Search for new physics in final states with a single photon and missing transverse momentum in proton-proton collisions at $\sqrt{s} =$ 13 TeV

A search is conducted for new physics in final states containing a photon and missing transverse momentum in proton-proton collisions at $\sqrt{s} =$ 13 TeV, using the data collected in 2016 by the CMS experiment at the LHC, corresponding to an integrated luminosity of 35.9 fb$^{-1}$. No deviations from the predictions of the standard model are observed. The results are interpreted in the context of dark matter production and models containing extra spatial dimensions, and limits on new physics parameters are calculated at 95% confidence level. For the two simplified dark matter production models considered, the observed (expected) lower limits on the mediator masses are both 950 (1150) GeV for 1 GeV dark matter mass. For an effective electroweak-dark matter contact interaction, the observed (expected) lower limit on the suppression parameter $\Lambda$ is 850 (950) GeV. Values of the effective Planck scale up to 2.85-2.90 TeV are excluded for between 3 and 6 extra spatial dimensions.


Introduction
Production of events with a photon with large transverse momentum (p T ) and large missing transverse momentum (p miss T ) at the CERN LHC is a sensitive probe of physics beyond the standard model (SM). This final state is often referred to as the "monophoton" signature, and has the advantage of being identifiable with high efficiency and purity. Among the extensions of the SM that can be studied with this final state are particle dark matter (DM) and large extra spatial dimensions.
At the LHC, the DM particles may be produced in high-energy proton-proton (pp) collisions, if they interact with the SM quarks or gluons via new couplings at the electroweak (EWK) scale [1][2][3]. Although DM particles cannot be directly detected, their production could be inferred from the observation of events with a large p T imbalance, when high-energy SM particles recoil against the DM particle candidate. In DM production through a vector or axialvector mediator, a photon can be radiated from the incident quarks ( Fig. 1, left), resulting in a monophoton final state. In the simplified models considered in this analysis, Dirac DM particles couple to a vector or axial-vector mediator, which in turn couples to the SM quarks. These models have been identified by the ATLAS-CMS Dark Matter Forum [4] as benchmarks to compare DM production sensitivity from various final states. They are characterized by a set of four parameters: the DM mass m DM , the mediator mass M med , the universal mediator coupling to quarks g q , and the mediator coupling to DM particles g DM . In this analysis, we fix the values of g q and g DM to 0.25 and 1.0, respectively, and scan the M med -m DM plane as recommended by the LHC Dark Matter Working Group [5].
It is also possible that the DM sector couples preferentially to the EWK sector, leading to an effective interaction qq → Z/γ * → γχχ [6], where χ is the DM particle ( Fig. 1, center). This model is characterized by a set of four parameters: the DM mass m DM , the suppression scale Λ, and the couplings k 1 , k 2 to the U(1) and SU(2) gauge sectors, respectively. In this analysis, we fix the values of k 1 and k 2 to 1.0, and set limits on Λ at various values of m DM .
The model of large extra dimensions proposed by Arkani-Hamed, Dimopoulos, and Dvali (ADD) [7,8] postulates n extra spatial dimensions compactified at a characteristic scale R that reflects an effective Planck scale M D through M 2 Pl ≈ M n+2 D R n , where M Pl is the conventional Planck scale. If M D is of the same order as the EWK scale (M EWK ∼ 10 2 GeV), the large value of M Pl can be interpreted as being a consequence of large-volume (∼R n ) enhancement from extra dimensional space. This model predicts a process qq → γG ( Fig. 1 right), where G represents one or more Kaluza-Klein gravitons, each of which can have any mass up to M D . Since the gravitons escape detection, this process leads to the monophoton final state.
In this paper we describe a search for an excess of monophoton events over the SM prediction. Data collected by the CMS experiment in 2016, corresponding to an integrated luminosity of 35.9 fb −1 , are analyzed. Results are interpreted in the context of the three processes represented in Fig. 1.
The primary irreducible background for the γ + p miss T signal is the SM Z boson production associated with a photon, Z(→ νν)+γ. Other SM background processes include W(→ ν)+γ (where the charged lepton escapes detection), W → ν (where is misidentified as a photon), γ+jets, quantum chromodynamic (QCD) multijet events (with a jet misidentified as a photon), γγ, tγ, ttγ, VVγ (where V refers to a W or a Z boson), and Z(→ )+γ. Additionally, a small residual number of events from noncollision sources, such as beam halo [9] interactions and detector noise [10], contribute to the total background. integrated luminosity of 36.1 fb −1 , has been reported by the ATLAS experiment [11]. No significant excess over the SM prediction was observed. For the DM simplified model, a lower limit of 1200 GeV for both the vector and axial-vector mediator mass was set for low DM masses under the same assumption on the new-physics coupling values. For the EWK-DM effective interaction, a lower limit for the suppression parameter of the coupling was set at 790 GeV.
The previous search in the same final state by the CMS experiment [12] is based on √ s = 13 TeV data corresponding to an integrated luminosity of 12.9 fb −1 , which is a subset of the data analyzed in this paper. In addition to benefiting from a larger sample size, the new analysis achieves improved sensitivity by using a simultaneous fit to the distributions of the p T of the photon (E γ T ) in various signal and control regions to estimate the signal contribution, rather than the "cut-and-count" method deployed previously.
The paper is organized as follows. The CMS detector apparatus is described in Section 2, along with the algorithm used to reconstruct particles in pp collision events within the detector. Section 3 lists the requirements that events must pass in order to be selected for inclusion in the signal and control regions. Section 4 lists the Monte Carlo generators used to model various signal and background processes, and Section 5 describes the methods used to estimate the expected background yields in the signal and control regions. These yields are tabulated in Section 6, which also presents the limits obtained for each new physics model. The overall results are summarized in Section 7. Appendix A gives a detailed description of the higher order corrections applied to the predicted differential cross sections of the leading background processes.

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 (HCAL), each composed of a barrel (|η| < 1.48) and two endcap (1.48 < |η| < 3.00) sections, where η is the pseudorapidity. The ECAL consists of 75 848 lead tungstate crystals, with 61 200 in the barrel and 7324 in each of the two endcaps. In the η-φ plane, HCAL cells in the barrel map on to 5×5 arrays of ECAL crystals to form calorimeter towers projecting radially outwards from close to the nominal interaction point. Forward calorimeters extend the η coverage provided by the barrel and endcap detectors. Muons are detected in gas-ionization chambers embedded in the steel flux-return yoke outside the solenoid.
Events of interest are selected using a two-level trigger system [13]. The first level, composed of custom hardware processors, uses information from the calorimeters and muon detectors to select events at a rate of around 100 kHz within a time interval of less than 4 µs. The second level, known as the high-level trigger (HLT), consists of a farm of processors running a version of the full event reconstruction software optimized for fast processing, and reduces the event rate to less than 1 kHz before data storage. A more detailed description of the CMS detector, together with a definition of the coordinate system and kinematic variables, can be found in Ref. [14].
Global event reconstruction follows the particle-flow (PF) algorithm [15], which aims to reconstruct and identify each individual particle in an event with an optimized combination of all subdetector information. In this process, the identification of the particle type (photon, electron, muon, charged hadron, neutral hadron) plays an important role in the determination of the particle direction and energy. Photons are identified as ECAL energy clusters not linked to the extrapolation of any charged particle trajectory to the ECAL, while electrons are identified as ECAL energy clusters with such a link. Muons are identified as tracks in the central tracker consistent with either a track or several hits in the muon system, and associated with calorimeter deposits compatible with the muon hypothesis. Charged hadrons are identified as tracks neither identified as electrons nor as muons. Note that all three types of charged candidates can be associated to a reconstructed interaction vertex through their tracks. Finally, neutral hadrons are identified as HCAL energy clusters not linked to any charged hadron trajectory, or as ECAL and HCAL energy excesses with respect to the expected charged hadron energy deposit.
Reconstruction of pp interaction vertices proceeds from tracks using a deterministic annealing filter algorithm [16]. The reconstructed vertex with the largest value of summed physics-object p 2 T is taken to be the primary pp interaction vertex. Here, the physics objects are the jets, clustered using the jet finding algorithm [17,18] with the tracks assigned to the vertex as inputs, and the associated missing transverse momentum, taken as the negative vector sum of the p T of those jets. These definitions of the jets and missing transverse momentum are specific to the context of vertex reconstruction, and are distinct from the definitions in the remainder of the analysis, as described in the following.
For each event, hadronic jets are clustered from these reconstructed PF candidates using the anti-k T algorithm [17,18] with a distance parameter of 0.4. The jet momentum is determined as the vector sum of all particle momenta in the jet. Because of the large number of additional pp interactions within the same or nearby bunch crossings (pileup), particles emerging from multiple interactions can be clustered into a jet. To mitigate this effect, charged candidates associated with vertices other than the primary one are discarded from clustering, and an offset correction is applied to the p T of the jet to subtract the remaining contributions [19]. Jet energy corrections are derived from simulation to bring, on average, the measured response of jets to that of particle level jets. Measurements on data of the momentum balance in dijet, photon + jet, Z + jet, and multijet events are used to account for any residual differences in jet energy scale in data and simulation. Additional selection criteria are applied to each jet to remove jets potentially dominated by anomalous contributions from various subdetector components or reconstruction failures [19].
The missing transverse momentum vector ( p miss T ) is defined as the negative vector sum of the transverse momenta of all PF candidates in an event. The magnitude of p miss T is the missing transverse momentum, p miss T . ECAL clusters are identified starting from cluster seeds, which are ECAL crystals with energies above a minimum threshold, that must also exceed the energies of their immediate neighbors. Topological clusters are grown from seeds by adding adjacent crystals with energies above a lowered threshold, which could include other seeds. A topological cluster is finally separated into distinct clusters, one for each seed it contains, by fitting its energy distribution to a sum of Gaussian-distributed contributions from each seed.
Photon and electron reconstruction begins with the identification of ECAL clusters having little or no observed energy in the corresponding HCAL region. For each candidate cluster, the reconstruction algorithm searches for hits in the pixel and strip trackers that can be associated with the cluster. Such associated hits are called electron seeds, and are used to initiate a special track reconstruction based on a Gaussian sum filter [20,21] which is optimized for electron tracks. The energy of electrons is determined from a combination of the electron momentum at the primary interaction vertex as determined by the tracker, the energy of the corresponding ECAL cluster, and the energy sum of all bremsstrahlung photons spatially compatible with originating from the electron track. An ECAL cluster with no associated electron seed, or with a significant energy excess relative to any compatible tracks, gives rise to a photon candidate. The energy of a photon is determined only from its corresponding ECAL cluster.

Event selection
The integrated luminosity of the analyzed data sample is (35.9 ± 0.9) fb −1 [22]. The data sample is collected with a single-photon trigger that requires at least one photon candidate with p T > 165 GeV. The photon candidate must have H/E < 0.1 to discriminate against jets, where H/E is the ratio of HCAL to ECAL energy deposits in the central calorimeter tower corresponding to the candidate. The photon energy reconstructed at the HLT is less precise relative to that derived later in the offline reconstruction. Therefore, the thresholds in the trigger on both H/E and E γ T , are less restrictive than their offline counterparts. The trigger efficiency is measured to be about 98% for events passing the analysis selection with E γ T > 175 GeV. From the recorded data, events are selected by requiring p miss T > 170 GeV and at least one photon with E γ T > 175 GeV in the fiducial region of the ECAL barrel (|η| < 1.44). Photon candidates are selected based on calorimetric information, isolation, and the absence of an electron seed, where the first two categories of the selection requirements are designed to discriminate the photon candidates from electromagnetic (EM) showers caused by hadrons, and the third is designed to discriminate photon candidates from electrons.
The calorimetric requirements for photons comprise H/E < 0.05 and σ ηη < 0.0102. The variable σ ηη , described in detail in Ref. [23], represents the width of the EM shower in the η direction, which is generally larger in showers from hadronic activity. For a photon candidate to be considered as isolated, the scalar sums of the transverse momenta of charged hadrons, neutral hadrons, and photons within a cone of ∆R = √ (∆η) 2 + (∆φ) 2 < 0.3 around the candidate photon must all fall below a set of corresponding bounds chosen to give 80% signal efficiency. Only the PF candidates that do not overlap with the EM shower of the candidate photon are included in the isolation sums. Ideally, the isolation sum over PF charged hadrons should be computed using only the candidates sharing an interaction vertex with the photon candidate. However, because photon candidates are not reconstructed from tracks, their vertex association is ambiguous. When an incorrect vertex is assigned, nonisolated photon candidates can appear isolated. To reduce the rate for accepting nonisolated photon candidates, the maximum charged-hadron isolation value over all vertex hypotheses (worst isolation) is used. Stray ECAL clusters produced by mechanisms other than pp collisions can be misidentified as photons. In particular, anomalous ECAL energy deposits resulting from the interaction of particles in the ECAL photodetectors, from here on referred to as "ECAL spikes", as well as beam halo muons that accompany proton beams and penetrate the detector longitudinally have been found to produce spurious photon candidates at nonnegligible rates. The ECAL spike background is reduced by requiring that the photon candidate cluster must comprise more than a single ECAL crystal. To reject the beam halo induced EM showers, the ECAL signal in the seed crystal of the photon cluster is required to be within ±3 ns of the arrival time expected for particles originating from a collision. In addition, the maximum of the total calorimeter energy summed along all possible paths of beam halo particles passing through the cluster (halo total energy), calculated for each photon candidate, must be below 4.9 GeV. The two requirements combined with the shower shape constraint rejects the beam halo background effectively, while retaining 95% of signal photons. Furthermore, using features described in Section 5.4, the signal region is split into two parts according to φ to constrain the beam halo normalization. The region defined by |sin(φ)| < sin(0.5) is called the horizontal region, and its complement in φ is called the vertical region.
Events with a high-p T photon and large p miss T are subjected to further requirements to suppress SM background processes that feature a genuine high-energy photon, but not a significant amount of p miss T . One such SM process is γ+jets, where an apparent large p miss T is often the result of a mismeasured jet energy. In contrast to signal processes, p miss T is typically smaller than E γ T in these events, so requiring the ratio of E γ T to p miss T to be less than 1.4 rejects this background effectively with little effect on signal efficiency. Events are also rejected if the minimum opening angle between p miss T and the directions of the four highest p T jets, min∆φ( p miss T , p jet T ), is less than 0.5. Only jets with p T > 30 GeV and |η| < 5 are considered in the min∆φ( p miss T , p jet T ) calculation. In the γ+jets process, rare pathological mismeasurement of E γ T can also lead to large p miss T . For this reason, the candidate photon p T and p miss T must be separated by more than 0.5 radians. Another SM process to be rejected is W(→ ν)+γ, for which events are vetoed if they contain an electron or a muon with p T > 10 GeV that is separated from the photon by ∆R > 0.5.
The residual contributions from the W(→ ν)+γ process, where the lepton could not be identified or was out of the detector acceptance, are modeled by fitting to observed data, as described in Section 5. The same method is employed to model the contribution from the Z(→ νν)+γ process to the signal region. This method utilizes control regions where one or two leptons (electrons or muons) are identified in addition to the photon, as defined in the following.
The single-electron (single-muon) control region is defined by a requirement of exactly one electron (muon) with p T > 30 GeV and |η| < 2.5 (2.4) in addition to a photon requirement that is identical to the one for the signal region. To suppress the contributions from large-p miss T processes other than W(→ ν)+γ, the transverse mass ] must be less than 160 GeV. Additionally, for the single-electron control region, p miss T must be greater than 50 GeV to limit the contribution from the γ+jets process, where a jet is misidentified as an electron. Finally, the recoil vector U = p miss T + p T , which serves as this region's analogue for p miss T in the signal region, must satisfy identical requirements to those for the p miss T in the signal region.
The dielectron (dimuon) control region is defined by exactly two electrons (muons) in addition to the photon, with 60 < m < 120 GeV, where m is the invariant mass of the dilepton system. The recoil vector of this region is U = p miss T + ∑ p T and must satisfy identical requirements to those for the p miss T in the signal region.

Signal and background modeling
Monte Carlo simulation is used to model the signal and some classes of SM background events. For all simulated samples, the NNPDF3.0 [24] leading order (LO) parton distribution function (PDF) set with the strong coupling constant value α S = 0.130 is employed. For the SM background processes, the primary hard interaction is simulated using the MADGRAPH5 aMC@NLO version 2.2.2 [25] generator at LO in QCD. The simulated events for the Z(→ νν)+γ, Z(→ )+γ, and W(→ ν)+γ background processes, collectively denoted as V+γ, are generated with MADGRAPH5 aMC@NLO at LO in QCD with up to two extra partons in the matrix element calculations. These are then normalized to the next-to-leading order (NLO) EW and next-to-next-to-leading order (NNLO) QCD cross-sections using correction factors described in Section 5.1. Parton showering and hadronization are provided by PYTHIA 8.212 with the underlying-event tune CUETP8M1 [26]. Multiple simulated minimum bias events are overlaid on the primary interaction to model the distribution of pileup in data. Generated particles are processed through the full GEANT4-based simulation of the CMS detector [27,28].

Z(→ νν)+γ and W(→ ν)+γ background
The most significant SM background processes in this search are the associated production of a high-energy γ with either a Z boson that subsequently decays to a pair of neutrinos, or a W boson that decays to a charged lepton and a neutrino. The two processes are denoted as Z(→ νν)+γ and W(→ ν)+γ. Together, they account for approximately 70% of the SM background, with 50% from the former and 20% from the latter. Contributions from these two background processes are estimated using observed data in the four mutually exclusive singleelectron, single-muon, dielectron, and dimuon control regions defined in Section 3. The ratios between the expected yields of these processes are constrained by MC simulations of V+γ processes.
The individual MC simulation samples of V+γ processes receive multiple correction factors. First is the selection efficiency correction factor ρ, which accounts for subtle differences between simulation and observation in the reconstruction and identification efficiencies for various particle candidates. The value of ρ typically lies within a few percent of unity. The second factor is the higher-order QCD correction, which matches the distribution of the generator-level E γ T to that calculated at NNLO in QCD using the DYRES program [29]. The third factor further corrects the E γ T distributions to account for NLO EW effects, and is taken from Refs. [30,31], updated using the LUXqed17 PDF set [32].
Four sources of systematic uncertainties considered for E γ T distribution ratios among the V+γ processes are PDFs, higher-order QCD corrections, higher-order EWK corrections, and data-to-simulation correction factors ρ. The PDF uncertainty is evaluated by varying the weight of each event using the weights provided in the NNPDF set, and taking the standard deviation of the resulting E γ T distributions. This uncertainty is considered fully correlated in the ratio between the Z(→ νν)+γ and W(→ ν)+γ processes, i.e., the variation of the ratio is bounded by the ratios of the upward and downward variations. Uncertainties related to higher-order QCD corrections are considered uncorrelated in the ratio between the Z(→ νν)+γ and W(→ ν)+γ processes. Because EW corrections become increasingly important at higher E γ T , but are known only up to NLO accuracy, their uncertainties are estimated by a special prescription similar to that discussed in Ref. [33], where independent degrees of freedom are assigned to the uncertainty in the overall scale of the correction and the uncertainty in the variation of the correlation with E γ T . Additionally, the full correction due to photon-induced Z + γ and W + γ production cross sections is considered as an uncertainty. Further details concerning the higher-order QCD and EWK corrections are given in Appendix A. Finally, data-to-simulation correction factors ρ for the lepton identification efficiencies have associated uncertainties that do not cancel when taking ratios between regions defined by different lepton selection requirements.
The background estimation method exploits cancellation of some of the systematic uncertainties, both experimental and theoretical, in the ratios of the photon E γ T distributions of V+γ processes, from here on referred to as "transfer factors". For example, in the transfer factor between the Z(→ νν)+γ and Z(→ )+γ processes, denoted R Zγ γ , the uncertainties due to photon energy calibration, jet energy resolution, and higher-order QCD effects are significantly reduced compared to when such effects are considered for individual processes. The only uncertainties in the transfer factor R Zγ γ that do not largely cancel are those on lepton identification efficiency and the statistical uncertainty due to the limited MC sample size. Figure 2 shows the transfer factor R Zγ eeγ (R Zγ µµγ ) between the dielectron (dimuon) control region and the combined signal regions, for which the numerator is the expected Z(→ νν)+γ yield in the combined signal regions and the denominator is the expected Z(→ )+γ yield in the relevant control region.
[GeV] and orange (outer) show the systematic uncertainty, and the combination of systematic and statistical uncertainty arising from limited MC sample size, respectively. The systematic uncertainties considered are the uncertainties in the data-to-simulation correction factors ρ for the lepton identification efficiencies.
Using the transfer factor R Zγ γ , the total estimated event yield T γ in each dilepton control region in the i th bin of the E γ T distribution can be expressed as where N Zγ is the number of Z(→ νν)+γ events in the combined signal regions and b γ is the predicted contribution from other background sources in the dilepton control region, namely ttγ, VVγ, and misidentified hadrons. The subscript i indicates that the quantities are evaluated in bin i of the E γ T distribution. Similar considerations apply to events arising from W(→ ν)+γ processes. The charged lepton from these processes may either pass our identification criteria or fail, and in the ratio of these two classes of events, denoted R Wγ γ , the only uncertainties that remain non-negligible are those associated with the lepton identification efficiency and the MC statistical uncertainty. Figure 3 shows the transfer factor R Wγ eγ (R Wγ µγ ) between the single-electron (single-muon) control region and the combined signal regions, for which the numerator is the estimated W(→ ν)+γ yield in the combined signal regions, and the denominator is the estimated W(→ ν)+γ yield in the relevant control region.   Fig. 13 in Appendix A. Figure 4 shows the transfer factor f Zγ Wγ between the Z(→ νν)+γ and W(→ ν)+γ processes in the combined signal region. For every transfer factor described above, both the numerator and the denominator are estimated in MC.
For increasing E γ T , the Z boson in a Z(→ )+γ event tends to emerge with lower rapidity, and hence so do its decay products. As a consequence, the charged leptons are more likely to fall within the inner tracker acceptance, which increases the dilepton control region selection efficiency of these events. In contrast, the signal region selection efficiency of Z(→ νν)+γ events is unaffected by the rapidity of the final state neutrinos, as long as the observed p miss T has the appropriate magnitude and azimuthal direction. This causes the distinctive drop in the ratio R where b γ is the predicted contribution from other background sources in the single-lepton regions, namely misidentified electrons and hadrons and other minor SM processes.

Electron misidentification background
An important background consists of W → eν events in which the electron is misidentified as a photon. The misidentification occurs because of an inefficiency in seeding electron tracks. A seeding efficiency of for electrons with p T > 160 GeV is measured in data using a tag-andprobe [34] technique in Z → ee events, and is validated with MC simulation. Misidentified electron events are modeled by a proxy sample of electron events, defined in data by requiring an ECAL cluster with a pixel seed. The proxy events must otherwise pass the same criteria used to select signal candidate events. The number of electron proxy events is then scaled by R = (1 − )/ to yield an estimated contribution of events from electron misidentification to our signal candidate selection. The ratio R was measured to be 0.0303 ± 0.0022 and uniform across the considered E γ T spectrum, with the dominant uncertainty in this estimate coming from the statistical uncertainty in the measurement of .

Jet misidentification background
Electromagnetic showers from hadronic activity can also mimic a photon signature. This process is estimated by counting the numbers of events in two different subsets of a low-p miss T multijet data sample. The first subset consists of events with a photon candidate that satisfies the signal selection criteria. These events contain both genuine photons and jets that are misidentified as photons. The second subset comprises events with a candidate photon that meets less stringent shower shape requirements and inverted isolation criteria with respect to the signal candidates. Nearly all of the candidate photons in these events arise from jet misidentification. The hadron misidentification ratio is defined as the ratio between the number of misidentified events in the first subset to the total number of events in the second subset.
The numerator is estimated by fitting the observed shower shape distribution of the photon candidate in the first subset with a combination of simulated distributions and distributions obtained from the observed data. For genuine photons, the shower width distribution is formed using simulated γ + jets events. For jets misidentified as photons, the distribution is obtained from a sample selected by inverting the charged-hadron isolation and removing the showershape requirement entirely.
The hadron misidentification ratio is measured to be between 0.08 and 0.12 with a few percent relative uncertainty depending on the energy of the photon candidate. The dominant uncertainty is systematic, and comprises the shower shape distribution fit and shower shape modelling uncertainty, along with uncertainties associated with variations in the charged hadron isolation threshold, low-p miss T requirement, and template bin width.
The final estimate of the contribution of jet misidentification background to our signal candidate selection is computed by multiplying the hadron misidentification ratio by the number of events in the high-p miss T control sample with a photon candidate that satisfies the conditions used to select the second subset of the low-p miss T control sample.

Beam halo and spikes background
Estimates of beam halo background and spike background are derived from fits of the angular and timing distributions of the calorimeter clusters. Energy clusters in the ECAL due to beam halo muons are observed to concentrate around |sin(φ)| ∼ 0, while all other processes (collision-related processes and ECAL spikes) produce photon candidates that are uniformly distributed in φ [9], motivating the splitting of the signal region introduced in Section 3.
The splitting of the signal region can be thought of as a two-bin fit. Collision processes occupy the relative fractions of phase space in the horizontal (H) and vertical (V) signal regions, C H = 1/π and C V = (π − 1)/π, respectively. The corresponding fractions for beam halo events are determined by selecting a halo-enriched sample where the halo identification is inverted. Thus, a fit of the two signal regions provides an estimate of the overall normalization of the beam halo background, denoted h. The E γ T dependence of the halo background is encoded in n halo K,i , the unit-normalized beam halo prediction in bin i of the signal region K ∈ {H, V}. Using the notation introduced in Section 5.1, the total estimated background T K in the two signal regions are is the total contribution to bin i of region K from electron and hadron misidentification, ECAL spikes, and other minor SM background processes.
The distribution of the cluster seed timing provides a cross-check on the beam halo background estimate and an independent means to estimate the ECAL spikes contribution [10]. A threecomponent fit of the cluster seed timing using the halo, spike, and prompt-photon templates are performed. The timing distribution of the spike background is obtained by inverting the lower bound on the shower shape requirement in the candidate photon selection. A total spike background of 22.9 ± 5.8 events is predicted, where the dominant uncertainty is statistical.

Other minor SM background processes
The SM ttγ, VVγ, Z(→ )+γ, W → ν, and γ+jets processes are minor (∼10%) background processes in the signal region. Although Z(→ )+γ and γ+jets do not involve high-p T invisible particles, the former can exhibit large p miss T when the leptons fail to be reconstructed, and the latter when jet energy is severely mismeasured. The estimates for all five processes are taken from MADGRAPH5 aMC@NLO simulations at LO in QCD and can be found in Tables 1 and 2.

Signal extraction
The potential signal contribution is extracted from the data via simultaneous fits to the E γ T distributions in the signal and control regions. Uncertainties in various quantities are represented by nuisance parameters in the fit. Predictions for Z(→ νν)+γ, W(→ ν)+γ, and the beam halo backgrounds are varied in the fit. Beam halo is not a major background, but the extraction of its rate requires a fit to the observed distributions in the signal region. The background-only likelihood that is maximized in the fit is following the notation introduced in Section 5, and where P (n|λ) is the Poisson probability of n for mean λ, N denotes the unit normal distribution, and d X,i is the observed number of events in bin i of region X. Systematic uncertainties are treated as nuisance parameters in the fit and are represented by θ. Each quantity Q j with a nominal value Q j and a standard deviation of the systematic uncertainty σ j appears in the likelihood function as Q j exp(σ j θ j ).
The systematic uncertainties considered in this analysis, including the ones already mentioned in Section 5, are: • Theoretical uncertainties in V+γ differential cross sections, incorporated as uncertainties on the transfer factors (see Section 5.1) • Uncertainties in trigger efficiency and photon and lepton identification efficiencies • Electron and jet misidentification rate uncertainties (see Sections 5.2 and 5.3) • Photon and jet energy scale uncertainties (see Refs. [35] and [19]) • Beam halo and ECAL spike rate and distribution uncertainties (see Section 5.4) • Minor SM background cross section uncertainties • Uncertainty in integrated luminosity (see Ref. [22]) Of the listed uncertainties, only the first two categories have a significant impact on the result of the signal extraction fit. Figure 5 shows the observed E γ T distributions in the four control regions compared with the results from simulations before and after performing the simultaneous fit across all the control samples and signal region, and assuming absence of any signal. Figure 6 shows the observed E γ T distributions in the horizontal and vertical signal regions compared with the results from simulations before and after performing a combined fit to the data in all the control samples, not including the signal region. The observed distributions are in agreement with the prediction from SM and noncollision backgrounds. The dominant systematic uncertainties in the signal model include those on the integrated luminosity, jet and γ energy scales, p miss T resolution, and data-to-simulation scale factors discussed in Section 5.

Pre-fit and post-fit distributions
The expected yields in each bin of E γ T for all backgrounds in the horizontal and vertical signal regions after performing a combined fit to data in all the control samples, excluding data in the Table 1: Expected event yields in each E γ T bin for various background processes in the horizontal signal region. The background yields and the corresponding uncertainties are obtained after performing a combined fit to data in all the control samples, excluding data in the signal region. The observed event yields in the horizontal signal region are also reported.       Tables 1 and 2, respectively. The covariances between the predicted background yields across all the E γ T bins in the two signal regions are shown in Fig. 15 in Appendix A. The expected yields together with the covariances can be used with the simplified likelihood approach detailed in Ref. [36] to reinterpret the results for models not studied in this paper.

Limits
No significant excess of events beyond the SM expectation is observed. Upper limits are determined for the production cross section of three new-physics processes mentioned in Section 1. For each model, a 95% confidence level (CL) upper limit is obtained utilizing the asymptotic CL s criterion [37][38][39], using a test statistic based on the negative logarithm of the likelihood in Section 6.1.
The simplified DM models parameters proposed by the ATLAS-CMS Dark Matter Forum [4] are designed to facilitate the comparison and translation of various DM search results. Figure 7 shows the 95% CL upper cross section limits with respect to the corresponding theoretical cross section (µ 95 = σ 95% /σ theory ) for the vector and axial-vector mediator scenarios, in the M med -m DM plane. The solid black (dashed red) curves are the observed (expected) contours of µ 95 = 1. The σ theory hypothesis is excluded at 95% CL or above in the region with µ 95 < 1. The uncertainty in the expected upper limit includes the experimental uncertainties. For the simplified DM LO models considered, mediator masses up to 950 GeV are excluded for values of m DM less than 1 GeV.
The results for vector, axial-vector, and pseudoscalar mediators are compared to constraints from the observed cosmological relic density of DM as determined from measurements of the cosmic microwave background by the Planck satellite experiment [40]. The expected DM abundance is estimated, separately for each model, using the thermal freeze-out mechanism implemented in the MADDM [41] framework and compared to the observed cold DM density Ω c h 2 = 0.12 [40], where Ω c is the DM relic abundance and h is the dimensionless Hubble constant.
The exclusion contours in Fig. 7 are also translated into the σ SI/SD -m DM plane, where σ SI/SD are the spin-independent/spin-dependent DM-nucleon scattering cross sections as shown in Fig. 8. The translation and presentation of the result follows the prescription given in Ref. [5]. In particular, to enable a direct comparison with results from direct detection experiments, these limits are calculated at 90% CL [4]. When compared to the direct detection experiments, the limits obtained from this search provide stronger constraints for DM masses less than 2 GeV (spin independent) and less than 200 GeV (spin dependent). For the DM model with a contact interaction of type γγχχ, upper limits are placed on the production cross section, which are then translated into lower limits on the suppression scale Λ for k 1 = k 2 = 1.0. The 95% CL observed and expected lower limits on Λ as a function of dark matter mass m DM are shown in Fig. 9. For m DM between 1 and 100 GeV, we exclude Λ values up to 850 (950) GeV, observed (expected) at 95% CL.  Table 3, and in Fig. 11. Values of M D up to 2.90 TeV for n = 6 are excluded by the current analysis.
The sensitivity of the analysis to new physics, as measured by the stringency of the expected cross section upper limits, has improved by approximately 70% in comparison to the previ-     On the plots, the median expected 90% CL curve overlaps the observed 90% CL curve. Also shown are corresponding exclusion contours, where regions above the curves are excluded, from the recent results by CDMSLite [42], LUX [43], PandaX-II [44], XENON1T [45], CRESST-II [46], PICO-60 [47], Ice-Cube [48], PICASSO [49] and Super-Kamiokande [50] Collaborations.    ous CMS results [12]. A threefold increase in the data set size accounts for one fourth of the improvement, with the rest of the gain resulting from by the use of the simultaneous fit to multiple signal and control regions.

Summary
Proton-proton collisions producing a high transverse momentum photon and large missing transverse momentum have been investigated to search for new phenomena, using a data set corresponding to 35.9 fb −1 of integrated luminosity recorded at √ s = 13 TeV at the LHC. An analysis strategy of performing a simultaneous fit to multiple signal and control regions is employed on this final state for the first time, enhancing the sensitivity to potential signal events. No deviations from the standard model predictions are observed. For the simplified dark matter production models considered, the observed (expected) lower limit on the mediator mass is 950 (1150) GeV in both cases for 1 GeV dark matter mass. For an effective electroweak-dark matter contact interaction, the observed (expected) lower limit on the suppression parameter Λ is 850 (950)

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 centers and personnel of the Worldwide LHC Computing Grid for delivering so effectively the computing infrastructure essential to our analyses.

A Higher-order corrections to V+γ differential cross sections
In order to account for higher-order electroweak corrections, we apply additional factors as a function of E γ T . Of the various electroweak higher-order effects, ones that can give sizeable ( O(α)) corrections to the differential cross section are Sudakov suppression at high photon p T and potentially the addition of photon-induced scattering processes [30,31]. We apply the correction factors shown in Fig. 12, which are combinations of Sudakov suppression factors and photon-induced enhancements, and are provided by the authors of Ref. [31] in addition to the NNLO QCD correction. Uncertainty due to γ-induced production is negligible in Z(→ νν)+γ production.
The differential cross section after the full higher-order corrections is therefore denoted as where k NNLO QCD = dσ NNLO QCD /dσ LO , and the two κ terms are the Sudakov suppression and photon-induced enhancement components of the electroweak correction, respectively.
We estimate the magnitude of the uncertainty in κ EW Sudakov and κ EW qγ to be (κ EW Sudakov ) 2 and κ EW qγ , i.e., square of the correction for Sudakov suppression and the 100% of the correction itself for the photon-induced enhancement. The choice of using the square of κ EW Sudakov is motivated by the fact that fully resummed leading-log Sudakov suppression is an exponential of κ EW Sudakov .
For the Sudakov suppression, which is the dominant term in the electroweak correction, we further consider two types of systematic variations, inspired by Ref. [33], which provides a prescription for electroweak correction uncertainties for V + jets processes. In that paper, electroweak correction as a function of the boson p T is varied in overall scale and in slope. The slope variation is realized by selecting a point in the boson p T spectrum and letting the shift in correction cross over at the point. Figure 13 shows the effect of systematic uncertainty in the ratio between the Z(→ νν)+γ and W(→ ν)+γ processes with respect to nominal value for Zγ and Wγ respectively.  Figure 13: Systematic uncertainty in the transfer factors for Z(→ νν)+γ (left) and W(→ ν)+γ (right). The last bin includes all events with E γ T > 1000 GeV. Figure 14 shows the comparison between data and the post-fit background predictions in the horizontal and vertical signal regions, where the background prediction is obtained from a combined fit performed in all control regions, excluding the signal regions. The covariances between the predicted background yields across all the E γ T bins in the two signal regions are shown in Fig. 15.
Additionally, Table 4 shows the step-by-step efficiency of various selections for the irreducible Zγ and Wγ processes as well as two representative signal models.   Step-by-step efficiencies of various selections for irreducible Zγ and Wγ processes as well as two representative signal models: a 1 TeV vector mediator decaying to 1 GeV DM particles and an ADD graviton model with 8 extra dimensions and M D = 3 TeV. The statistical uncertainties on these values are generally on the order of half a percent.