Measurements of the pp to W gamma gamma and pp to Z gamma gamma cross sections and limits on anomalous quartic gauge couplings at sqrt(s) = 8 TeV

Measurements are presented of W gamma gamma and Z gamma gamma production in proton-proton collisions. Fiducial cross sections are reported based on a data sample corresponding to an integrated luminosity of 19.4 inverse femtobarns collected with the CMS detector at a center-of-mass energy of 8 TeV. Signal is identified through the W to l nu and Z to ll decay modes, where l is a muon or an electron. The production of W gamma gamma and Z gamma gamma, measured with significances of 2.6 and 5.9 standard deviations, respectively, is consistent with standard model predictions. In addition, limits on anomalous quartic gauge couplings in W gamma gamma production are determined in the context of a dimension-8 effective field theory.


Introduction
Production of three-boson final states in proton-proton collisions is predicted by the SU(2)×U (1) gauge structure of the standard model (SM). Cross sections for these processes include contributions from quartic gauge couplings (QGCs), which are sensitive to new phenomena that modify those couplings. In this paper, we present cross section measurements for the pp → Wγγ and pp → Zγγ processes and a search for anomalous QGCs (aQGCs). The W → ν and Z → decay modes are selected for analysis, where is a muon or an electron. The cross sections are measured in fiducial regions that are defined by selection criteria similar to those used to select signal events. In particular, to avoid infrared divergences, minimum photon transverse momenta p T of 25 and 15 GeV are required in the Wγγ and Zγγ measurements, respectively. A dimension-8 effective field theory is used to model aQGCs, which would enhance Wγγ production at high momentum scales. The Wγγ and Zγγ processes were recently observed by the ATLAS Collaboration [1,2] using 20.3 fb −1 of integrated luminosity at √ s = 8 TeV. Cross sections for Wγγ and Zγγ production have also been computed with QCD corrections up to next-to-leading order (NLO) in Ref. [3,4].

The CMS detector and particle reconstruction
The data used in these measurements amount to 19.4 fb −1 collected in 2012 with the CMS detector at the CERN LHC in proton-proton collisions at a center-of-mass energy of 8 TeV. A detailed description of the CMS detector, together with definitions of the coordinate system and relevant kinematic variables, can be found in Ref. [5]. 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 field volume are a silicon pixel and strip tracker, a lead tungstate crystal electromagnetic calorimeter (ECAL), and a brass and plastic scintillator hadron calorimeter (HCAL), each composed of a barrel and two endcap sections. Extensive forward calorimetry utilizing a steel absorber with embedded quartz fibers complements the coverage provided by the barrel and endcap detectors. Muons are measured in gas-ionization detectors embedded in the steel flux-return yoke outside the solenoid.
The particle-flow (PF) algorithm [6] reconstructs and identifies five types of particles with an optimized combination of information from the various elements of the CMS detector. Particle flow candidates provide the basis for the selection and measurement of muons, electrons, photons, jets, and the transverse momentum imbalance. In addition, the isolation characteristics of identified leptons and photons are measured using the p T of PF charged hadrons, neutral hadrons, and photons.
Muons are identified as tracks in the muon spectrometer that are matched to tracks in the inner detector. Quality requirements are placed on tracks measured in the inner detector and muon spectrometer, as well as on the matching between them. Muons must also be isolated from nearby PF candidates. Selected muons in the momentum range 20 < p T < 100 GeV have a relative p T resolution of 1.3-2.0% in the barrel (|η| < 1.2) and less than 6% in the endcaps (1.2 < |η| < 2.4) [7].
Photons and electrons are identified as clusters of energy deposits in the ECAL. The energy of photons is directly obtained from the ECAL measurement. Electrons are further identified by matching the ECAL cluster to a track reconstructed in the inner detector. The momenta of electrons are determined from a combination of the track momentum at the primary interaction vertex, the energy of the corresponding ECAL cluster, and the energy sum of all bremsstrahlung photons spatially compatible with originating from the electron track. To take into account electron bremsstrahlung in the inner-detector material, a Gaussian sum filter algorithm [8] is used to measure the track momentum. The momentum resolution for electrons from Z → e + e − decays ranges from 1.7% for electrons in the barrel region to 4.5% for electrons that begin to shower before the calorimeter in the endcaps [9].
Electrons are selected in the Wγγ analysis using a multivariate classifier based on the spatial distribution of the electron shower, the energy deposited in the HCAL region matched to the ECAL shower, and the quality of the inner-detector track. Electrons are selected in the Zγγ analysis by imposing looser requirements on the same variables, yielding improved signal acceptance. In both cases, electrons passing the selection must also be isolated from nearby PF candidates.
Photons are identified using a selection that requires a narrow shower in the ECAL, minimal energy deposited in the HCAL region matched to the ECAL shower, and isolation from nearby PF candidates. Separate isolation requirements are placed on the energies of PF charged hadrons, neutral hadrons, and photons. Photons that convert to an electron-positron pair are included and the same selection criteria are applied. The energy resolution is about 1% in the barrel section of the ECAL for unconverted or late converting photons in the tens of GeV energy range. The remaining barrel photons have a resolution of about 1.3% up to a pseudorapidity of |η| = 1, rising to about 2.5% at |η| = 1.4. In the endcaps, which cover a pseudorapidity of 1.5 < |η| < 2.5, the resolution of unconverted photons is about 2.5%, while converted photons have a resolution between 3 and 4% [10].
The transverse momentum imbalance vector p miss T is defined as the projection on the plane perpendicular to the beams of the negative vector sum of the p T of all reconstructed PF candidates in the event. Its magnitude is referred to as p miss T . Corrections to the energy scale and resolution of jets, described in [11], are propagated to the calculation of p miss T .

Event selection
Events are recorded using single-lepton triggers for the Wγγ selection and dilepton triggers for the Zγγ selection [12]. The single-lepton triggers have p T thresholds of 24 and 27 GeV for muons and electrons, respectively. The dimuon and dielectron triggers both have p T thresholds of 17 and 8 GeV on the leading and subleading leptons, respectively. To ensure uniform trigger efficiency, reconstructed leptons are required to have p T above the trigger thresholds. The p T requirement is determined by measuring the efficiency of the trigger as a function of p T and selecting the value at which the efficiency becomes approximately independent of p T . For the Wγγ (Zγγ) analysis the muons and electrons must have minimum p T of 25 (10) and 30 (20) GeV, respectively.
Events selected for the Wγγ analysis must have one muon or electron and two photons. Each photon is required to have p T greater than 25 GeV. Events are removed if a second lepton is present having p T above 10 GeV. All reconstructed leptons and photons must be separated from each other by ∆R > 0.4, where ∆R = (∆φ) 2 + (∆η) 2 and φ is the azimuthal angle.
To identify leptonic W boson decays and remove backgrounds not having genuine p miss T , the transverse mass, defined as to electrons in which only one electron is correctly identified, the other is misidentified as a photon, and an additional prompt photon is present in the event. Both photons are required to pass an electron veto that rejects photons that match to tracks in the pixel detector. This requirement decreases the signal efficiency by removing converted photons, which are commonly matched to tracks in the pixel detector. However, the background contamination from electrons is further decreased by a factor of two. Events are also removed if the invariant mass of any combination of the electron and one or both photons is near the Z boson mass. In particular, events are removed if they have 86 < m eγ < 96 GeV for either combination of a photon with the electron, or if 86 < m eγγ < 96 GeV, in which case one photon is likely to be from final-state radiation (FSR).
Events selected for the Zγγ analysis must have two electrons or muons of opposite charge and two photons. Each photon is required to have a minimum p T of 15 GeV. Photons are required to pass an electron veto that has a higher signal efficiency than that used in the electron channel of the Wγγ analysis. All reconstructed leptons and photons must be separated from each other by ∆R > 0.4. The dilepton invariant mass must be greater than 40 GeV to remove backgrounds that have low dilepton invariant masses.
In both analyses, photons reconstructed in the barrel and endcaps are treated separately. The geometry of the ECAL differs between the barrel and endcaps and therefore different selection criteria are imposed for each case. Photons that are reconstructed in the endcaps are more likely to originate from misidentified jets. Events in which both reconstructed photons are in the endcaps are not considered in the analysis because of the unfavorable signal-to-background ratio.
Simulated aQGC events are assigned a set of weights, each of which reproduces the effect of an anomalous QGC. The weights are obtained by loading models of effective theories, provided in the Universal FeynRules Output format [20], into the event generator. The diboson and triboson predictions are normalized to the NLO cross section predictions obtained with MCFM (v.6.6) [21] and MADGRAPH5 aMC@NLO (v5 2.2.2), respectively. All τ leptons included in samples showered with PYTHIA are decayed with TAUOLA (v.1.1.1a) [22].
The influence of additional proton-proton collisions in data events (pileup) is corrected by adding minimum-bias collisions to the simulated events. The number of added pileup collisions follows a distribution that is similar to the distribution observed in data and an additional weight is applied such that the simulated pileup distribution accurately represents the data. Finally, all simulated samples are passed through a detailed GEANT4 simulation [23] of the CMS detector.
Corrections for differences between the simulation and the data in the selection efficiencies of muons, electrons, and photons and in the trigger efficiencies are determined using the tag-and-probe method and applied to the simulated events. Differences in the momentum scale of muons, electrons, and photons are determined from the Z boson line shape, and the simulation is corrected to agree with the data.

Background estimation
The main background contribution in both analyses consists of events in which one or two jets are misidentified as photons. In fact, while the photon shower and isolation requirements are designed to reject misidentified jets, the relatively large production rate of electroweak bosons with jets leads to a large contribution of jets misidentified as photons. A jet is commonly misidentified as a photon when it contains a neutral meson that decays to overlapping photons. If the photons carry a large fraction of the jet energy such that the other hadronization products have low momentum, the reconstructed photon can pass the isolation requirements.
The probability for a jet to be misidentified as a photon is sensitive to how jets interact with the detector and is therefore difficult to predict with simulation. Moreover, the generation of a sufficiently large simulated sample is impractical because of the large rejection factor obtained through the photon identification criteria. A data-based method is therefore used to estimate the contamination from this source.
The background estimate is based on an analysis of the two-dimensional distribution of the charged hadron isolation variables I ch,1 and I ch,2 of the leading and subleading photon candidates, respectively. The isolation I ch is defined as the scalar p T sum of charged hadron PF candidates having ∆R < 0.3 with respect to the photon candidate. Charged hadron PF candidates are required to have energy deposits in the HCAL and originate from the primary vertex, defined as the vertex with the highest sum of squared transverse momenta of its associated tracks [24]. Prompt photons have low values of I ch while jets that are misidentified as photons tend to have larger values. The distribution of I ch,1 versus I ch,2 (a "template") is determined for each of the four sources of diphoton candidates: prompt-prompt (PP), prompt-jet (PJ), jetprompt (JP), and jet-jet (JJ). The PP template represents the signal, while the PJ and JP templates represent background events having one prompt photon, and the JJ template represents background events having no prompt photons. Each template consists of four bins. The distribution of I ch is divided into a "tight" region and a "loose" control region for each of the two photons. The tight region contains photon candidates that satisfy the nominal I ch criterion, while the loose region contains photon candidates that fail the nominal, but pass a less stringent requirement. The value of the less stringent requirement is chosen such that candidates in the loose region are enriched in photon-like jets that are independent of, but sufficiently similar to those that contaminate the signal region. The four-bin structure of the templates provides discrimination between prompt photons and jets and allows for a straightforward matrix equation solution, taking account of correlations between I ch,1 and I ch,2 . The contribution of each source is determined from control data samples. Three control data samples are formed from the combinations of the tight and loose regions: tight-loose (TL) and loose-tight (LT), where one photon passes the requirement and the other fails, and loose-loose (LL), where both photons fail the requirement. The signal region is labeled tight-tight (TT). The TL and LT regions are treated separately to take into account differences in photon p T and differences between photons that are reconstructed in the barrel and endcaps. The normalizations of the four sources of photon candidates are determined through the matrix equation TT  PP  TT  PJ  TT  JP  TT  JJ  TL  PP  TL  PJ  TL  JP  TL  JJ  LT  PP LT where N XY is the observed number of events in region XY, XY AB is the probability for an event from source AB to appear in region XY, as determined from the templates, and α AB is the normalization of source AB. Each column in the matrix corresponds to the four bins from one template, and the entries in the column sum to unity by construction. The predicted number of events from source AB reconstructed in region XY is given by the product α AB XY AB . The final background estimate is the sum of the contributions from the sources involving at least one jet: Templates are constructed from both Monte Carlo (MC) simulation and data control samples. This procedure is applied separately for different ranges of photon p T and η. The templates for the PP, PJ, and JP sources are determined from prompt and jet I ch distributions obtained from single-photon events. The single-photon I ch distributions are binned in the same manner as the templates to create two-bin distributions representing the leading and subleading photon. Products of the two-bin distributions corresponding to the leading and subleading photons are used to determine the four-bin templates, the entries of which appear in Eq. (1).
The I ch distribution for prompt photons is taken from simulated Wγ events. Simulated events are required to contain one reconstructed photon that matches a photon in the generator record within ∆R = 0.2 and passes all selection criteria except the I ch requirement. The distributions obtained from simulation are validated with data events in which an FSR photon is identified in a Z boson decay to µ + µ − . To ensure that the photon results from FSR, the three-body invariant mass is required to be consistent with the Z boson mass and the photon must be within ∆R = 1 of a muon. The available data sample is adequate to make this comparison for photons with p T up to 40 GeV, and good agreement is observed between data and simulation. An uncertainty of 10-20% is applied, depending on the photon p T and η, to take into account the observed differences and for the extrapolation to higher photon p T .
The I ch distribution for jets is taken from data. For this purpose, events are selected that contain two reconstructed muons with invariant mass consistent with the Z boson mass and a reconstructed photon that passes all selection criteria except the I ch requirement. To exclude genuine photons from FSR, the photon is required to be separated from each muon by ∆R > 1. The remaining contribution from prompt photons is subtracted using the prediction from a sample of simulated Zγ events normalized to its production cross section calculated at nextto-next-to-leading order [25]. This normalization is checked with a control data sample similar to that used to validate the I ch distribution for prompt photons. Based on this comparison, a systematic uncertainty of 20%, dominated by the statistical uncertainty in the control sample, is assessed to the Zγ normalization.
Events that have two jets misidentified as photons represent approximately 30% and 10% of the total misidentified jet background in the Wγγ and Zγγ analyses, respectively. In such events, nonnegligible correlations exist between the leading and subleading photons. These correlations originate from the event activity that affects the measured isolation energies of both photons. The JJ templates are therefore determined from a sample of candidate diphoton events in data that is independent of the signal region. For this selection, the requirement on the ECAL transverse shower shape is inverted and the PF photon isolation requirement is relaxed. This procedure can result in a bias through correlations between the ECAL shower shape and the isolation. The systematic uncertainties are estimated by varying the maximum value of the relaxed requirements on the PF photon isolation. The largest deviation is taken as an estimate of the systematic uncertainty, which is approximately 10%. Using this method, rather than treating the photons as uncorrelated, increases the contribution from jet-jet events, which increases the estimated background by as much as 30%.
The total uncertainties in the estimated background contamination from misidentified jets are 19% and 28% for the muon and electron Wγγ channels, respectively, and 14% for the muon and electron Zγγ channels. These uncertainties take into account systematic effects in the derivation of the probabilities for prompt photons and jets described above, and statistical uncertainties in the observed data. The larger uncertainty in the electron channel of the Wγγ analysis results from the smaller amount of data as well as larger systematic variations in the JJ template determination.
In the electron channel of the Wγγ analysis, a nonnegligible contamination is present from Z(→ee)γ events in which an electron is misidentified as a photon. An electron veto based on pixel tracks is used as a discriminating variable to determine a misidentification ratio. This ratio relates the number of events that fail the electron veto to the number that pass. The misidentification ratio is determined as a function of p T and η in a control sample of data enriched in single Z boson events that have one reconstructed electron and one photon. The contamination in the signal region is obtained by multiplying the observed number of events outside the Z boson mass window where one photon fails the electron veto by the misidentification ratio. The number of electrons resulting from Z boson decays is extracted from a fit to the eγ invariant mass distribution using a Z boson line shape determined from simulation and a background function that models the contribution from events without a Z boson. The misidentification ratio is 0.01-0.03, depending on the p T and η of the photon. A systematic uncertainty of 10% in the misidentification ratio is determined from a closure test in simulation. The contamination from misidentified jets in the control samples is determined using the method described above and subtracted from the data. This contamination is approximately 10% for events in which both photons are in the barrel and 20% for the remaining events.
Additional background contributions involving prompt photons are determined using MC simulations. The simulated events are corrected for observed differences in the selection efficiencies between data and simulation of electrons, muons, and photons and in the trigger efficiencies. In the Wγγ analysis, the contamination from Zγγ is estimated using the Zγγ MC sample described in Section 4. The Zγγ contamination constitutes about 90% of the background that contains two prompt photons. The simulated sample is normalized to the NLO cross section with an uncertainty of 12.5%, based on the uncertainty in the theoretical prediction and differences in identification and reconstruction efficiencies between data and simulation. Contributions of less than an event per channel from top quark production and other multiboson processes, including ttγγ, tWγγ, and VVγγ, where V is a W or Z boson, are present in both the Wγγ and Zγγ final states. These background sources are estimated using leading-order MC simulation. A systematic uncertainty of 20% is applied to the sum of these contributions to take into account higher-order corrections and differences in identification and reconstruction efficiencies between data and simulation. Table 1 summarizes the background predictions and the observed numbers of events, which are consistent with the presence of signal. Figure 1 shows the diphoton p T distribution with the predicted background, signal, and observed data for the Wγγ and Zγγ analyses, separately in the electron and muon channels. Figure 2 shows the same distributions with the electron and muon channels combined. The Wγγ and Zγγ signals are observed with significances of 2.6 and 5.9 standard deviations, respectively. The significances of the signals are calculated using a profile likelihood that considers the observed data and predicted backgrounds in each of the muon and electron channels. In this calculation, separate categories are defined for events having both photons in the barrel and only one photon in the barrel, to take advantage of the higher signal-to-background ratio in the first category as compared to the second.

Cross section measurements
The Wγγ and Zγγ cross sections are measured within fiducial regions identified by the selection criteria listed in Table 2. The acceptances of the fiducial regions for the signal processes as well as their reconstruction and selection efficiencies are determined using the signal MC samples described in Section 4. In the MC simulation, photons are required to satisfy a Frixione isolation requirement with a distance parameter of 0.05 [26]. The fiducial selection criteria are applied to the generated lepton four-momenta after a correction for FSR, which is obtained by adding to the generated four-momentum of each lepton the generated four-momenta of all photons within ∆R < 0.1. The fiducial cross sections are defined for W and Z boson decays to a single lepton family ( ).
Leptonic decays of τ leptons resulting from W and Z decays also contribute to signal events. Based on simulation the τ lepton contamination in the Wγγ fiducial region is approximately 2.5%, while in the Zγγ fiducial region it is less than 1%. The combined acceptances and efficiencies, after subtracting the τ lepton contribution, are 17.3 and 26.7% for the electron and muon channels of the Wγγ analysis, respectively, and 22.5 and 29.1% for the Zγγ analysis.
Uncertainties in the acceptances result from uncertainties in the PDFs of the proton, the perturbative QCD renormalization and factorization scales, the number of additional pileup interactions, and the selection efficiencies of leptons, photons, and p miss T . The PDF uncertainties are evaluated by comparing the acceptances obtained with the NNPDF-NLO error sets and between the nominal NNPDF-NLO set and the MSTW-NLO 2008 [27] and CT10-NLO [28] PDF sets. The maximum deviation from the nominal acceptance is taken as a systematic uncertainty.  The uncertainties related to the renormalization and factorization scales are evaluated by varying them independently by factors of 0.5 and 2. The largest variation is applied as a systematic uncertainty. The uncertainty in the pileup distribution is evaluated by varying the assumed minimum-bias cross section by ±5%. Uncertainties in the selection efficiencies of electrons, muons, and photons and in the trigger requirements are derived from uncertainties in the tagand-probe analyses. Estimates of the energy scale uncertainty for the electron, photon, and muon are made from comparisons of the Z boson line shape between data and simulation. Uncertainties in the p miss T energy scale are estimated by propagating the energy scale uncertainty for each object used in the p miss T calculation. The total uncertainties in the combined acceptances and efficiencies are 1-2%. The integrated luminosity used for these measurements is 19.4 fb −1 with an uncertainty of 2.6% [29]. A summary of the systematic uncertainties affecting the Wγγ and Zγγ fiducial cross section measurements is reported in Table 3.
The cross sections measured in the electron and muon channels of each analysis are combined, assuming lepton universality, using the method of best linear unbiased estimates [30][31][32], thereby decreasing the statistical uncertainties. We measure fiducial cross sections of 4.9 ± 1.4 (stat) ± 1.6 (syst) ± 0.1 (lumi) fb and 12.7 ± 1.4 (stat) ± 1.8 (syst) ± 0.3 (lumi) fb for the Wγγ and Zγγ processes, respectively. The measured cross sections are in agreement with the NLO theoretical predictions of 4.8 ± 0.5 fb and 13.0 ± 1.5 fb for the Wγγ and Zγγ final states, respectively. The predicted cross sections are calculated within the fiducial phase space given in Table 2 using MADGRAPH5 aMC@NLO . Table 4 summarizes these results.

Channel Prediction
Wγγ → ± νγγ 4.8 ± 0.5 fb Zγγ → + − γγ 13.0 ± 1.5 fb sionality lead to baryon and lepton number violation and are therefore not considered here. The dimension-8 term is then the lowest-dimension term that produces aQGCs. Fourteen dimension-8 operators contribute to the WWγγ vertex [34,35]. We focus our study on the couplings that contain products of electroweak field strength tensors, in particular those that are constrained by this analysis: f M,2 , f M,3 , f T,0 , f T,1 , and f T,2 [36]. Anomalous QGCs enhance the production of signal events at high momentum scales. To increase sensitivity to these enhancements, limits on aQGCs are obtained using only events in which the leading-photon p T exceeds 70 GeV. Figure 3 shows the predicted yield from an aQGC with f T,0 /Λ 4 = 50 TeV −4 , compared to the signal and background predictions for the sum of the electron and muon channels. A profile likelihood is used to establish 95% confidence level (CL) intervals for the aQGC parameters. Each coupling is profiled individually, with the other couplings set to their SM values. Since all couplings predict an excess of the data at large photon p T , the observed limits are larger than the expected limits for all couplings. The resulting limits are reported in Table 5.

Summary
Cross sections have been measured for Wγγ and Zγγ production in pp collisions at √ s = 8 TeV using data corresponding to an integrated luminosity of 19.4 fb −1 collected with the CMS experiment. The cross sections were measured in fiducial regions that are defined by criteria similar to those used to select signal events. The fiducial cross sections are defined for W and Z boson decays to a single lepton family. The measured fiducial cross sections for these final states are, respectively, 4.9 ± 2.1 fb and 12.7 ± 2.3 fb, consistent with the NLO theoretical predictions of 4.8 ± 0.5 fb and 13.0 ± 1.5 fb. These measurements correspond to significances for observing the signal of 2.6 and 5.9 standard deviations for the Wγγ and Zγγ final states, respectively. In comparison, the ATLAS experiment measured the Wγγ and Zγγ final states with significances of greater than three standard deviations and equal to 6.3 standard deviations, respectively [1,2]. The Wγγ final state is used to place limits at 95% CL on anomalous quartic gauge couplings using a dimension-8 effective field theory. In particular, stringent limits are placed on the f T,0 coupling parameter of −33.5 < f T,0 /Λ 4 < 34.0 TeV −4 .