background-only fit. The computation is performed with a one-sided test based on the positive or negative tail of the Poisson distribution, depending on the sign of the difference between the event yield and the fit estimate, with negative significance values quoted for negative differences [39]. 012008-12 SEARCH FOR PAIRS OF HIGHLY COLLIMATED PHOTON … PHYS. REV. D 99, 012008 (2019) 2.5 104 95% CL limit on σX×B(X→aa→4γ ) [fb] 25 ATLAS ATLAS Obs. Exp. m = 200 GeV X s=13 TeV, 36.7 fb-1 s = 13 TeV, 36.7 fb-1 Obs. Exp. m = 400 GeV X→aa→4γ NWA Obs. X Exp. m = 600 GeV 2 103 Local significance [σ] X 20 Obs. Exp. m = 800 GeV X Obs. Exp. m = 1000 GeV X Obs. Exp. m = 2000 GeV 1.5 X Expected ±1σ for mX = 200 GeV ma [GeV] 15 102 Expected ±2σ 10 1 10 5 0.5 1 0 0 500 1000 1500 2000 2500 10−1 mX [GeV] 0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 ma/mX FIG. 7. Results of the search for deviations from the back- ground-only hypothesis in the observed distributions of the mγR γ R , FIG. 9. The observed and expected upper limits on the expressed in significance. They are presented as a function of ma production cross section times the product of branching ratios and mX for the benchmark signal scenario involving a scalar for the benchmark signal scenario involving a scalar particle X particle X with narrow width decaying via X → aa → 4γ. with narrow width decaying via X →aa→4γ, σ X × BðX → aaÞ× Bða → γγÞ2 . They are evaluated as a function of ma =mX for fixed values of mX . The limits are calculated using the asymptotic 103 approximation. This leads to an underestimate of the limits, 95% CL limit on σX×B(X→aa→4γ ) [fb] ATLAS Obs. Exp. ma = 0.1 GeV s = 13 TeV, 36.7 fb-1 Obs. Exp. ma = 1 GeV especially for mX > 1 TeV and large ma . The results for the X→aa→4γ NWA 102 Obs. Exp. ma = 2 GeV X → aa → 6π 0 case are qualitatively similar. Obs. Exp. ma = 5 GeV Obs. Exp. ma = 10 GeV 10 103 95% CL limit on σX×B(X→aa→6π0) [fb] ATLAS Obs. Exp. ma = 0.5 GeV s = 13 TeV, 36.7 fb-1 X→aa→6π0 NWA Obs. Exp. ma = 1 GeV 1 102 Obs. Exp. ma = 2 GeV Obs. Exp. ma = 5 GeV Obs. Exp. ma = 10 GeV 10−1 10 10−2 0 500 1000 1500 2000 1 mX [GeV] 10−1 FIG. 8. The observed and expected upper limits on the pro- duction cross-section times the product of branching ratios for the benchmark signal scenario involving a scalar particle X with 10−2 0 500 1000 1500 2000 narrow width decaying via X → aa → 4γ, σ X × BðX → aaÞ× mX [GeV] Bða → γγÞ2 . The limits are calculated using the asymptotic approximation. This leads to an underestimate of the limits, FIG. 10. The observed and expected upper limits on the pro- especially for mX > 1 TeV and large ma . The limits for ma ¼ duction cross section times the product of branching ratios for the 5 GeV and 10 GeV do not cover as large a range as the other mass benchmark signal scenario involving a scalar particle X with points, since the region of interest is limited to ma < 0.01 × mX . narrow width decaying via X → aa → 6π 0 , σ X × BðX → aaÞ× Bða → 3π 0 Þ2 . The limits are calculated using the asymptotic limits. Second, for larger values of ma =mX , the decrease approximation. This leads to an underestimate of the limits, in the signal selection efficiency leads to weaker upper especially for mX > 1 TeV and large ma . The limits for ma ¼ 5 limits. and 10 GeV do not cover as large a range as the other mass points, The 95% C.L. observed and expected upper limits on the since the region of interest is limited to ma < 0.01 × mX . cross-section times product of branching ratios for the decay of the a into three neutral pions, σ X × BðX → aaÞ× X. CONCLUSION Bða → 3π 0 Þ2 , are shown in Fig. 10, separately for different values of ma . This result shows features similar to that A search for pairs of highly collimated groupings of shown in Fig. 8, with slight differences arising mainly from photons—photon-jets—that are identified as single, pho- the different trend of the category fraction, f, with respect tonlike energy clusters in the EM calorimeter of the ATLAS to the mass values mX and ma . detector at the LHC is presented. Data from proton-proton 012008-13 M. AABOUD et al. PHYS. REV. D 99, 012008 (2019) collisions at a center-of-mass energy of 13 TeV collected in YerPhI, Armenia; ARC, Australia; BMWFW and FWF, 2015 and 2016, corresponding to an integrated luminosity Austria; ANAS, Azerbaijan; SSTC, Belarus; CNPq and of 36.7 fb−1 , are used. Pairs of photon-jets can arise, for FAPESP, Brazil; NSERC, NRC and CFI, Canada; CERN; example, as the final-state decay products of a new high- CONICYT, Chile; CAS, MOST and NSFC, China; mass resonance decaying via new light resonances into COLCIENCIAS, Colombia; MSMT CR, MPO CR and highly collimated groupings of photons. Candidate photon- VSC CR, Czech Republic; DNRF and DNSRC, Denmark; jet events are initially selected with a loose diphoton trigger IN2P3-CNRS, CEA-DRF/IRFU, France; SRNSFG, and then potential photon-jets are selected using a combi- Georgia; BMBF, HGF, and MPG, Germany; GSRT, nation of variables that model EM shower development. Greece; RGC, Hong Kong SAR, China; ISF, I-CORE Sensitivity to photon-jets is then increased by categorizing and Benoziyo Center, Israel; INFN, Italy; MEXT and reconstructed photons by one of those shower shape JSPS, Japan; CNRST, Morocco; NWO, Netherlands; variables and narrow resonances are searched for in the RCN, Norway; MNiSW and NCN, Poland; FCT, resulting mass distributions of two reconstructed photons. Portugal; MNE/IFA, Romania; MES of Russia and NRC The observed mass spectra are consistent with the SM KI, Russian Federation; JINR; MESTD, Serbia; MSSR, background expectation. Slovakia; ARRS and MIZŠ, Slovenia; DST/NRF, South The results are interpreted in the context of a BSM Africa; MINECO, Spain; SRC and Wallenberg Foundation, scenario containing a high-mass scalar particle with narrow Sweden; SERI, SNSF and Cantons of Bern and Geneva, width, X, that decays into photon-jets via low-mass Switzerland; MOST, Taiwan; TAEK, Turkey; STFC, intermediate particles with spin 0, a. For the range United Kingdom; DOE and NSF, United States of of mX investigated, from 200 GeV to 2 TeV, upper limits America. In addition, individual groups and members have on σ × BðX → aaÞ × Bða → γγÞ2 are found to range from received support from BCKDF, the Canada Council, 0.2 to 1 fb over most of the range of mX , for CANARIE, CRC, Compute Canada, FQRNT, and the 100 MeV < ma < 2 GeV, rising to 10–100 fb for values Ontario Innovation Trust, Canada; EPLANET, ERC, of mX at the low end of the range, depending upon ma . ERDF, FP7, Horizon 2020 and Marie Skłodowska-Curie Similarly, upper limits on σ × BðX → aaÞ × Bða → 3π 0 Þ2 Actions, European Union; Investissements d’Avenir Labex are found to range from 0.2 fb to 1 fb over most of the range and Idex, ANR, Région Auvergne and Fondation Partager of mX , for 500 MeV < ma < 2 GeV, rising to 10–100 fb le Savoir, France; DFG and AvH Foundation, Germany; for values of mX at the low end of the range. These limits Herakleitos, Thales and Aristeia programmes co-financed are calculated using an asymptotic approximation. In by EU-ESF and the Greek NSRF; BSF, GIF and Minerva, addition to the calculated upper limits for this benchmark Israel; BRF, Norway; CERCA Programme Generalitat de signal scenario, the results, including the evaluation of the Catalunya, Generalitat Valenciana, Spain; the Royal observed upper limits, are provided in HepData [40] in a Society and Leverhulme Trust, United Kingdom. The largely model-independent way, to enable reinterpretation crucial computing support from all WLCG partners is in the context of other signal models containing highly acknowledged gratefully, in particular from CERN, the collimated photon-jets of low or high photon multiplicity. 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Hohov,129 012008-18 SEARCH FOR PAIRS OF HIGHLY COLLIMATED PHOTON … PHYS. REV. D 99, 012008 (2019) T. R. Holmes,36 M. Holzbock,112 M. Homann,45 S. Honda,166 T. Honda,79 T. M. Hong,136 A. Hönle,113 B. H. Hooberman,170 W. H. Hopkins,128 Y. Horii,115 P. Horn,46 A. J. Horton,149 L. A. Horyn,36 J-Y. Hostachy,56 A. Hostiuc,145 S. Hou,155 A. Hoummada,34a J. Howarth,98 J. Hoya,86 M. Hrabovsky,127 J. Hrdinka,35 I. Hristova,19 J. Hrivnac,129 A. Hrynevich,106 T. Hryn’ova,5 P. J. Hsu,62 S.-C. Hsu,145 Q. Hu,29 S. Hu,58c Y. Huang,15a Z. Hubacek,139 F. Hubaut,99 M. Huebner,24 F. Huegging,24 T. B. Huffman,132 E. W. Hughes,38 M. Huhtinen,35 R. F. H. Hunter,33 P. Huo,152 A. M. Hupe,33 N. Huseynov,77,e J. Huston,104 J. Huth,57 R. Hyneman,103 G. Iacobucci,52 G. Iakovidis,29 I. Ibragimov,148 L. Iconomidou-Fayard,129 Z. Idrissi,34e P. Iengo,35 R. Ignazzi,39 O. Igonkina,118,ee R. Iguchi,160 T. Iizawa,52 Y. Ikegami,79 M. Ikeno,79 D. Iliadis,159 N. Ilic,150 F. Iltzsche,46 G. Introzzi,68a,68b M. Iodice,72a K. 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D 99, 012008 (2019) (ATLAS Collaboration) 1 Department of Physics, University of Adelaide, Adelaide, Australia 2 Physics Department, SUNY Albany, Albany, New York, USA 3 Department of Physics, University of Alberta, Edmonton, Alberta, Canada 4a Department of Physics, Ankara University, Ankara, Turkey 4b Istanbul Aydin University, Istanbul, Turkey 4c Division of Physics, TOBB University of Economics and Technology, Ankara, Turkey 5 LAPP, Université Grenoble Alpes, Université Savoie Mont Blanc, CNRS/IN2P3, Annecy, France 6 High Energy Physics Division, Argonne National Laboratory, Argonne, Illinois, USA 7 Department of Physics, University of Arizona, Tucson, Arizona, USA 8 Department of Physics, University of Texas at Arlington, Arlington, Texas, USA 9 Physics Department, National and Kapodistrian University of Athens, Athens, Greece 10 Physics Department, National Technical University of Athens, Zografou, Greece 11 Department of Physics, University of Texas at Austin, Austin, Texas, USA 12a Bahcesehir University, Faculty of Engineering and Natural Sciences, Istanbul, Turkey 12b Istanbul Bilgi University, Faculty of Engineering and Natural Sciences, Istanbul, Turkey 12c Department of Physics, Bogazici University, Istanbul, Turkey 12d Department of Physics Engineering, Gaziantep University, Gaziantep, Turkey 13 Institute of Physics, Azerbaijan Academy of Sciences, Baku, Azerbaijan 14 Institut de Física d’Altes Energies (IFAE), Barcelona Institute of Science and Technology, Barcelona, Spain 15a Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China 15b Physics Department, Tsinghua University, Beijing, China 15c Department of Physics, Nanjing University, Nanjing, China 15d University of Chinese Academy of Science (UCAS), Beijing, China 16 Institute of Physics, University of Belgrade, Belgrade, Serbia 17 Department for Physics and Technology, University of Bergen, Bergen, Norway 18 Physics Division, Lawrence Berkeley National Laboratory and University of California, Berkeley, California, USA 19 Institut für Physik, Humboldt Universität zu Berlin, Berlin, Germany 20 Albert Einstein Center for Fundamental Physics and Laboratory for High Energy Physics, University of Bern, Bern, Switzerland 21 School of Physics and Astronomy, University of Birmingham, Birmingham, United Kingdom 22 Centro de Investigaciónes, Universidad Antonio Nariño, Bogota, Colombia 23a Dipartimento di Fisica e Astronomia, Università di Bologna, Bologna, Italy 23b INFN Sezione di Bologna, Italy 24 Physikalisches Institut, Universität Bonn, Bonn, Germany 25 Department of Physics, Boston University, Boston, Massachusetts, USA 26 Department of Physics, Brandeis University, Waltham, Massachusetts, USA 27a Transilvania University of Brasov, Brasov, Romania 27b Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest, Romania 27c Department of Physics, Alexandru Ioan Cuza University of Iasi, Iasi, Romania 27d National Institute for Research and Development of Isotopic and Molecular Technologies, Physics Department, Cluj-Napoca, Romania 27e University Politehnica Bucharest, Bucharest, Romania 27f West University in Timisoara, Timisoara, Romania 28a Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovak Republic 28b Department of Subnuclear Physics, Institute of Experimental Physics of the Slovak Academy of Sciences, Kosice, Slovak Republic 29 Physics Department, Brookhaven National Laboratory, Upton, New York, USA 30 Departamento de Física, Universidad de Buenos Aires, Buenos Aires, Argentina 31 Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom 32a Department of Physics, University of Cape Town, Cape Town, South Africa 32b Department of Mechanical Engineering Science, University of Johannesburg, Johannesburg, South Africa 32c School of Physics, University of the Witwatersrand, Johannesburg, South Africa 33 Department of Physics, Carleton University, Ottawa, Ontario, Canada 34a Faculté des Sciences Ain Chock, Réseau Universitaire de Physique des Hautes Energies - Université Hassan II, Casablanca, Morocco 012008-24 SEARCH FOR PAIRS OF HIGHLY COLLIMATED PHOTON … PHYS. 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D 99, 012008 (2019) 34b Centre National de l’Energie des Sciences Techniques Nucleaires (CNESTEN), Rabat, Morocco 34c Faculté des Sciences Semlalia, Université Cadi Ayyad, LPHEA-Marrakech, Morocco 34d Faculté des Sciences, Université Mohamed Premier and LPTPM, Oujda, Morocco 34e Faculté des sciences, Université Mohammed V, Rabat, Morocco 35 CERN, Geneva, Switzerland 36 Enrico Fermi Institute, University of Chicago, Chicago, Illinois, USA 37 LPC, Université Clermont Auvergne, CNRS/IN2P3, Clermont-Ferrand, France 38 Nevis Laboratory, Columbia University, Irvington, New York, USA 39 Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark 40a Dipartimento di Fisica, Università della Calabria, Rende, Italy 40b INFN Gruppo Collegato di Cosenza, Laboratori Nazionali di Frascati, Italy 41 Physics Department, Southern Methodist University, Dallas, Texas, USA 42 Physics Department, University of Texas at Dallas, Richardson, Texas, USA 43a Department of Physics, Stockholm University, Sweden 43b 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 Kern- und Teilchenphysik, Technische Universität Dresden, Dresden, Germany 47 Department of Physics, Duke University, Durham, North Carolina, USA 48 SUPA - School of Physics and Astronomy, University of Edinburgh, Edinburgh, United Kingdom 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, Genève, Switzerland 53a Dipartimento di Fisica, Università di Genova, Genova, Italy 53b INFN Sezione di Genova, Italy 54 II. Physikalisches Institut, Justus-Liebig-Universität Giessen, Giessen, Germany 55 SUPA - School of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom 56 LPSC, Université Grenoble Alpes, CNRS/IN2P3, Grenoble INP, Grenoble, France 57 Laboratory for Particle Physics and Cosmology, Harvard University, Cambridge, Massachusetts, USA 58a Department of Modern Physics and State Key Laboratory of Particle Detection and Electronics, University of Science and Technology of China, Hefei, China 58b Institute of Frontier and Interdisciplinary Science and Key Laboratory of Particle Physics and Particle Irradiation (MOE), Shandong University, Qingdao, China 58c School of Physics and Astronomy, Shanghai Jiao Tong University, KLPPAC-MoE, SKLPPC, Shanghai, China 58d Tsung-Dao Lee Institute, Shanghai, China 59a Kirchhoff-Institut für Physik, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany 59b Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany 60 Faculty of Applied Information Science, Hiroshima Institute of Technology, Hiroshima, Japan 61a Department of Physics, Chinese University of Hong Kong, Shatin, N.T., Hong Kong, China 61b Department of Physics, University of Hong Kong, Hong Kong, China 61c Department of Physics and Institute for Advanced Study, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China 62 Department of Physics, National Tsing Hua University, Hsinchu, Taiwan 63 Department of Physics, Indiana University, Bloomington, Indiana, USA 64a INFN Gruppo Collegato di Udine, Sezione di Trieste, Udine, Italy 64b ICTP, Trieste, Italy 64c Dipartimento di Chimica, Fisica e Ambiente, Università di Udine, Udine, Italy 65a INFN Sezione di Lecce, Italy 65b Dipartimento di Matematica e Fisica, Università del Salento, Lecce, Italy 66a INFN Sezione di Milano, Italy 66b Dipartimento di Fisica, Università di Milano, Milano, Italy 67a INFN Sezione di Napoli, Italy 67b Dipartimento di Fisica, Università di Napoli, Napoli, Italy 68a INFN Sezione di Pavia, Italy 68b Dipartimento di Fisica, Università di Pavia, Pavia, Italy 69a INFN Sezione di Pisa, Italy 69b Dipartimento di Fisica E. Fermi, Università di Pisa, Pisa, Italy 70a INFN Sezione di Roma, Italy 012008-25 M. AABOUD et al. PHYS. REV. D 99, 012008 (2019) 70b Dipartimento di Fisica, Sapienza Università di Roma, Roma, Italy 71a INFN Sezione di Roma Tor Vergata, Italy 71b Dipartimento di Fisica, Università di Roma Tor Vergata, Roma, Italy 72a INFN Sezione di Roma Tre, Italy 72b Dipartimento di Matematica e Fisica, Università Roma Tre, Roma, Italy 73a INFN-TIFPA, Italy 73b Università degli Studi di Trento, Trento, Italy 74 Institut für Astro- und Teilchenphysik, Leopold-Franzens-Universität, Innsbruck, Austria 75 University of Iowa, Iowa City, Iowa, USA 76 Department of Physics and Astronomy, Iowa State University, Ames, Iowa, USA 77 Joint Institute for Nuclear Research, Dubna, Russia 78a Departamento de Engenharia Elétrica, Universidade Federal de Juiz de Fora (UFJF), Juiz de Fora, Brazil 78b Universidade Federal do Rio De Janeiro COPPE/EE/IF, Rio de Janeiro, Brazil 78c Universidade Federal de São João del Rei (UFSJ), São João del Rei, Brazil 78d Instituto de Física, Universidade de São Paulo, São Paulo, Brazil 79 KEK, High Energy Accelerator Research Organization, Tsukuba, Japan 80 Graduate School of Science, Kobe University, Kobe, Japan 81a AGH University of Science and Technology, Faculty of Physics and Applied Computer Science, Krakow, Poland 81b 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, United Kingdom 88 Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom 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, United Kingdom 91 Department of Physics, Royal Holloway University of London, Egham, United Kingdom 92 Department of Physics and Astronomy, University College London, London, United Kingdom 93 Louisiana Tech University, Ruston, Louisiana, USA 94 Fysiska institutionen, 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, United Kingdom 99 CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France 100 Department of Physics, University of Massachusetts, Amherst, Massachusetts, USA 101 Department of Physics, McGill University, Montreal, Quebec, Canada 102 School of Physics, University of Melbourne, Victoria, Australia 103 Department of Physics, University of Michigan, Ann Arbor, Michigan, USA 104 Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan, 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, Quebec, Canada 108 P.N. Lebedev Physical Institute of the Russian Academy of Sciences, Moscow, Russia 109 Institute for Theoretical and Experimental Physics (ITEP), Moscow, Russia 110 National Research Nuclear University MEPhI, Moscow, Russia 111 D.V. Skobeltsyn Institute of Nuclear Physics, M.V. Lomonosov Moscow State University, Moscow, Russia 112 Fakultät für Physik, Ludwig-Maximilians-Universität München, München, Germany 113 Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), München, Germany 114 Nagasaki Institute of Applied Science, Nagasaki, Japan 115 Graduate School of Science and Kobayashi-Maskawa Institute, Nagoya University, Nagoya, Japan 116 Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico, USA 012008-26 SEARCH FOR PAIRS OF HIGHLY COLLIMATED PHOTON … PHYS. REV. D 99, 012008 (2019) 117 Institute for Mathematics, Astrophysics and Particle Physics, Radboud University Nijmegen/Nikhef, Nijmegen, Netherlands 118 Nikhef National Institute for Subatomic Physics and University of Amsterdam, Amsterdam, Netherlands 119 Department of Physics, Northern Illinois University, DeKalb, Illinois, USA 120a Budker Institute of Nuclear Physics and NSU, SB RAS, Novosibirsk, Russia 120b Novosibirsk State University Novosibirsk, Russia 121 Institute for High Energy Physics of the National Research Centre Kurchatov Institute, Protvino, Russia 122 Department of Physics, New York University, New York, New York, USA 123 The Ohio State University, Columbus, Ohio, USA 124 Faculty of Science, Okayama University, Okayama, Japan 125 Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma, Norman, Oklahoma, USA 126 Department of Physics, Oklahoma State University, Stillwater, Oklahoma, USA 127 Palacký University, RCPTM, Joint Laboratory of Optics, Olomouc, Czech Republic 128 Center for High Energy Physics, University of Oregon, Eugene, Oregon, USA 129 LAL, Université Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, Orsay, France 130 Graduate School of Science, Osaka University, Osaka, Japan 131 Department of Physics, University of Oslo, Oslo, Norway 132 Department of Physics, Oxford University, Oxford, United Kingdom 133 LPNHE, Sorbonne Université, Paris Diderot Sorbonne Paris Cité, CNRS/IN2P3, Paris, France 134 Department of Physics, University of Pennsylvania, Philadelphia, Pennsylvania, USA 135 Konstantinov Nuclear Physics Institute of National Research Centre “Kurchatov Institute”, PNPI, St. Petersburg, Russia 136 Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania, USA 137a Laboratório de Instrumentação e Física Experimental de Partículas - LIP, Portugal 137b Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Lisboa, Portugal 137c Departamento de Física, Universidade de Coimbra, Coimbra, Portugal 137d Centro de Física Nuclear da Universidade de Lisboa, Lisboa, Portugal 137e Departamento de Física, Universidade do Minho, Braga, Portugal 137f Departamento de Física Teorica y del Cosmos, Universidad de Granada, Granada (Spain), Spain 137g Dep Física and CEFITEC of Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Caparica, Portugal 138 Institute of Physics, Academy of Sciences of the Czech Republic, Prague, Czech Republic 139 Czech Technical University in Prague, Prague, Czech Republic 140 Charles University, Faculty of Mathematics and Physics, Prague, Czech Republic 141 Particle Physics Department, Rutherford Appleton Laboratory, Didcot, United Kingdom 142 IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette, France 143 Santa Cruz Institute for Particle Physics, University of California Santa Cruz, Santa Cruz, California, USA 144a Departamento de Física, Pontificia Universidad Católica de Chile, Santiago, Chile 144b Departamento de Física, Universidad Técnica Federico Santa María, Valparaíso, Chile 145 Department of Physics, University of Washington, Seattle, Washington, USA 146 Department of Physics and Astronomy, University of Sheffield, Sheffield, United Kingdom 147 Department of Physics, Shinshu University, Nagano, Japan 148 Department Physik, Universität Siegen, Siegen, Germany 149 Department of Physics, Simon Fraser University, Burnaby, British Columbia, Canada 150 SLAC National Accelerator Laboratory, Stanford, California, USA 151 Physics Department, Royal Institute of Technology, Stockholm, Sweden 152 Departments of Physics and Astronomy, Stony Brook University, Stony Brook, New York, USA 153 Department of Physics and Astronomy, University of Sussex, Brighton, United Kingdom 154 School of Physics, University of Sydney, Sydney, Australia 155 Institute of Physics, Academia Sinica, Taipei, Taiwan 156a E. Andronikashvili Institute of Physics, Iv. Javakhishvili Tbilisi State University, Tbilisi, Georgia 156b High Energy Physics Institute, Tbilisi State University, Tbilisi, Georgia 157 Department of Physics, Technion, Israel Institute of Technology, Haifa, Israel 158 Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv, Israel 159 Department of Physics, Aristotle University of Thessaloniki, Thessaloniki, Greece 160 International Center for Elementary Particle Physics and Department of Physics, University of Tokyo, Tokyo, Japan 161 Graduate School of Science and Technology, Tokyo Metropolitan University, Tokyo, Japan 012008-27 M. AABOUD et al. PHYS. REV. D 99, 012008 (2019) 162 Department of Physics, Tokyo Institute of Technology, Tokyo, Japan 163 Tomsk State University, Tomsk, Russia 164 Department of Physics, University of Toronto, Toronto, Ontario, Canada 165a TRIUMF, Vancouver, British Columbia, Canada 165b Department of Physics and Astronomy, York University, Toronto, Ontario, Canada 166 Division of Physics and Tomonaga Center for the History of the Universe, Faculty of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Japan 167 Department of Physics and Astronomy, Tufts University, Medford, Massachusetts, USA 168 Department of Physics and Astronomy, University of California Irvine, Irvine, California, USA 169 Department of Physics and Astronomy, University of Uppsala, Uppsala, Sweden 170 Department of Physics, University of Illinois, Urbana, Illinois, USA 171 Instituto de Física Corpuscular (IFIC), Centro Mixto Universidad de Valencia - CSIC, Valencia, Spain 172 Department of Physics, University of British Columbia, Vancouver, British Columbia, Canada 173 Department of Physics and Astronomy, University of Victoria, Victoria, British Columbia, Canada 174 Fakultät für Physik und Astronomie, Julius-Maximilians-Universität Würzburg, Würzburg, Germany 175 Department of Physics, University of Warwick, Coventry, United Kingdom 176 Waseda University, Tokyo, Japan 177 Department of Particle Physics, Weizmann Institute of Science, Rehovot, Israel 178 Department of Physics, University of Wisconsin, Madison, Wisconsin, USA 179 Fakultät für Mathematik und Naturwissenschaften, Fachgruppe Physik, Bergische Universität Wuppertal, Wuppertal, Germany 180 Department of Physics, Yale University, New Haven, Connecticut, USA 181 Yerevan Physics Institute, Yerevan, Armenia a Deceased. b Also at Department of Physics, King’s College London, London, United Kingdom. c Also at Istanbul University, Department of Physics, Istanbul, Turkey. d Also at Instituto de Física Teórica de la Universidad Autónoma de Madrid, Spain. e Also at Institute of Physics, Azerbaijan Academy of Sciences, Baku, Azerbaijan. f Also at TRIUMF, Vancouver, British Columbia, Canada. g Also at Department of Physics and Astronomy, University of Louisville, Louisville, Kentucky, USA. h Also at Department of Physics, California State University, Fresno, California, USA. i Also at Department of Physics, University of Fribourg, Fribourg, Switzerland. j Also at Departament de Fisica de la Universitat Autonoma de Barcelona, Barcelona, Spain. k Also at Tomsk State University, Tomsk, and Moscow Institute of Physics and Technology State University, Dolgoprudny, Russia. l Also at The Collaborative Innovation Center of Quantum Matter (CICQM), Beijing, China. m Also at Departamento de Física, Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal. n Also at Universita di Napoli Parthenope, Napoli, Italy. o Also at Institute of Particle Physics (IPP), Canada. p Also at II. Physikalisches Institut, Georg-August-Universität Göttingen, Göttingen, Germany. q Also at Dipartimento di Fisica E. Fermi, Università di Pisa, Pisa, Italy. r Also at Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest, Romania. s Also at CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France. t Also at Department of Physics, St. Petersburg State Polytechnical University, St. Petersburg, Russia. u Also at Borough of Manhattan Community College, City University of New York, New York, USA. v Also at Department of Financial and Management Engineering, University of the Aegean, Chios, Greece. w Also at Centre for High Performance Computing, CSIR Campus, Rosebank, Cape Town, South Africa. x Also at Louisiana Tech University, Ruston, Louisiana, USA. y Also at California State University, East Bay, Hayward, California, USA. z Also at Institucio Catalana de Recerca i Estudis Avancats, ICREA, Barcelona, Spain. aa Also at Department of Physics, University of Michigan, Ann Arbor, Michigan, USA. bb Also at LAL, Université Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, Orsay, France. cc Also at Graduate School of Science, Osaka University, Osaka, Japan. dd Also at Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Freiburg, Germany. ee Also at Institute for Mathematics, Astrophysics and Particle Physics, Radboud University Nijmegen/Nikhef, Nijmegen, Netherlands. ff Also at Near East University, Nicosia, North Cyprus, Mersin, Turkey. gg Also at Institute of Theoretical Physics, Ilia State University, Tbilisi, Georgia. hh Also at CERN, Geneva, Switzerland. ii Also at Department of Physics, Stanford University, Stanford, California, USA. 012008-28 SEARCH FOR PAIRS OF HIGHLY COLLIMATED PHOTON … PHYS. REV. D 99, 012008 (2019) jj Also at Manhattan College, New York, New York, USA. kk Also at Hellenic Open University, Patras, Greece. ll Also at LPNHE, Sorbonne Université, Paris Diderot Sorbonne Paris Cité, CNRS/IN2P3, Paris, France. mm Also at The City College of New York, New York, New York, USA. nn Also at Departamento de Física Teorica y del Cosmos, Universidad de Granada, Granada (Spain), Spain. oo Also at Department of Physics, California State University, Sacramento, Stanford, California, USA. pp Also at Moscow Institute of Physics and Technology State University, Dolgoprudny, Russia. qq Also at Département de Physique Nucléaire et Corpusculaire, Université de Genève, Genève, Switzerland. rr Also at Department of Physics and Astronomy, University of Sheffield, Sheffield, United Kingdom. ss Also at School of Physics, Sun Yat-sen University, Guangzhou, China. tt Also at Department of Applied Physics and Astronomy, University of Sharjah, Sharjah, United Arab Emirates. uu Also at Institut für Experimentalphysik, Universität Hamburg, Hamburg, Germany. vv Also at National Research Nuclear University MEPhI, Moscow, Russia. ww Also at Institute for Particle and Nuclear Physics, Wigner Research Centre for Physics, Budapest, Hungary. xx Also at Giresun University, Faculty of Engineering, Giresun, Turkey. yy Also at Department of Physics, Nanjing University, Nanjing, China. zz Also at Institute of Physics, Academia Sinica, Taipei, Taiwan. aaa Also at Department of Physics, University of Malaya, Kuala Lumpur, Malaysia. 012008-29