Search for new physics in multijet events with at least one photon and large missing transverse momentum in proton-proton collisions at 13 TeV

A search for new physics in final states consisting of at least one photon, multiple jets, and large missing transverse momentum is presented, using proton-proton collision events at a center-of-mass energy of 13 TeV. The data correspond to an integrated luminosity of 137 fb$^{-1}$, recorded by the CMS experiment at the CERN LHC from 2016 to 2018. The events are divided into mutually exclusive bins characterized by the missing transverse momentum, the number of jets, the number of b-tagged jets, and jets consistent with the presence of hadronically decaying W, Z, or Higgs bosons. The observed data are found to be consistent with the prediction from standard model processes. The results are interpreted in the context of simplified models of pair production of supersymmetric particles via strong and electroweak interactions. Depending on the details of the signal models, gluinos and squarks of masses up to 2.35 and 1.43 TeV, respectively, and electroweakinos of masses up to 1.23 TeV are excluded at 95% confidence level.


Introduction
Several extensions of the standard model (SM) of elementary particles attempt to provide an explanation for the origin of dark matter (DM) [1,2] and to resolve the gauge hierarchy problem [3][4][5][6]. Supersymmetry (SUSY) [7][8][9][10][11][12][13][14] is a hypothesized symmetry between fermions and bosons, which, when included in extensions to the SM, predicts a new bosonic (fermionic) superpartner for each SM fermion (boson). In SUSY models with R-parity conservation [15], the lightest supersymmetric particle (LSP) is stable and often neutral and weakly interacting, making it a possible DM candidate. In addition, gauge coupling unification is a natural possibility in supersymmetric theories [16].
Superpartners would contribute to quantum corrections to the Higgs boson (H) mass such that the H mass parameter would have only a logarithmic dependence on the scale of new physics. This effect could reduce the need for fine-tuning of the H mass [6], thereby preserving naturalness, if the superpartners with the largest contributions to the corrections are sufficiently light. These particles include the gluino, top squark, and bottom squark, which are the superpartners of the SM gluon, top quark, and bottom quark, respectively. If those color-charged superpartners are not accessible at the LHC, SUSY may still satisfy naturalness conditions if the higgsino, the superpartner of the Higgs boson, is near the electroweak scale [17].
This paper explores the signatures of SUSY particles produced via strong and electroweak interactions in proton-proton (pp) collisions, with a particular focus on final states containing at least one photon, multiple jets, and large missing transverse momentum. In gauge-mediated SUSY-breaking scenarios, the LSP is a gravitino ( G), the superpartner of the graviton, and it is expected to be roughly a few GeV in mass [18,19]. If the next-to-LSP (NLSP) is a chargino (neutralino), its decay will result in a W boson (photon, Z boson, or Higgs boson) and a G. The neutralino is an admixture of neutral wino, bino, and/or higgsino components that can couple to photons. Such decays are especially prominent if sleptons, the superpartners of SM leptons, are sufficiently massive that decays to sleptons are suppressed.
We interpret the results of this search using simplified models [20][21][22][23][24] of SUSY particle production via strong and electroweak interactions. Specifically, we consider several models of squark-and gluino-mediated production of charginos and neutralinos, in which each of the latter particles subsequently decays to the LSP and an SM boson. We also consider the production of neutralinos and charginos, collectively referred to as electroweakinos, via electroweak interactions. In all simplified models considered in this paper, the decays of SUSY particles are assumed to be prompt, and the mass of the gravitino, m G , is fixed to be 1 GeV. The event kinematic properties do not depend strongly on the exact choice of m G in the phase space explored in this analysis. This search therefore targets final states with at least one photon produced from the decay of a neutralino and missing transverse momentum from the LSP, which escapes the collision region without detection.
Representative diagrams depicting simplified models [24] of gluino ( g) pair production and top squark ( t) pair production are shown in Fig. 1. In the gluino pair production models, the gluino decays to a neutralino ( χ 0 1 ) and a pair of quarks; any possible χ 0 1 decays occur with equal probability. The T5qqqqHG model is defined by the decay of gluinos to a pair of light-flavored quarks (qq) and χ 0 1 , followed by χ 0 1 → H G or χ 0 1 → γ G with 50% branching fraction each. The mass of the χ 0 1 is taken to be 127 GeV or above. In the T5bbbbZG and T5ttttZG models, g → bb χ 0 1 and g → tt χ 0 1 , respectively, and the χ 0 1 decays to Z G or γ G with 50% branching fraction each. In the top squark pair production model T6ttZG, each top squark decays to a top quark and a χ 0 1 , followed by a decay χ 0 1 → Z G or χ 0 1 → γ G with 50% branching fraction each.
Previous searches by the CMS Collaboration for signatures of squark, gluino, and electroweakino production involving photons with data corresponding to an integrated luminosity of 36  This paper is structured as follows. A brief description of the CMS detector and event reconstruction is given in Section 2. The data sets are described in Section 3 and the event selection in Section 4. The methods used to estimate SM backgrounds are presented in Section 5 and the systematic uncertainties in the predictions are provided in Section 6. The results and summary are presented in Sections 7 and 8, respectively. Tabulated results are provided in the HEPData record for this search [31]. Figure 2: Diagrams of simplified models of electroweakino pair production: TChiWG (upper), TChiNG (lower left), and TChiNGnn (lower right). Only the χ ± 1 χ 0 1 and χ ± 1 χ ∓ 1 cases are shown for the TChiWG and TChiNG models, respectively. The models are defined in the text. "Soft" indicates particles with momentum too low to be detectable.

The CMS detector and event reconstruction
The central feature of the CMS apparatus is a superconducting solenoid of 6 m internal diameter, providing a magnetic field of 3.8 T. Within the solenoid volume are a silicon pixel and strip tracker, a lead tungstate crystal electromagnetic calorimeter (ECAL), and a brass and scintillator hadron calorimeter, each composed of a barrel and two endcap sections. The tracker systems cover a pseudorapidity range of |η| < 2.5, and the calorimeter systems cover |η| < 3.0. Forward calorimeters extend the coverage provided by the barrel and endcap detectors up to |η| < 5.2. Muons are measured in gas-ionization detectors embedded in the steel flux-return yoke outside the solenoid. A more detailed description of the CMS detector, together with a definition of the coordinate system used and the relevant kinematic variables, can be found in Ref. [32]. Events of interest are selected using a two-stage trigger system, described in Ref. [33].
Collision events are reconstructed using the particle-flow (PF) algorithm [34] which combines information from various subdetectors in an optimized way to give a list of PF candidates, namely photons, electrons, muons, charged hadrons, and neutral hadrons. Charged-particle tracks are used to reconstruct pp interaction vertices in the event. The primary vertex is taken to be the vertex corresponding to the hardest scattering in the event, evaluated using tracking information alone, as described in Section 9.4.1 of Ref. [35]. This vertex is required to be within 24 cm of the center of the detector in the z direction, and within 2 cm in the transverse direction. The remaining reconstructed vertices are referred to as pileup vertices and correspond to additional pp interactions in the same bunch crossing.
Reconstructed PF candidates are clustered into jets using the infrared and collinear safe antik T algorithm [36,37] with a distance parameter of 0.4 (0.8), referred to as AK4 (AK8) jets. The pileup contribution to the AK4 jet momentum is mitigated by discarding all the chargedparticle tracks associated with pileup vertices and applying an offset correction to mitigate the average contribution of neutral particles [38,39]. To mitigate the effect of pileup interactions on the AK8 jet momentum, a pileup per particle identification algorithm [39] is used, which makes use of local shape information to distinguish particles originating from hard scatter and pileup interactions. To account for the nonuniformity of the detector response across the jet p T and η ranges, jet energy corrections (JECs) are derived from the simulation in order to make the response of reconstructed jets equal to the particle-level jets on average. Residual differences in response between data and simulation are corrected based on dedicated measurements of the momentum balance in dijet, γ+jet, Z+jet, and multijet events [40]. The jet energy resolution (JER) in the simulation is also modified by smearing the jet p T , using scale factors derived from data ranging from 1.1-1.2. Jets potentially dominated by contributions from anomalous detector signals or reconstruction failures are discarded using dedicated jet identification (ID) criteria [41]. The AK4 jets used in this search are required to have p T > 30 GeV and |η| < 2.4.
The hadronization products from a hadronic decay of an energetic W, Z, or Higgs boson can be clustered into a single wide jet, which is reconstructed as an AK8 jet. The AK8 jets considered in this search are required to have p T > 200 GeV and |η| < 2.4. The AK8 jet mass, m J , is reconstructed using the soft-drop algorithm [42], which improves jet mass resolution by removing soft and wide-angle contributions. Requirements are applied to m J to identify W, Z, or Higgs boson candidates. The same requirement 65 < m J < 105 GeV is used for both W and Z bosons, as the difference in the particle masses is smaller than the m J resolution; jets that pass this requirement are called V-tags, where V = W or Z. For Higgs bosons, the requirement 105 < m J < 140 GeV is applied, and passing jets are called H-tags.
Jets originating from b quarks are identified by a combined secondary vertex algorithm based on a deep neural network (DEEPCSV), applied to the reconstructed AK4 jets [43]. A medium working point is used for the DEEPCSV discriminator. This corresponds to a b jet tagging efficiency of 65% for jets with p T > 30 GeV with corresponding misidentification probability for gluon and light-quark (charm-quark) jets of 1.6% (13%).
The negative vector ⃗ p T sum of all PF particles is defined as the ⃗ p miss T , and its magnitude is the missing transverse momentum (p miss T ) used in this analysis. The ⃗ p miss T is corrected for the changes in the ⃗ p T of jets after applying JECs. Events in which p miss T is identified to be originating from a mismeasured jet, detector noise, nonfunctional calorimetric channels, or reconstruction failures are rejected by dedicated algorithms [44]. Events with p miss T > 200 GeV are used in this analysis.
In order to improve the quality of the PF reconstruction, additional identification criteria are applied to photon candidates [45]. To suppress the misidentification of neutral pions, which are copiously produced in jets, as photons, the reconstructed photon candidates are required to be isolated. The isolation variable is defined as the p T sum of a given type of PF particle candidate within a cone of radius ∆R = 0.3, where ∆R = √ (∆η) 2 + (∆ϕ) 2 and ϕ is the azimuthal angle in radians, around the direction of the photon, excluding the photon itself. Separate isolation sums are computed for charged hadrons, photons, and neutral hadrons. The isolation sums are adjusted using η-dependent effective-area corrections, which account for the variation of energy density in a given event based on pileup interactions [45]. The charged-hadron isolation sum is required to be less than 1.694 (2.089) GeV for photons in the ECAL barrel (endcap); the requirements for the other isolation sums are expressed as linear or quadratic functions of the photon p T for photon or neutral-hadron isolation, respectively. Isolated photons with p T > 100 GeV and |η| < 2.4, excluding the ECAL barrel-endcap transition region 1.44 < |η| < 1.56, are considered for further analysis. The efficiency of the photon identification and isolation requirements is 90% and the misidentification rate is 15-25%.
As with photons, additional identification criteria are applied to electron [45] and muon [46] candidates. The electron and muon candidates are also required to have p T > 10 GeV and to be isolated, based on a variable defined as the scalar p T sum of the charged hadron, neutral hadron, and photon PF candidates within a variable-radius cone around the lepton direction, divided by the lepton p T . The expected contributions of neutral particles from pileup interactions are subtracted from the isolation sum [38]. The radius of the cone is 0.2 for lepton p T < 50 GeV, 10 GeV/p T for 50 < p T < 200 GeV, and 0.05 for p T > 200 GeV. The decreasing radius of the cone with lepton p T is motivated by the increased collimation of the decay products from the lepton's parent particle with increasing Lorentz boost and helps to retain high lepton isolation efficiency in events with large number of jets or pileup interactions. The isolation variable is required to be less than 0.1 (0.2) for electrons (muons).
Charged-particle tracks, subsequently referred to as tracks, are used to reject events potentially containing hadronic decays of τ leptons; electrons or muons that could not be identified with the criteria described earlier; and low-momentum leptons from hadron decays. An isolation requirement is applied to these tracks, based on the p T sum of other tracks within a cone of 0.3 around each track. The isolation sum divided by the track p T is required to be less than 0.2 (0.1) for tracks identified as a PF electron or muon (PF charged hadron). The leptonic tracks are required to have p T > 5 GeV and the hadronic tracks p T > 10 GeV, along with the transverse mass between the track p T and p miss T , defined as m T = 2p ℓ T p miss T (1 − cos ∆ϕ), less than 100 GeV. Here, ∆ϕ is the angular separation between the track ⃗ p T and the ⃗ p miss T . This m T requirement preferentially selects isolated tracks from W → ℓν decays.

Collision and simulated data sets
We select collision events that are recorded based on the p miss T reconstructed at the trigger level. The trigger-level p miss T threshold varies from 90-140 GeV for the data set used in this search. The efficiencies of these p miss T triggers are measured using data sets recorded with single-electron triggers, as a function of the reconstructed p miss T . Trigger efficiencies for events with reconstructed p miss T of at least 200 (300) GeV are found to be 70, 60, and 60% (95, 95, and 97%) for data collected in 2016, 2017, and 2018, respectively. In addition to the p miss T -triggered data set, single-electron and single-muon data sets are also used for the estimation of the background from electrons misidentified as photons, described in Section 5.2. The estimation of backgrounds primarily relies on observed data, with Monte Carlo (MC) events used to derive correction factors and scale factors, to validate various background estimation methods, and to assess systematic uncertainties.
We use the MADGRAPH5 aMC@NLO event generator (version 2.2.2 for 2016, and 2.4.2 for 2017-2018) [47,48] at leading order (LO) precision for simulating the production of the tt +jets, W+jets, Z+jets, QCD multijet, and Wγ processes and at next-to-LO (NLO) precision for the tt γ process. The tt γ events are simulated with up to one additional parton at the matrix element level, while the Wγ events have up to two additional partons, the tt +jets events up to three additional partons, and the other samples up to four additional partons. The single top quark process is modeled at NLO in perturbative QCD, with MADGRAPH5 aMC@NLO used for s-channel production. Signal events are generated with the MADGRAPH5 aMC@NLO generator at LO precision in a manner similar to the SM backgrounds, with up to two additional partons at the matrix element level. The decays of gluinos, top squarks, and neutralinos are modeled with PYTHIA8 [49].
The SM MC events are processed through a detailed simulation of the CMS detector based on the GEANT4 [62] software. The simulated events are then reconstructed using the same algorithms as used for the collision data. The detector simulation of signal events is performed with the CMS fast simulation package [63,64]. The signal samples are corrected for differences with respect to the GEANT4-based simulation. Both the SM background samples and the signal samples are generated with nominal distributions of the number of pileup interactions, which are then reweighted to match the distribution measured in data.

Event selection
Events are selected using a set of criteria, referred to as the baseline selection, summarized in Table 1. The events are required to have p miss T > 300 GeV, and N jets ≥ 2, where N jets is the number of AK4 jets with p T > 30 GeV and |η| < 2.4. The events must also contain at least one photon with p T > 100 GeV and |η| < 2.4. The photons are required to be separated from the jets by ∆R(j, γ) > 0.3. The scalar p T sum of the jets and the photon, denoted S T , reflects the visible energy scale of the event and is required to be larger than 300 GeV. Significant mismeasurement of jet p T can lead to high p miss T , which is generally aligned with the mismeasured jet. To suppress such events, we require ∆ϕ(⃗ p jet T , ⃗ p miss T ) > 0.3 for the two highest p T jets in the event. As the final state targeted contains only photons and hadronic jets, events with isolated electron and muon candidates are rejected to suppress the SM background arising from leptonic W decays. Further, events with an isolated leptonic or hadronic track are rejected, eliminating an additional ≈40% of the relevant SM background processes. The event samples used for estimation of backgrounds are referred to as control regions (CRs) and are defined to be nonoverlapping with the baseline selection. These are designed-based on the presence of leptons (e or µ), lower p miss T values, or lower ∆ϕ(⃗ p jet T , ⃗ p miss T ) values-to be dominated by SM processes and are expected to have small signal contributions.
The events satisfying the baseline criteria are further classified into mutually exclusive signal regions (SRs) to enhance the sensitivity of the analysis to different signal scenarios. We define two sets of SRs called the electroweak (EW) and strong production (SP) SRs to target different types of signal models. The EW SRs include events with 2 ≤ N jets ≤ 6 and at least one V-or H-tag. These SRs are sensitive to electroweakino models like TChiWG, in which an energetic W, Z, or Higgs boson is expected in addition to low N jets . They are also sensitive to gluino production models like T5qqqqZg in scenarios in which the difference between the masses of the gluino and the NLSP is small, resulting in soft jets and a boosted massive vector boson. The SP SRs include all baseline events not satisfying the EW SR selection criteria and are sensitive to gluino and squark pair production.
Both the SP and EW SRs are binned in p miss T , with lower bin edges of 300, 370, 450, 600, 750, and 900 GeV. These bins are chosen to ensure that each has an appreciable number of expected SM background events. For the SP SRs, each of the p miss T bins is further divided into bins of N jets = 2-4, 5-6, and ≥ 7, and N b-tags = 0 and ≥ 1, where N b-tags is defined as the number of b-tagged jets in the event. For events with N b-tags = 0 and N jets = 5-6, the two highest p miss T bins are combined. For events with N b-tags = 0 and N jets ≥ 7, and for all events with N b-tags ≥ 1, the three highest p miss

Background estimation
There are several SM processes that can result in final states containing at least one highp T photon, p miss T , and multiple jets. The production of Wγ+jets, tt γ+jets, W+jets, tt +jets, Zγ+jets, γ+jets, and QCD multijet events are all non-negligible backgrounds for this search. The Wγ+jets and tt γ+jets events, with a prompt photon and a W → ℓ ′ ν (ℓ ′ = e, µ, and τ leptons) decay, enter the search regions as the "lost-lepton background" if the e or µ leptons are not identified, and therefore cannot be vetoed, or the τ leptons decay hadronically (τ h ). The W+jets and tt +jets events contribute to the background if an electron originating from a W boson decay is misidentified as a photon. The Zγ+jets process, with Z → νν, is an irreducible background to this search. In all these processes, the presence of one or more neutrinos in the final states is the main source of p miss T . In γ+jets events, a p T mismeasurement of one or more jets can lead to large p miss T in the reconstructed events. The QCD multijet background arises similarly from artificial p miss T because of mismeasurement, but also requires that a jet be misidentified as a photon.

Lost-lepton background
An e or a µ is considered "lost" when it fails reconstruction, identification, or isolation, or if it is outside the detector or kinematic acceptance, as described in Section 2. Events containing a τ h candidate that is not rejected by the isolated track veto also contribute to the background, as the τ h candidate is reconstructed as a jet. We estimate both these contributions together as the lostlepton background, given their similar origins. The CRs used to estimate this background are collected by the same p miss T triggers as used for the SR events. There is one CR corresponding to each SR. Except the e, µ, and isolated track veto, the CRs are required to satisfy all criteria used to define the SRs. Instead, we require the presence of exactly one electron or one muon, and no additional isolated tracks in the event. It is important to note explicitly that these CR events are required to have a reconstructed photon in the final state. We require m T (p ℓ T , p miss T ) < 100 GeV to veto events potentially arising from new physics in similar single-lepton final states. The relative composition of Wγ+jets and tt γ+jets events in the single-e and single-µ CRs, in the bins of N jets and N b-tags for SP SRs and V-and H-tags for EW SRs, is shown in Fig. 4 (left). The SR events are shown as events containing a lost e, a lost µ, or a τ h candidate. Since we do not use a dedicated τ h veto, the last type of events are a large fraction of the lost-lepton background for this search. The background estimation makes use of transfer factors (TFs) from the simulation. The TFs are defined as the ratio of the number of events in the SRs to the number of events in the respective CRs. The simulated event yields are corrected for known differences with data in lepton identification, b tagging, and trigger efficiency. The TFs are calculated in the bins of N jets and N b-tags for the SP SRs and in the bins of V-and H-tag for the EW SRs; they are not binned in p miss T and include events with p miss T > 200 GeV. The number of events predicted in SR bin i, N data 0ℓγ (i), is obtained from the number of events in the corresponding CR, N data 1ℓγ (i), as Here, the TFs are applied to the single e and µ data CRs as per-event weights, depending on the event characteristics in terms of N jets and N b-tags for the SP SRs and V-or H-tag for the EW SRs. As shown in the lower panel of Fig. 4 (left), these TFs vary from 0.5 to 1.0, depending on the SR.
We validate the background estimation method and the applicability of these TFs in the simulation by using the 1e γ and 1µ γ CRs to predict the events in the SRs using Eq. (1). Comparisons of the expected and predicted event yields in the SRs are presented in Fig. 4 (right). The discrepancies between the expected and predicted yields, especially in the high p miss T or high N jets bins, are covered by the statistical uncertainties.
The predicted number of lost-lepton background events can be affected by several sources of uncertainty that impact the TFs. To account for potential mismodeling of collinear photon radiation from quarks and leptons, the cross sections of relevant simulated samples are varied by 20% [65] to account for differences in the modeling of photon radiation in different simulated samples and the effect on the TFs is found to be 4%. The uncertainty in the PDFs is evaluated by varying event weights from 100 PDF replicas [50,51], resulting in a 3% effect. To evaluate the renormalization (µ R ) and factorization (µ F ) scale uncertainties, different weights obtained by varying the scales independently by 0.5 and 2 [66,67] are used. The effect of this uncertainty is found to be 2% on the predicted number of lost-lepton background events. The uncertainties in the corrections applied to the simulation are propagated by varying their values and recalculating the predicted event yields in each SR. The variation in the number of predicted event yields with respect to the central values is taken as the respective uncertainty for each correction. The uncertainties in the lepton identification efficiency, b tagging efficiency, and the JEC and JER lead to 0.6, 0.7, 6, and 6% uncertainties in the lost-lepton background, respectively. The limited size of the simulated samples results in a 2-10% uncertainty in the predicted event yields. The estimated numbers of lost-lepton background events in each SR, along with uncertainties, are shown in Section 7.

Misidentification of electrons as photons
If the track associated with an electron is not reconstructed or linked to it, the energy deposited by the electron in the ECAL could potentially be misidentified as a photon. Such electrons typically arise from W+jets, tt +jets, and single top quark events in which a W boson decays to an electron and a neutrino. To estimate the background from electrons misidentified as photons, CRs are defined to include events containing exactly one electron with p T > 100 GeV and zero photons satisfying the criteria described in Section 2. Similar to the lost-lepton CRs, we require the m T of the electron and p miss T to be < 100 GeV. Jets that have ∆R < 0.3 with respect to the selected electron are not considered when computing S T and N jets .
The misidentification rate, f , is defined as the ratio of the number of events with a misidentified electron to the number of single-electron events. The rate f is determined using a sample of simulated W+jets and tt +jets events containing W → eν decays. It depends on the kinematic properties of the electron and the presence of jets and other particles near the electron. The activity around the electron is characterized using the charged multiplicity, denoted Q mult and defined as the number of charged constituents of the closest jet to the electron or photon with ∆R(jet, e or γ) < 0.3.
A correction factor α is included to account for differences in the rate f between data and simulation. The factor α is obtained from data and simulated events containing an e + e − pair with the "tag and probe" method [68]. The tag electron is required to have p T > 40 GeV and to match within ∆R < 0.2 with a generator-level electron arising from a Z boson in simulation or a trigger-level electron object in data. The probe electron (photon) is selected with requirements similar to the electron in the 1e CR (SR). The pair of the tag electron and the probe electron or photon is also required to satisfy ∆R(tag, probe) > 0.2 and to have an invariant mass within 80-100 GeV. In this case, the rate f is defined as the ratio of the number of events with a photon as the probe to the number of events with an electron as the probe. The factor α is determined as the ratio of the rate f measured in data and simulated events, evaluated separately for events with N b-tags = 0 and ≥1. To account for different run conditions, the factor α is also measured separately for data recorded in 2016, 2017, and 2018. The values of α vary from 1.9-2.4.
The number of events with the electrons misidentified as photons in the SR bin i, N data γ (i), is estimated from the number of events in the corresponding CR, N data 1e 0γ (i), as For a given CR, the rate f is applied as a per-event weight according to the p T of the electron and the value of Q mult for the jet closest to the electron. A comparison of the number of events expected in the SRs and predicted by the single-electron CRs, with both the SRs and CRs taken from simulated W+jets and tt +jets events, is shown in Fig. 5. The uncertainties in the b tagging efficiencies, JECs, and JER smearing are propagated to the simulated events used to determine the rate f , and their effects on the final predicted event yields are found to be <1, 3, and 4%, respectively. The overall systematic uncertainty in α from topological differences in Z(ee) compared to tt and W+jets is estimated to be 20%, based on comparing simulated f values in e + e − events for the tag-and-probe and single-electron or single-photon selections. This component dominates the total systematic uncertainty in the predicted number of events with electrons misidentified as photons and is taken to be correlated across all SR bins. The uncertainties arising from the limited number of CR and SR events in the simulated samples are up to 20%. The statistical uncertainty in the single-electron CR in data contributes up to a 20% uncertainty in the predicted number of background events in the SRs. The background prediction in the SRs, along with the uncertainties, is shown in Section 7.

Z(νν)γ+jets background
The presence of energetic neutrinos in Z(νν)γ+jets events manifests as large p miss T and results in significant background for searches in final states requiring zero leptons, particularly in low-N jets and high-p miss T SRs. We use Z(νν)γ+jets simulated events to estimate the predicted event yields in the SP SRs, which are defined by N jets , N b-tags , and p miss T . These event yields are adjusted by the ratio of the number of Z(ee)γ+jets and Z(µµ)γ+jets events, collectively called Z(ℓℓ)γ events, measured in data and simulation to account for any potential mismodeling of Zγ+jets production. The leptonic final states of Z boson decays have limited numbers of events because of their small branching fractions and hence are not directly used to estimate the Z(νν)γ+jets background.
To select Z(ℓℓ)γ events, we require a pair of light leptons with the same flavor, opposite charge, and invariant mass in the range of 80-100 GeV, depicted in Fig. 6 (left). The p miss T in these events is required to be less than 200 GeV. However, to mimic the kinematic properties of the Z(νν) process in the SRs, the dilepton system should be treated as invisible. Therefore, the magnitude of the sum of the dilepton ⃗ p T and the ⃗ p miss T , shown in Fig. 6 (right), must be greater than 300 GeV, following the baseline selection. We also require ∆R(ℓ, γ) > 0.2 to ensure that the photon is not radiated from one of the leptons. The numbers of events obtained in data and simulation using these criteria are denoted N data ℓℓγ and N MC ℓℓγ , respectively. Here, the subscript ℓ refers to electrons and muons. The number of events in the SRs is obtained using the expression: where N data Z(νν)γ (i) and N MC Z(νν)γ (i) are the numbers of events predicted in SR i in data and simulation, respectively, and β ℓℓγ = 1 − N tt γ /N ℓℓγ is a correction factor to account for the contribution of tt γ+jets processes to the ℓℓγ events in data. The index j = 0 or 1 corresponds to N b-tags = 0 or ≥1. The contribution of tt γ is estimated from simulation and it is found to be statistically compatible with the number of opposite-sign, different-flavor (e ± µ ∓ ) events from data. As the contamination of tt γ events is expected to be higher in the SRs with N b-tags ≥1, the factor β ℓℓγ is derived separately for the regions with and without a b-tagged jet.
The corrections to Z(νν)γ+jets events from ℓℓγ events are 1.07 ± 0.09 and 1.01 ± 0.28 for N b-tags = 0 and ≥1, respectively. These uncertainties are propagated to the predicted number of events in the SRs along with the statistical uncertainty in the Z(νν)γ+jets simulated samples, which ranges from 2-70%. In both the SP and EW SRs, the statistical uncertainty is larger in the high-p miss T bins. To account for any mismodeling of photon p T in the simulation, we apply an additional systematic uncertainty, which ranges 18-40%, depending on the p miss T bin. This is assessed based on the results presented in Ref. [69]. The number of Z(νν)γ+jets events for each SR, along with the uncertainty in the prediction, is presented in Section 7.

γ+jets and QCD multijet background
QCD multijet and γ+jets events with a well-reconstructed photon can contribute to the SRs if they also contain large p miss T resulting from significant mismeasurement of one or more jets or from the presence of neutrinos from the semileptonic decays of heavy-flavor hadrons. We use an "ABCD" method to estimate this background, where the regions A, B, and C are data CRs designed to be nonoverlapping with the SRs and the region D corresponds to the SRs. To define these CRs, we use events with 200 < p miss T < 300 GeV (low-p miss T ) or ∆ϕ(⃗ p jet T , ⃗ p miss T ) < 0.3, indicating at least one of the two leading jets is aligned with the direction of p miss T (low-∆ϕ). These events are required to satisfy all other baseline selection criteria. From the observed event yields in every CR, we subtract the contributions from the lost-lepton, misidentified electron, and Zγ+jets backgrounds, which are obtained using the same methods as used for the SRs.
The CRs A and C consist of events with low-p miss T , with the former being low-∆ϕ and the latter being high-∆ϕ. These events are divided into the same exclusive regions based on N jets , N b-tags , V-and H-tag as used to define the SP and EW SRs. In each of these regions, a ratio R low-p miss T is defined as the number of events with high-∆ϕ (CR C) to that with low-∆ϕ (CR A). The CR B consists of events with high-p miss T and low-∆ϕ. These events are divided into the same regions as the SRs, including the p miss T binning. The predicted number of events in SR i is then: where the index i refers to the SR and the index r refers to the bins defined based on N jets , N b-tags , V-tag, and H-tag as used for the SRs. The factor κ(r) is used as a correction determined from the simulation to account for any differences in the ratios of the low-p miss T regions A and C compared to the high-p miss T regions B and D. It is calculated in the same bins as used for R low-p miss This method is validated in the simulation. The CRs and SRs are defined using the simulated γ+jets and QCD multijet events. The same event sample is also used to measure R low-p miss T . The numbers of events predicted by the method in various SRs are found to be consistent with the expected values, within the statistical precision. The test of the method in simulation is nontrivial because the parametrization of κ is based on N jets , N b-tags , V-and H-tag bins, whereas the predictions are done for each of the SRs, which also include p miss T binning.
Since κ is an important ingredient for this background estimation and it is obtained from the simulation, we validate these factors in data and simulation samples using events that do not contain a photon, referred to as zero-photon events. The zero-photon region is dominated by multijet events. The contributions from the other SM background processes are small, so  they are estimated from the simulation and subtracted from the zero-photon event yields. The values of κ derived from data and simulation differ by 10-36%, as shown in Fig. 7. The observed differences are treated as systematic uncertainties in the predicted number of events. There is one κ value for each set of N jets , N b-tags , V-tag, and H-tag requirements, so the uncertainty in κ is correlated among all the corresponding SRs. The statistical uncertainties in κ and the number of events in low-p miss T regions vary in the range 10-50%. Section 7 summarizes the predicted number of γ+jets and QCD multijet events in the SRs.

Systematic uncertainties
The sources of systematic uncertainty and their effects on the predicted numbers of events for the lost-lepton, electron misidentified as photon, Z(νν)+jets, and γ+jets backgrounds have been discussed in Section 5. The following sources of systematic uncertainty are considered for the simulated signal event yields. The uncertainties in the total integrated luminosity [70][71][72] affect the signal yield in each SR. This effect is taken to be 1.6% for all the SRs and all signal models. The uncertainties in the JEC and JER measurements from data are propagated to individual jets, and their effect on event yields is taken as an uncertainty in the respective SR bins. The effect of variations in the pileup reweighting is estimated in a similar way. The uncertainties related to pileup, JECs, and JER contribute approximately 2% each. The uncertainty in the trigger efficiency for simulated signal events varies from 3-10%, with larger values for SRs with lower p miss T . The uncertainties related to the isolated track veto and jet ID modeling in the fast simulation are 2 and 1%, respectively. The b tagging efficiency and light flavor quark mistagging rates in the fast simulation signal samples are corrected with factors derived from the GEANT4-based simulation and data. The uncertainties in these corrections are propagated to the final signal yield, and their effect in the SP SRs is up to 10%. The statistical uncertainty from the limited number of simulated events in the signal samples ranges 0.7-38% when considering all bins; when considering only the most sensitive bins, this uncertainty decreases to 0.1-7%.
The PDF uncertainty, and the µ R and µ F scale uncertainties that affect the total production cross section are treated as theoretical uncertainties. The effects of these on the signal yield are 2 and 5%, respectively. The modeling of initial-state radiation (ISR) in the signal simulation is corrected by applying data-to-simulation correction factors [73]. The corrections depend on the number of ISR jets and the p T of the chargino-neutralino system for the strong production and the electroweak signal models, respectively. These uncertainties have magnitudes of 25% for strong production and 10% for electroweak signal models. Table 2 summarizes the sources of systematic uncertainty and their effects on the predicted backgrounds and signal yields.

Results and interpretation
We perform a simultaneous maximum likelihood fit to the number of events in the low-and high-∆ϕ regions to predict the number of SM background events in the SRs. The profile likelihood ratio q µ is used as the test statistic to compute limits in the modified frequentist CL s approach [74,75], employing the asymptotic approximation [76]. The statistic is defined as q µ = −2 ln(L µ /L max ), where µ is the SUSY signal strength, L max is the maximum likelihood from varying all parameters including µ, and L µ is the maximum likelihood for a fixed µ. The observed numbers of events in various CRs are modeled using gamma distributions, which correctly represent the statistical uncertainties. The predicted yield of signal events in each CR is found to be negligible. The other systematic uncertainties listed in Table 2 are modeled as log-normal constraints in the likelihood. The results obtained from the CR-only fit under the background-only hypothesis are shown in Fig. 8. The numerical values, including the uncertainties in each background prediction, are given in Appendix A. In most of the SRs, the observed event yields are consistent with the predictions, indicating no significant presence of signal events. The maximum deviation observed is about 2 standard deviations below the prediction, in bin 13 (5 ≤ N jets ≤ 6, N b-tags = 0, p miss T ≥ 750 GeV), bin 16 (N jets ≥ 7, N b-tags = 0, 370 < p miss T < 450 GeV), and bin 44 (H-tag, 600 < p miss T < 750 GeV).
The measured backgrounds along with their uncertainties and the observed number of events in the SRs are used to determine 95% confidence level (CL) upper limits on the production cross sections of various SUSY models, discussed in Section 1, using a maximum likelihood fit. We compare these upper limits with theoretical production cross sections, and determine lower CRs. The lost-lepton, electron misidentified as photon, Zγ+jets, and γ+jets and QCD multijet backgrounds are stacked histograms. The observed numbers of events in data are presented as black points. For illustration, the expected event yields are presented for the signal model T5bbbbZG, for small (blue) and large (purple) differences in the masses of the g and NLSP. Also shown is the expected distribution of events for the signal model TChiWG (red). The numerical values in parentheses in the legend entries for the signal models indicate the g and NLSP mass values in GeV for strong production and the NLSP mass value for electroweak production. The lower panel shows the ratio of the observed number of data events and the predicted backgrounds. The error bars represent the statistical uncertainty in the data events, and the shaded band represents the statistical and systematic uncertainties in the predicted background. The p miss T bin 200-300 GeV is used for the estimation of the γ+jets and QCD multijet background.
limits on masses of the SUSY particles in specific models and final states, which are excluded by this search. The exclusion limits in terms of masses of particles involved in a given model are shown in Fig. 9 for gluino and squark pair production scenarios. Figure 10 presents the same for the production of electroweakino pairs.
For the gluino production model with a decay to bb and NLSP (T5bbbbZG), the observed (expected) gluino mass exclusion is up to 2.32 (2.27) TeV for small NLSP masses. In the T5qqqqHG and the T5ttttZG models, the observed (expected) upper limits on the gluino masses extend to 2.35 (2.30) and 2.26 (2.25) TeV, respectively. The mass limits degrade for very high and very low NLSP masses. When the NLSP masses are large, the p miss T is large but the events contain lower hadronic activity (N jets ). For the low NLSP masses, hadronic activity is high, but p miss T is low. In these scenarios, either the signal acceptance is low or the signals populate SRs with larger backgrounds, resulting in a decrease in the sensitivity of the analysis. These features are illustrated in the open histograms shown in Fig. 8. For the T5qqqqHG scenario, the observed limits are stronger than the expected ones because of the small deficit in the observed event yields in the 137 fb Figure 9: The 95% CL upper limits on the production cross sections for g pairs, with g → bb χ 0 1 followed by χ 0 1 → Z G or χ 0 1 → γ G (upper left, T5bbbbZG model), g → qq χ 0 1 followed by χ 0 1 → H G or χ 0 1 → γ G (upper right, T5qqqqHG model), g → tt χ 0 1 followed by χ 0 1 → Z G or χ 0 1 → γ G (lower left, T5ttttZG model), or top squark pairs assuming the top squark decays to a top quark and a χ 0 1 followed by χ 0 1 → Z G or χ 0 1 → γ G (lower right, T6ttZG model). The thick black curve represents the observed exclusion contour and the thin black curves show the effect of varying the signal cross section within the theoretical uncertainties by ±1σ theory . The thick red curve indicates the expected exclusion contour and the thin red curves show the variations from ±1σ experiment uncertainties.
high-N jets and N b-tags = 0 regions and in the high-p miss T H-tag regions. In the strong production models that involve off-shell Z bosons and very low NLSP masses, the limits are stronger than those from on-shell Z bosons, because the former imparts larger p T to the gravitinos, leading to larger p miss T . In the T5qqqqHG model, off-shell Higgs boson decays are not considered. For the top squark pair production model (T6ttZg), where the top squark decays into a top quark and NLSP, the expected mass limit is 1.38 TeV and the observed mass limit is 1.43 TeV. There is an approximately 0.7 standard deviation difference between the expected and observed limits, which comes from signal regions with high p miss T , high N jets , and N b-tags ≥ 1. In electroweak production models, for sufficiently large electroweakino masses, the signal events mostly populate large p miss T and V-or H-tag signal regions. In the TChiWG scenario, we observe (expect) the exclusion of χ ± 1 χ 0 1 masses up to 1.23 (1.17) TeV, assuming wino-like χ ± 1 χ 0 1 production. In the TChiNG model, the χ ± 1 , χ 0 1 , and χ 0 2 are nearly mass degenerate, and we use higgsino-like cross sections to interpret the results. Electroweakino masses below 1.05 (0.95) TeV are observed (expected) to be excluded, assuming the χ ± 1 and χ 0 2 decays give rise to χ 0 1 and soft particles. The expected upper limit on the mass is about 60-80 GeV smaller than the observed upper limit because of a deficit in the observed event yields in the highest p miss  Cross sections for: or the single process χ 0 1 χ 0 2 (blue) are considered.
p miss T bins, which have observed event yields higher than the predictions by about one standard deviation. This leads to higher than predicted observed upper limits on the production cross section. Alternatively, if only the χ 0 1 χ 0 2 process occurs in this model, there is no exclusion in the range of NLSP masses considered in this search, based on the theoretically predicted cross section. In the TChiNGnn model, with only the χ 0 1 χ 0 2 process, the observed (expected) NLSP mass limit is 0.50 (0.65) TeV. The observed limit is weaker than expected because of upward fluctuations in several low-N jets N b-tags ≥ 1, V-tag, and H-tag SR bins with intermediate p miss T values.

Summary
A search for supersymmetry (SUSY) is presented using events with final states containing at least one photon, large missing transverse momentum, and jets that may or may not arise from b quarks. These signatures are motivated by models with gauge-mediated SUSY breaking (GMSB), in which the lightest SUSY particle (LSP) is a gravitino ( G) and the next-to-LSP (NLSP) is a chargino ( χ ± 1 ) or neutralino ( χ 0 1 ), collectively called electroweakinos. Several simplified models of strong production of pairs of gluinos ( g) and top squarks ( t) are considered, with the gluino decaying to a pair of quarks along with an NLSP or the top squark decaying to a top quark and an NLSP; the NLSP then decays to a neutral gauge boson (photon, Z boson, or Higgs boson) and an LSP. Models of pair production of electroweakinos are also considered, with the neutralinos decaying as described above, and the charginos decaying to a W boson and an LSP.
Compared to previous searches, this search achieves increased sensitivity to scenarios with small mass differences between the gluino and the NLSP with dedicated search regions based on identifying boosted massive bosons. In addition, the search strategy is expanded to provide sensitivity to the production of electroweakino pairs. The observations are consistent with the standard model expectations and 95% confidence level upper limits are set on the production cross sections of SUSY particles. In the GMSB simplified models, the lower gluino mass limit reaches up to 2.35 TeV for models with g → qq χ 0 1 followed by χ 0 1 → H G or γ G with equal probability, and the top squark mass limit reaches up to 1.43 TeV for models with t → t χ 0 1 followed by χ 0 1 → Z G or γ G with equal probability. These results extend the previous mass limits [27] on gluinos and top squarks by 150-200 GeV. For electroweakino pair production, chargino and neutralino masses up to 1.23 TeV are excluded, assuming wino-like electroweakinos with decays χ ± 1 → W G and χ 0 1 → γ G. The higgsino-like electroweakino mass limits reach up to 1.05 TeV for models with χ 0 1 → γ G, Z G, or H G with 50, 25, and 25% branching fractions, respectively. These are the best mass limits to date on electroweakino production with photons in the final state.

Acknowledgments
We congratulate our colleagues in the CERN accelerator departments for the excellent performance of the LHC and thank the technical and administrative staffs at CERN and at other CMS institutes for their contributions to the success of the CMS effort. In addition, we gratefully acknowledge the computing centres and personnel of the Worldwide LHC Computing Grid and other centres for delivering so effectively the computing infrastructure essential to our analyses. Finally, we acknowledge the enduring support for the construction and operation of the LHC, the CMS detector, and the supporting computing infrastructure provided by the    In this appendix, we present the numerical values and uncertainties for each of the signal and low-p miss T regions defined in Fig. 3. These values correspond to the results presented in Fig. 8.