Measurement of the W gamma and Z gamma inclusive cross sections in pp collisions at sqrt(s) = 7 TeV and limits on anomalous triple gauge boson couplings

Measurements of W gamma and Z gamma production in proton-proton collisions at sqrt(s) = 7 TeV are used to extract limits on anomalous triple gauge couplings. The results are based on data recorded by the CMS experiment at the LHC that correspond to an integrated luminosity of 5.0 inverse femtobarns. The cross sections are measured for photon transverse momenta pt[gamma]>15 GeV, and for separations between photons and final-state charged leptons in the pseudorapidity-azimuthal plane of Delta R[l, gamma]>0.7 in l nu gamma and ll gamma final states, where l refers either to an electron or a muon. A dilepton invariant mass requirement of m[ll]>50 GeV is imposed for the Z gamma process. No deviations are observed relative to predictions from the standard model, and limits are set on anomalous WW gamma, ZZ gamma, and Z gamma gamma triple gauge couplings.


I. INTRODUCTION
The standard model (SM) has been enormously successful in describing the electroweak (EW) and strong interactions. However, important questions remain unanswered regarding possible extensions of the SM that incorporate new interactions and new particles. The selfinteractions of the electroweak gauge bosons comprise an important and sensitive probe of the SM, as their form and strength are determined by the underlying SUð2Þ × Uð1Þ gauge symmetry. A precise measurement of the production of pairs of EW bosons ("diboson" events) provides direct information on the triple gauge couplings (TGCs), and any deviation of these couplings from their SM values would be indicative of new physics. Even if the new phenomena involve the presence of objects that can only be produced at large energy scales, i.e., beyond the reach of the Large Hadron Collider (LHC), they can nevertheless induce changes in the TGCs. In addition, since diboson processes represent the primary background to the SM Higgs production, their precise measurement is important for an accurate evaluation of Higgs boson production at the LHC, particularly in association with gauge bosons.
Aside from γγ production, the EW Wγ and Zγ production processes at hadron colliders provide the largest and cleanest yields, as backgrounds to Wγ and Zγ production can be significantly suppressed through the identification of the massive W and Z vector bosons via their leptonic decay modes. Measurements from LEP [1][2][3][4], the Tevatron [5][6][7][8][9], and initial analyses at the LHC [10][11][12] have already explored some of the parameter space of anomalous TGCs (ATGCs) in Wγ and Zγ processes.
We describe an analysis of inclusive Wγ and Zγ events, collectively referred to as "Vγ" production, based on the leptonic decays W → eν, W → μν, Z → ee, and Z → μμ, observed in pp collisions at a center-of-mass energy of 7 TeV. The data, corresponding to an integrated luminosity L ¼ 5.0 fb −1 , were collected in 2011 with the Compact Muon Solenoid (CMS) detector at the LHC. The previous results from pp collisions at ffiffi ffi s p ¼ 7 TeV at the LHC were limited by the statistics of the data samples, and this analysis achieves a significant improvement in precision.
Vγ production can be represented by the Feynman diagrams of Fig. 1. Three processes contribute: (a) initialstate radiation, where a photon is radiated by one of the incoming virtual partons; (b) final-state radiation, where a photon is radiated by one of the charged leptons from V decay; and (c) TGC at the WWγ vertex in Wγ production, and at the ZZγ and Zγγ vertices in Zγ production. In the SM, contributions from the TGC process are expected only for Wγ production, because neutral TGCs are forbidden at tree level [13,14].
FIG. 1. The three lowest-order diagrams for Vγ production, with V corresponding to both virtual and on-shell γ, W, and Z bosons. The three diagrams reflect contributions from (a) initialstate radiation, (b) final-state radiation, and (c) TGC. The TGC diagram does not contribute at the lowest order to SM Zγ production, since photons do not couple to particles without electric charge.
Backgrounds from tt, W þ jets, Z þ jets, WW, and γγ events are also simulated with the MADGRAPH program interfaced with PYTHIA. Multijet, γ þ jets, and WZ and ZZ diboson events are generated using the stand-alone PYTHIA MC program and have negligible impact on the analysis. All these MC event samples, generated using the CTEQ6L1 leading-order (LO) PDF [22], are passed through a detailed simulation of the CMS detector based on GEANT4 [23] and reconstructed with the same software that is used for data.

III. SELECTION OF CANDIDATE EVENTS
The requirements for selecting isolated muons follow closely the standard CMS muon identification criteria [24]. However, electron and photon selection criteria are optimized specifically for this analysis and are described in greater detail in the following subsections, as are the reconstruction of transverse momentum imbalance or the "missing" transverse momentum (E T ), all trigger requirements, and the selections used to enhance the purity of signal.
The presence of pileup from additional overlapping interactions is taken into account in the analysis and cross-checked by studying the effectiveness of the selection criteria, separately, for small and large pileup rates in data. There are on average 5.8 overlapping interactions per collision for low-pileup data, and 9.6 interactions for high-pileup data, which correspond, respectively, to integrated luminosities of L ≈ 2.2 fb −1 (referred to subsequently as run 2011A) and L ≈ 2.7 fb −1 (referred to as run 2011B).

A. Electron identification and selection
Electrons are identified as "superclusters" (SCs) of energy deposition [25] in the ECAL fiducial volume that are matched to tracks from the silicon tracker. Tracks are reconstructed using a Gaussian sum filter algorithm that takes into account possible energy loss due to bremsstrahlung in the tracker. The SCs are required to be located within the acceptance of the tracker (jηj < 2.5). Standard electron reconstruction in the transition regions between the central barrel (EB) and the end cap (EE) sections of the ECAL (1.44 < jηj < 1.57) has reduced efficiency, and any electron candidates found in these regions are therefore excluded from consideration. The reconstructed electron tracks are required to have hits observed along their trajectories in all layers of the inner tracker. Electron candidates must have p T > 35 and > 20 GeV for the Wγ and Zγ analyses, respectively.
Particles misidentified as electrons are suppressed through the use of an energy-weighted width quantity in pseudorapidity (σ ηη ) that reflects the dispersion of energy in η ("shower shape") in a 5 × 5 matrix of the 25 crystals centered about the crystal containing the largest energy in the SC [25]. The σ ηη parameter is defined through a mean η ¼ P η i w i = P w i as follows: (1) area of (η; ϕ) for background from pileup, computed event by event using the FASTJET package [26]. The Wγ analysis uses individual I r contributions from the three subdetectors. Also, to minimize the contributions from Zγ events, a less restrictive selection is applied to the additional electron. The efficiencies for these criteria are measured in Z → ee data and in MC simulation, using the "tag and probe" technique of Ref. [27]. An efficiency correction of ≈3% is applied to the MC simulation to match the performance observed in data.

B. Photon identification and selection
Photon candidates in the fiducial volume of the ECAL detector are reconstructed as SCs with efficiencies very close to 100% for p γ T > 15 GeV, as estimated from MC simulation. The photon energy scale is measured using Z → μμγ events, following the "PHOSPHOR" procedure described in Refs. [28,29].
As in the previous CMS analysis of Vγ final states [11], we reduce the rate of jets misreconstructed as photons by using stringent photon identification criteria, including isolation and requirements on the shapes of electromagnetic (EM) showers. In particular, (i) the ratio of HCAL to ECAL energies deposited within a cone of ΔR ¼ 0.15 relative to the axis of the seed ECAL crystal must be <0.05; (ii) the value of σ ηη must be <0.011 in the barrel and <0.030 in the end cap; and (iii) to reduce background from misidentified electrons, photon candidates are rejected if there are hits present in the first two inner layers of the silicon pixel detector that can originate from an electron trajectory that extrapolates to the location of the deposited energy in an ECAL SC of E T > 4 GeV. This requirement is referred to as the pixel veto.
However, unlike in the previous analysis [11], the pileup conditions during run 2011 require modifications to photon isolation criteria to achieve reliable modeling of pileup effects. In particular, for photon candidates, the scalar sum of the p T for all tracks originating from within jd z j < 0.1 cm of the primary vertex, that have jd T j < 0.02 cm, and that are located within a 0.05 < ΔR < 0.4 annulus of the direction of each photon candidate, are required to have p TRK where A eff is the effective area used to correct each photon shower for event pileup. This procedure ensures that the isolation requirement does not exhibit a remaining dependence on pileup. For each photon candidate, the scalar sum of the p T deposited in the ECAL in an annulus 0.06 < ΔR < 0.40, excluding a rectangular strip of Δη × Δϕ ¼ 0.04 × 0.40 to reduce the impact of energy leakage from any converted γ → e þ e − showers, is computed. The isolation in the ECAL is required to have p ECAL T < 4.2 GeVþ 0.006 × p γ T þ A eff × ρ, and finally, the isolation criterion in the HCAL is p HCAL The expected values of A eff are defined by the ratio of slopes obtained in fits of the isolation and ρ parameters to a linear dependence on the number of vertices observed in data. These are summarized in Table I, separately for the three isolation parameters, calculated for EM showers observed in the barrel and end-cap regions of the ECAL.
To estimate the efficiency of requirements on the shape and isolation of EM showers, we use the similarity of photon and electron showers to select common shower parameters based on electron showers, but we use the isolation criteria that consider differences between the photon and electron characteristics. The results for data and MC simulation, as a function of p γ T and η γ , are shown in Fig. 2. The efficiencies obtained using generator-level information in Z → ee and in γ þ jets simulations are also shown in Fig. 2. The difference between these efficiencies is taken as an estimate of systematic uncertainty in the photon identification efficiency, based on results from Z → ee data. The ratios of efficiency in data to that in simulation, both measured by the tag-and-probe method (squares), and of efficiency in Z → ee simulation to that in the γ þ jets simulation, obtained from generator-level information (triangles) as a function of p T , integrated over the full range of η, are shown in Fig. 3. We find that the efficiencies in data and MC simulation agree to within 3% accuracy. As for the case of electrons and muons, we reweight the simulated events to reduce the residual discrepancy in modeling efficiency as a function of p γ T and η γ .
The efficiency of the pixel veto is obtained from Z → μμγ data, where the photon arises from final-state radiation. The purity of such photon candidates is estimated to exceed 99.6%, and they are therefore chosen for checking photon identification efficiency, energy scale, and energy resolution. We find that the efficiency of the pixel veto corresponds to 97% and 89% for photons in the barrel and end-cap regions of the ECAL, respectively.

C. Muon identification and selection
Muons are reconstructed off-line by matching particle trajectories in the tracker and the muon system. The candidates must have p T > 35 and >20 GeV for the Wγ and Zγ analyses, respectively. We require muon candidates to pass the standard CMS isolated muon selection criteria [24], with minor changes in requirements on the distance of closest approach of the muon track to the primary vertex. We require jd z j < 0.1 cm in the longitudinal direction and jd T j < 0.02 cm in the transverse plane. The efficiencies for these criteria are measured in data and in MC simulation using a tag-and-probe technique applied to Z → μμ events. An efficiency correction of ≈3% is also applied to the MC simulation to match the performance found in muon data.

D. Reconstruction of E T
Neutrinos from W → lν decay are not detected directly, but they give rise to an imbalance in reconstructed transverse momentum in an event. This quantity is computed using objects reconstructed with the particle-flow algorithm [30], which generates a list of four-vectors of particles  based on information from all subsystems of the CMS detector. The E T for each event is defined by the magnitude of the vector sum of the transverse momenta of all the reconstructed particles.

E. Trigger requirements
The Wγ → lνγ and Zγ → llγ events are selected using unprescaled isolated lepton triggers. The p T thresholds and isolation criteria imposed on lepton candidates at the trigger level changed with time to accommodate the instantaneous luminosity and are less stringent than the off-line requirements.
For the Wγ → eνγ channel, we use an isolated single-electron trigger, requiring electrons with jηj < 3 and a p T threshold of 32 GeV, except for the first part of run 2011A (L ¼ 0.2 fb −1 ), where the threshold is 27 GeV. In addition, for the last part (L ¼ 1.9 fb −1 ) of run 2011A and the entire run 2011B, a selection is implemented on the transverse mass (M W T ) of the system consisting of the electron candidate and the E T , requiring where Δϕ is the angle between the p l T and the E T vectors. The trigger used for the Zγ → eeγ events requires two isolated electron candidates with p T thresholds of 17 GeV on the leading (highest-p T ) candidate and 8 GeV on the trailing candidate.
The trigger for Wγ → μνγ events requires an isolated muon with p T > 30 GeV and jηj < 2.1. The dimuon trigger used to collect Zγ → μμγ events does not require the two muons to be isolated and has coverage for jηj < 2.4. For most of the data, the muon p T thresholds are 13 GeV for the leading and 8 GeV for the trailing candidates. For the first part of run 2011A (L ¼ 0.2 fb −1 ) and for most of the remaining data, these thresholds are 7 GeV for each muon candidate, except for the last part of run 2011B (L ¼ 0.8 fb −1 ), where these increase to 17 and 8 GeV, respectively.

F. Wγ event selections
The Wγ → lνγ process is characterized by a prompt, energetic, and isolated lepton, a prompt isolated photon, and significant E T that reflects the escaping neutrino. Both electrons and muons are required to have p T > 35 GeV, and photons are required to have p T > 15 GeV. The maximum allowed jηj values for electrons, photons, and muons are 2.5, 2.5, and 2.1, respectively. We require the photon to be separated from the lepton by ΔRðl; γÞ > 0.7. To minimize contributions from Zγ → llγ production, we reject events that have a second reconstructed lepton of the same flavor. This veto is implemented only for electrons that have p T > 20 GeV, jηj < 2.5, and pass looser electron selections, and for muons that have p T > 10 GeV and jηj < 2.4.
To suppress background processes without genuine E T , we require events to have M W T > 70 GeV. We find that the E T distribution is well modeled, but we apply a small efficiency correction to reduce the residual disagreement. The efficiencies of the M W T selection in data and simulation agree at the 1% level. The full set of lνγ selections yields 7470 electron and 10 809 muon candidates in the data. The selection criteria used to define the Wγ sample are summarized in Table II.

G. Zγ event selections
Accepted Zγ events are characterized by two prompt, energetic, and isolated leptons and an isolated, prompt photon. Both electrons and muons are required to have p T > 20 GeV, and the photons are required to have p T > 15 GeV. The maximum jηj values for accepted electrons, photons, and muons are 2.5, 2.5, and 2.4, respectively. We require photons to be separated from leptons by imposing a ΔRðl; γÞ > 0.7 requirement. Finally, the invariant mass of the two leptons is required to satisfy m ll > 50 GeV. Applying all these selections yields 4108 Zγ → eeγ and 6463 Zγ → μμγ candidates. The selection criteria used to define the Zγ sample are summarized in Table II.

IV. BACKGROUND ESTIMATES
The dominant background for both Wγ and Zγ production arises from events in which jets, originating mostly from W þ jets and Z þ jets events, respectively, are misidentified as photons. We estimate the background from . Ratio of efficiencies for selecting photons in data relative to MC simulation, obtained through the tag-andprobe method, and the ratio of electron to photon efficiencies, obtained at the MC generator level, with both sets of ratios given as a function of the transverse momentum of the photon. these sources as a function of p γ T using the two methods described in Sec. IVA.
For the Wγ channel, a second major background arises from Drell-Yan (qq → l þ l − ) and EW diboson production, when one electron is misidentified as a photon. This background is estimated from data as described in Sec. IV B.
Other backgrounds to Vγ processes include (i) jets misidentified as leptons in γ þ jet production; (ii) Vγ events, with V decaying into τν or ττ, and subsequently τ → lνν; (iii) ttγ events; and (iv) Zγ events, where one of the leptons from Z decay is not reconstructed properly. All these backgrounds are small relative to the contribution from V þ jets and are estimated using MC simulation.
A. Jets misidentified as photons

Template method
The template method relies on a maximum-likelihood fit to the distribution of σ ηη in data to estimate the background from misidentified jets in the selected Vγ samples. The fit makes use of the expected distributions ("templates") for genuine photons and misidentified jets. For isolated prompt photons, the σ ηη distribution is very narrow and symmetric, while for photons produced in hadron decays, the σ ηη distribution is asymmetric, with a slow falloff at large values. The distribution in σ ηη for signal photons is obtained from simulated Wγ events. The σ ηη distribution of electrons from Z-boson decays in data is observed to be shifted to smaller values relative to simulated events. The shift is 0.9 × 10 −4 and 2.0 × 10 −4 for the EB and EE regions, respectively, and corresponds to 1% and 0.8% shifts in the average of the simulated photon σ ηη values, which are corrected for the shift relative to data.
The σ ηη templates for background are defined by events in a background-enriched isolation sideband of data. These photon candidates are selected using the photon identification criteria described in Sec. III B, but without the σ ηη selection, and with inverted TRK isolation requirements: GeV, for 1.566 < jη γ j < 2.5. These requirements ensure that the contributions from genuine photons are negligible, while the isolation requirements remain close to those used for the selection of photons and thereby provide jets with large EM energy fractions that have properties similar to those of genuine photons. We observe that σ ηη is largely uncorrelated with the isolation parameter in simulated multijet events, so that the distribution observed for background from jets that are misidentified as photons (i.e., with inverted tracker isolation criteria) is expected to be the same as that for jets misidentified as isolated photons.
Because of the M W T requirement in selected Wγ events, the presence of significant E T can bias the estimation of the background. We therefore investigate possible correlations between the distribution in σ ηη for background events and the projection of E T along the p T of jets misidentified as photons. In particular, we define σ ηη templates for background using events in data with E T > 10 GeV and with the direction of the E T vector along the photonlike jet. The estimated systematic uncertainty is obtained from the smallest bin in p γ T (15 < p γ T < 20 GeV), as this is the bin that contains most of the background (Fig. 4) and corresponds to the largest control sample for input to the σ ηη template representing the background. Based on the modified templates, we assign a systematic uncertainty that reflects the largest discrepancy relative to the nominal yield, which is found to be 13% and 7% for the barrel and end cap, respectively. A more detailed discussion of systematic uncertainties in the background estimate is given in Sec. V D.
The systematic uncertainty in electron misidentification is estimated through changes made in the modeling of signal and background, the electron and photon energy resolutions, and the distributions for pileup in MC simulations.
The function fitted to the observed distribution of σ ηη is the sum of contributions from signal (S) and background (B): Only one lepton Only one lepton where N, N S , and N B are the total number of events and the number of signal and background candidates in data for any given bin of p γ T , respectively. The functions Sðσ ηη Þ and Bðσ ηη Þ represent the expected signal and background distributions in σ ηη . These distributions are smoothed using a kernel-density estimator [31], or through direct interpolation when the statistical uncertainties are small, which makes it possible to use unbinned fits to the data in regions where statistics are poor while preserving the good performance of the fit. The fit uses an unbinned extended likelihood [32] function (L) to minimize − ln L as a function of the signal fraction f S ¼ N S =N:

Ratio method
We use a second method, referred to as the "ratio method," to infer the V þ jets background as a cross-check of the results obtained with the template method at large p γ T , where the template method is subject to larger statistical uncertainties. The ratio method uses γ þ jets and multijet data to extract the misidentification rate, taking into account the quark/gluon composition of the jets in V þ jets events.
The ratio method exploits a category of jets that have properties similar to electromagnetic objects in the ECAL and are called photonlike jets. Photonlike jets are jets selected through the presence of photons that pass all photon selection criteria, but fail either the photon isolation or σ ηη requirements. However, these kinds of jets are still more isolated and have higher EM fractions than most generic jets.
The ratio method provides a ratio R p of the probability for a jet to pass photon selection criteria and that of passing photonlike requirements. Once R p is known, the number of jets that satisfy the final photon selection criteria (N Vþjets ) can be estimated as the product of R p and the number of photonlike jets in data.
We measure R p separately for each p γ T bin of the analysis for both the barrel and end-cap regions of the ECAL, using "diphoton" events, defined by the presence of either two photon candidates that pass the final photon selections, or of one photon candidate that passes the final selections and one that passes only photonlike jet selections. To reduce  . The R p ratio (described in text) as a function of the p T of photon candidates for the barrel region of the ECAL in γ þ jets and multijet data. The difference in R p values for the two processes is attributed to the fact that jets in γ þ jets events are dominated by quark fragmentation, while jets in multijet events are dominated by gluon fragmentation. correlations induced by the diphoton production kinematics, we require that the photons corresponding to each diphoton candidate be in the same η region and p γ T bin. A two-dimensional fit is performed based on templates of distributions in σ ηη of each photon candidate to estimate R p , and thereby subtract the contribution from genuine photons to the photonlike jet yield. As only 5%-10% of genuine photons in multijet events pass photonlike jet requirements, we correct the distribution in R p using MC simulation of multijet events and check the correction through Z → ee data and simulation.
The observed R p values for the barrel region of the ECAL are given in Fig. 5 as a function of p γ T . The difference between the two sets of R p values extracted in different ways indicates the sensitivity of the method to whether the photonlike jet originates from hadronization of a quark or a gluon. We use the simulation of the gluon-to-quark jet ratio in W þ jets and Z þ jets events to correct R p as a function of the p T of the photonlike jet. We find the predictions from the ratio method to be consistent with those from the template method, and we consider their difference as an additional source of systematic uncertainty in the analysis.

B. Background from electrons misidentified as photons in lνγ events
The criterion that differentiates electrons from photons is the presence in the pixel detector of a track that is associated with a shower in the ECAL. We use Z → ee data to measure the probability (P e→γ ) for an electron not to have a matching track by requiring one of the electrons to pass stringent electron identification criteria, and then by checking how often the other electron passes the full photon selection criteria, including the requirement of TABLE III. Yield of misidentified photons from jets in W þ jets events and their symmetrized associated systematic uncertainties as a function of p γ T in the Wγ → lνγ analyses. The results are specified in the second column by the number of events expected in the eνγ and μνγ channels, and by the uncertainties from each of the sources in the rest of the columns. having no associated track in the pixel detector. Fitting to the m ll distribution using a convolution of Breit-Wigner and Crystal Ball [33] functions to describe the signal and a falling exponential function for background, we obtain the probability for an electron to have no associated track as P e→γ ¼ 0.014 AE 0.003ðsystÞ and 0.028 AE 0.004ðsystÞ for the barrel and the end cap regions, respectively.
To estimate the background from sources where an electron is misidentified as a photon in the μνγ channel, we select events that pass all event selection criteria, except that the presence of a track in the pixel detector associated with the photon candidate is ignored. The contribution from genuine electrons misidentified as photons can therefore be calculated as where N e→γ is the background from misidentified electrons and N μνe is the number of events selected without any requirement on the pixel track. The systematic uncertainties associated with this measurement are discussed in detail in Sec. V D.
The background in the eνγ channel is dominated by Z þ jets events, where one of the electrons from Z → ee decays is misidentified as a photon. To estimate the Z → ee contribution to the Wγ → eνγ signal, we apply the full selection criteria and fit the invariant mass of the photon and electron candidates with a Breit-Wigner function convolved with a Crystal Ball function for the Z boson and an exponential form for the background. Contributions to eνγ events from other sources with genuine electrons misidentified as photons (e.g., tt þ jets and diboson processes) are estimated using MC simulation, in which a photon candidate is matched spatially to the generator-level electron.

C. Total background
The background from jets that are misidentified as photons is summarized as a function of p T of the photon in Table III for lνγ events and in Table IV   (53%) is from Zγ events, and the next largest is from γ þ jets with a contribution of 33%. For the μνγ channel, the dominant background to N other B is from Zγ, with a contribution of 84%. All the specific parameters will be discussed in more detail in Secs. V D-V F.

V. RESULTS
A. The Wγ process and radiation-amplitude zeros For photon transverse momenta >15 GeV and angular separations between the charged leptons and photons of ΔR > 0.7, the Wγ production cross section at NLO for each leptonic decay channel is expected to be 31.8 AE 1.8 pb [19,20]. This cross-section point is used to normalize the p γ T distributions for the signal in Fig. 6, which shows good agreement of the data with the expectations from the SM.
The three leading-order Wγ production diagrams in Fig. 1 interfere with each other, resulting in a vanishing of the yield at specific regions of phase space. Such phenomena are referred to as radiation-amplitude zeros (RAZs) [34][35][36][37][38], and the effect was first observed by the D0 Collaboration [6] using the charge-signed rapidity difference Q l × Δη between the photon candidate and the charged lepton candidate from W → lν decays [39]. In the SM, the minimum is at Q l × Δη ¼ 0 for pp collisions. Anomalous Wγ contributions can affect the distribution in Q l × Δη and make the minimum less pronounced. The differential yield as a function of charge-signed rapidity difference, shown in Fig. 7(a) for Wγ events normalized to the yield of signal in data, is obtained with the additional requirements of having no accompanying jets with p T > 30 GeV and a transverse three-body mass, or cluster mass [39] of the photon, lepton, and E T system >110 GeV. The three-body mass M T ðlγE T Þ is calculated as where M lγ denotes the invariant mass of the lγ system, and p T ðiÞ, i ¼ γ, l, and E T are the projections of the photon, lepton, and E T vectors on the transverse plane, respectively. Figure 7(b) shows the background-subtracted data. The shaded bars indicate statistical and systematic uncertainties on the MC prediction. The distributions demonstrate the characteristic RAZ expected for Wγ production. Both figures indicate no significant difference between data and expectations from SM MC simulations.

B. The Zγ process
The cross section for Zγ production at NLO in the SM, for p γ T > 15 GeV, ΔRðl; γÞ > 0.7 between the photon and either of the charged leptons from the Z → l þ l − decay, and m ll > 50 GeV, is predicted to be 5.45 AE 0.27 pb [19,20]. After applying all selection criteria, the p γ T distributions for data and contributions expected from MC simulation are shown for eeγ and μμγ final states in Figs. 8(a) and 8(b), respectively. Again, good agreement is found between data and the SM predictions.

C. Production cross sections
The cross section for any signal process of interest can be written as where N S is the number of observed signal events, A S is the geometric and kinematic acceptance of the detector, ϵ S is the selection efficiency for signal events in the region of acceptance, and L is the integrated luminosity. The value of A S in our analyses is calculated through MC simulation and is affected by the choice of PDF and other uncertainties of the model, while the value of ϵ S is sensitive to uncertainties in the simulation, triggering, and reconstruction. To reduce uncertainties in efficiency, we apply corrections to the efficiencies obtained from MC simulation, which reflect ratios of efficiencies ρ eff ¼ ϵ data =ϵ MC obtained by measuring the efficiency in the same way for data and simulation. The product A S × ϵ S can then be replaced by the product F S × ρ eff , where F S ≡ A S × ϵ MC corresponds to the fraction of generated signal events selected in the simulation.
Equation (5) can therefore be rewritten as in which we replace the number of signal events N S by subtracting the estimated number of background events N B from the observed number of selected events N. We calculate F S using MC simulation, with F S defined by N accept =N gen , where N accept is the number of signal events that pass all selection requirements in the MC simulation of signal, and N gen is the number of MC-generated events restricted to p γ T > 15 GeV and  7 (color online). Charge-signed rapidity difference Q l × Δη between the photon candidate and a lepton for Wγ candidates in data (filled circles) and expected SM signal and backgrounds (shaded regions) normalized to (a) data, and (b) backgroundsubtracted data. The hatched bands illustrate the full uncertainty in the MC prediction. ΔRðl; γÞ > 0.7 for Wγ, and with an additional requirement, m ll > 50 GeV, for Zγ.

D. Systematic uncertainties
Systematic uncertainties are grouped into five categories. The first group includes uncertainties that affect the signal, such as uncertainties on lepton and photon energy scales. We assess the systematic uncertainties in the electron and photon energy scales separately to account for the differences in the clustering procedure, the response of the ECAL, and calibrations between the electrons and photons. The estimated uncertainty is 0.5% in the EB and 3% in the EE for electrons, and 1% in the EB and 3% in the EE for photons. The uncertainties in the two scales are conservatively treated as fully correlated. For the muon channel, the muon momentum is changed by 0.2%. The systematic effect on the measured cross section is obtained by reevaluating N S for such changes in each source of systematic uncertainty. To extract the systematic effect of the energy scale on the signal yield, the data-driven background estimation is performed using signal and background templates modified to use the varied energy scale. This ensures that migrations of photons and misidentified photonlike jets across the low-p γ T boundaries are properly taken into account for this systematic uncertainty.
In the second group, we combine uncertainties that affect the product of the acceptance, reconstruction, and identification efficiencies of final-state objects, as determined from simulation. These include uncertainties in the lepton and photon energy resolution, effects from pileup, and uncertainties in the PDF. The uncertainty in the product of acceptance and efficiency (A S × ϵ S ) is determined from MC simulation of the Vγ signal and is affected by the lepton and photon energy resolution through the migration of events in and out of the acceptance. The electron energy resolution is determined from data using the observed width of the Z boson peak in the Z → ee events, following the same procedure as employed in Ref. [40]. To estimate the effect of electron resolution on A S × ϵ S , each electron candidate's energy is smeared randomly by the energy resolution determined from data before applying the standard selections. The photon energy resolution is determined simultaneously with the photon energy scale from data, following the description in Refs. [28,29]. The systematic effect of photon resolution on A S × ϵ S is calculated by smearing the reconstructed photon energy in simulation to match that in data.
The number of pileup interactions per event is estimated from data using a convolution procedure that extracts the estimated pileup from the instantaneous bunch luminosity. The total inelastic pp scattering cross section is used to estimate the number of pileup interactions expected in a given bunch crossing, with a systematic uncertainty from modeling of the pileup interactions obtained by changing the total inelastic cross section within its uncertainties [41] to determine the impact on A S × ϵ S . The uncertainties from the choice of PDF are estimated using the CTEQ6.6 PDF set [21]. The uncertainty in the modeling of the signal is taken from the difference in acceptance between MCFM and MADGRAPH predictions.
The third group of uncertainties includes the systematic sources affecting the relative ρ eff correction factors for efficiencies of the trigger, reconstruction, and identification requirements in simulations and data. Among these sources are the uncertainties in lepton triggers, lepton and photon reconstruction and identification, and E T for the Wγ process. The uncertainties in lepton and photon efficiencies are estimated by changing the modeling of the background and the range of the fits used in the tag-and-probe method.
The fourth category of uncertainties comprises the contributions from the background. These are dominated by uncertainties in estimating the W þ jets and Z þ jets backgrounds from data. The difference in σ ηη distributions between data and simulated events (Sec. IVA 1) is attributed to systematic uncertainties in signal templates, which are used to calculate the background estimate and measure its effect on the final result. To infer the background from photonlike jets that pass the full photon-isolation criteria, we use the σ ηη distributions obtained by reversing the original isolation requirement for the tracker. The possible correlation of σ ηη with tracker isolation and a contribution from genuine photons that pass the reversed isolation requirement can cause bias in the estimation of background. The first issue is investigated by comparing the sideband and true σ ηη distributions in simulated multijet events, where genuine photons can be distinguished from jets. The resulting bias on the background estimation is shown by the open circles in Fig. 9. The second issue, concerning the contamination of the background template by signal, is investigated by comparing the sideband σ ηη distributions of simulated samples, both with and without admixtures of genuine photons. The results of the bias studies are shown by the open squares in Fig. 9, and the overall effect, given by the filled black circles, is found to be small.
Since smoothing is used to define a continuous function for describing the σ ηη distribution for background, the effect of statistical sampling of the background probability density requires an appreciation of the features of the underlying distribution. This is studied as follows: The simulation is used to generate a distribution for background, which can be used to generate a template. These new distributions are also smoothed and used to fit the background fraction in data. The results of fits using each such distribution are saved, and the standard deviation associated with the statistical fluctuation in the template is taken as a systematic uncertainty. The systematic uncertainties from different inputs in the estimation of background from W þ jets and Z þ jets events were shown in Tables III and IV, respectively. The uncertainties in background from electrons misidentified as photons in Wγ candidate events are estimated by taking the difference in P e→γ between the measurement described in Sec. IV B and that obtained using a simple counting method. The uncertainties for lesser contributions TABLE VII. Summary of systematic uncertainties in the measurement of Wγ cross sections, separated into the main groups of sources for the eνγ and μνγ channels; "n/a" stands for "not applicable." eνγ μνγ to background are defined by the statistical uncertainties in the samples used for their simulation. Finally, the systematic uncertainty in the measured integrated luminosity is 2.2% [42].

E. Wγ cross section
In the summary of parameters used in the measurement of the pp → Wγ cross sections listed in Table V, N lνγ is the number of observed events, N lνγ S is the number of observed signal events after background subtraction, and A S × ϵ S , ρ eff , and L are as described in Sec. V C. A summary of all systematic uncertainties in the measured Wγ cross sections is given in  The mean of these cross sections, obtained using a best linear unbiased estimator (BLUE) [43], is σðpp → WγÞ × BðW → lνÞ ¼ 37.0 AE 0.8ðstatÞ AE 4.0ðsystÞ AE 0.8ðlumÞ pb: All three results are consistent within uncertainties with the NLO prediction of 31.8 AE 1.8 pb, computed with MCFM. The uncertainty on the prediction is obtained using the CTEQ6.6 PDF set [21].

F. Zγ cross section
In the summary of parameters used in the measurement of the pp → Zγ cross section listed in Table VI, N llγ is the number of observed events, and N llγ S is the number of observed signal events after background subtraction. The systematic uncertainties for the measurement of the Zγ cross sections are listed in and their mean, extracted using the BLUE method is σðpp → ZγÞ × BðZ → llÞ ¼ 5.33 AE 0.08ðstatÞ AE 0.25ðsystÞ AE 0.12ðlumÞ pb: All three results are also consistent within the uncertainties with the theoretical NLO cross section of 5.45 AE 0.27 pb, computed with MCFM. The uncertainty on the prediction is obtained using the CTEQ6.6 PDF set [21].

G. Ratio of Wγ and Zγ production cross sections
We calculate the ratio of the Wγ and Zγ cross sections using the BLUE method to account for correlated systematic uncertainties between individual channels for both measurements and predictions. The MCFM prediction of 5.8 AE 0.1 is consistent with the measured ratio, 6.9 AE 0.2ðstatÞ AE 0.5ðsystÞ.

H. Comparisons to MCFM predictions
Finally, we present a summary of the Wγ and Zγ cross sections measured with larger requirements on the minimum photon p γ T . After accounting for all systematic uncertainties for p γ T > 60 and >90 GeV, we find no significant disagreement with the MCFM predictions for the Vγ processes. These cross sections, predictions, and their uncertainties are summarized in Table IX and in Fig. 10.

VI. ANOMALOUS TRIPLE GAUGE COUPLINGS IN Wγ AND Zγ PRODUCTION
A. WWγ coupling The most general Lorentz-invariant, effective Lagrangian that describes WWγ and WWZ couplings has 14 independent parameters [44,45], seven for each triple-boson vertex. Assuming charge conjugation (C) and parity (P) invariance for the effective EW Lagrangian (L WWV ), normalized by its EW coupling strength (g WWV ), leaves only six independent couplings for describing the WWγ and WWZ vertices: where V ¼ γ or Z, W μ are the W AE fields, W μν ¼ ∂ μ W ν − ∂ ν W μ , with the overall couplings given by g WWγ ¼ −e and g WWZ ¼ −e cot θ W , where θ W is the weak mixing angle. Assuming electromagnetic gauge invariance, g γ 1 ¼ 1; the remaining parameters that describe the WWγ and WWZ couplings are g Z 1 , κ Z , κ γ , λ Z , and λ γ . In the SM, λ Z ¼ λ γ ¼ 0 and g Z 1 ¼ κ Z ¼ κ γ ¼ 1. In this analysis, we follow the convention that describes the couplings in terms of their deviation from the SM values: Δg Z 1 ≡ g Z 1 − 1, Δκ Z ≡ κ Z − 1, and Δκ γ ≡ κ γ − 1. Invariance under SUð2Þ L × Uð1Þ Y transformations reduces these to three independent couplings: where Δκ γ and λ γ are determined from Wγ production.

B. ZZγ and Zγγ couplings
The most general vertex function for ZZγ [46] can be written as

Γ αβμ
ZZγ ðq 1 ; q 2 ; pÞ ¼ with the Zγγ vertex obtained by the replacements The couplings h V i for V ¼ Z or γ and i ¼ 1, 2 violate CP symmetry, while those with i ¼ 3, 4 are CP even. Although at tree level all these couplings vanish in the SM, at the higher, one-loop level, the CP-conserving couplings are ≈10 −4 . As the sensitivity to CP-odd and CP-even couplings is the same when using p γ T to check for the presence of contributions from ATGCs, we interpret the results as limits on h V 3 and h V 4 only.

C. Search for anomalous couplings in Wγ and Zγ production
To extract limits on the ATGCs, we simply count the yield of events in bins of p γ T . The 95% confidence level (C.L.) upper limits on values of ATGCs are set using the modified frequentist CL s method [47].
As the simulation of the ATGC signal is not available in MADGRAPH, the signals are generated using the SHERPA MC program [18] to simulate Wγ þ jets and Zγ þ jets with up to two jets in the final state.
For the Wγ analysis, we set one-and two-dimensional limits on each ATGC parameter Δκ γ and λ γ , while g Z 1 is set to the SM value, assuming the "equal couplings" scenario of the LEP parameterization [48].
For the Zγ analysis, we set h V 1 and h V 2 to the SM values, and we set two-dimensional limits on the h V 3 and h V 4 anomalous couplings, with V ¼ Z or γ. For limits set on the Z-type couplings, the γ couplings are set to their SM values-i.e., to zero-and vice versa. In this study, we follow the CMS convention of not suppressing the anomalous TGCs by an energy-dependent form factor. The two-dimensional contours for upper limits at the 95% confidence level are given in Fig. 11 for the Wγ, and in Fig. 12 for the Zγ channels, with the corresponding one-dimensional limits listed in Table X for Wγ and in Table XI for Zγ.

VII. SUMMARY
We have presented updated measurements of the Vγ inclusive production cross sections in pp collisions at ffiffi ffi s p ¼ 7 TeV, based on leptonic decays of EW vector bosons W → eν, W → μν, Z → ee, and Z → μμ. The data were collected by the CMS experiment at the LHC in 2011 and correspond to an integrated luminosity of 5.0 fb −1 . A separation is required between the photon and the charged leptons in (η; ϕ) space of ΔR > 0.7, and an additional requirement of m ll > 50 GeV is placed on Zγ candidates. The measured cross sections for p γ T > 15 GeV, σðpp → WγÞ × BðW → lνÞ ¼ 37.0 AE 0.8ðstatÞAE4.0ðsystÞAE 0.8ðlumÞ pb, and σðpp → ZγÞ × BðZ → llÞ ¼ 5.33AE 0.08ðstatÞ AE 0.25ðsystÞ AE 0.12ðlumÞ pb are consistent with predictions of the SM; the ratio of these measurements, 6.9 AE 0.2ðstatÞ AE 0.5ðsystÞ, is also consistent with the SM value of 5.8 AE 0.1 predicted by MCFM. Measured cross sections for p γ T > 60 and > 90 GeV also agree with the SM. With no evidence observed for physics beyond the SM, we set the limits on anomalous WWγ, ZZγ, and Zγγ couplings given in Tables X and XI.

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. Finally,    13 (color online). Distributions in the W-boson transverse invariant mass for Wγ candidate events in data, with the signal and background MC simulation contributions to the (a) Wγ → eνγ and (b) Wγ → μνγ channels shown for comparison. The contributions for the number of jets with p T > 30 GeV are given in (c) and (d), respectively. The separation in R between the charged lepton and the photon is given in (e) for the electron channel, and that for muon channel is illustrated in (f).  14 (color online). Distributions in the dilepton invariant mass for Zγ candidate events in data, with the signal and background MC simulation contributions to the (a) Zγ → eeγ and (b) Zγ → μμγ channels shown for comparison. The contributions for the dilepton-plusphoton invariant mass are given in (c) and (d). The smallest separation in R between any charged leptons and the photon is given in (e) for the electron channel, and that for muon channel is illustrated in (f).