Measurement of the W γand Z γinclusivecrosssectionsin pp collisionsat √ 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. Abstract Measurements of W γ and Z γ production in proton-proton collisions at √ 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 fb − 1 . The cross sections are measured for photon transverse momenta p γ T > 15 GeV, and for separations between photons and ﬁnal-state charged leptons in the pseudorapidity-azimuthal plane of ∆ R ( (cid:96) , γ ) > 0.7 in (cid:96) νγ and (cid:96)(cid:96) γ ﬁnal states, where (cid:96) refers either to an electron or a muon. A dilepton invariant mass requirement of m (cid:96)(cid:96) > 50 GeV is imposed for the Z γ process. No deviations are observed relative to predictions from the standard model, and limits are set on anomalous WW γ , ZZ γ , and Z γγ triple gauge couplings. Physical Review γ , W, and Z bosons. The three diagrams reﬂect contributions from (a) initial-state and (b) ﬁnal-state radiation and (c) TGC. The TGC diagram does not contribute at the lowest order to SM Z γ production since photons do not couple to particles without electric charge.


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 self-interactions of the electroweak gauge bosons comprise an important and sensitive probe of the SM, as their form and strength are determined by the underlying SU(2) × U(1) 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 [5-9], and from 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 = 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 √ s = 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) initial-state 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 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].

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Appendix B

Other Anomalous Triple Gauge
Coupling Measurements Figure B.1: The LO ↵ S diagrams for V production, where V=W,Z, ⇤ . The W coupling occurs naturally in the SM, unlike Z . In the case of W production the charged lepton is radiating the photon in the FSR diagram.
The measurement of and limits on anomalous triple gauge couplings presented for the Z analysis were performed in tandem with the search for anomalous couplings in the W . The same class of Feynman diagrams, Figure B.1, describes the production of W as for Z with the exception that there is a naturally arising triple gauge vertex Figure 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 and (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.

Electron identification and selection
Electrons are identified as "superclusters" (SC) 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 SC are required to be located within the acceptance of the tracker (|η| < 2.5). Electron candidates in the transition regions between the central barrel (EB) and the endcap (EE) sections of the ECAL (1.4442 < |η| < 1.566) have reduced efficiency, and are therefore excluded. 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 meanη = ∑ η i w i / ∑ w i as follows: where the sum runs over all the elements of the 5 × 5 matrix, and η i = 0.0174η i , withη i denoting the η index of the ith crystal; the individual weights w i are given by 4.7 + ln(E i /E T ), unless any of the w i are found to be negative, in which case they are set to zero. In the ensuing analysis, the value of σ ηη is required to be consistent with expectations for electromagnetic showers, and the discriminant is used to suppress background as well as to assess contribution from signal and background in fits to the data discussed in Section 4.1.1.
In addition, the η and φ coordinates of the track trajectories extrapolated to the ECAL are required to match those of the SC, and limits are imposed on the amount of HCAL energy deposited within a cone of ∆R < 0.15 relative to the axis of the ECAL cluster. To reduce background from γ → e + e − conversions in the tracker material, the electron candidates are required to have no "partner" tracks within 2 mm of the extrapolated point in the transverse plane where both tracks are parallel to each other (near the hypothesized point of the photon conversion), and the difference in the cotangents of their polar angles must satisfy |∆ cot θ| > 0.02. To ensure that an electron trajectory is consistent with originating from the primary interaction vertex, taken to be the one with the largest scalar sum of the p 2 T of its associated tracks in the case of multiple vertices, the distances of closest approach are required to be |d z | < 0.1 cm and |d T | < 0.02 cm for the longitudinal and transverse coordinates, respectively.
To reduce background from jets misidentified as electrons, the electron candidates are required to be isolated from other energy depositions in the detector. The electron selection criteria are obtained by optimizing signal and background levels using simulated samples. This optimization is done separately for the EB and EE sections. Different criteria are used for the Wγ → eνγ and Zγ → eeγ channels because of the different trigger requirements and relative background levels. For the Zγ analysis, a relative isolation parameter (I r ) is calculated for each electron candidate through a separate sum of scalar p T in the ECAL, HCAL, and tracker (TRK), all defined relative to the axis of the electron, but without including its p T , within the spatial cone ∆R = (∆φ) 2 + (∆η) 2 < 0.3. This sum, reduced by ρ × π × 0.3 2 to account for the pileup contributions to the isolation parameter, and divided by the p T of the electron candidate, defines the I r for each subdetector. Here ρ is the mean energy (in GeV) per unit 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.

Photon identification and selection
Photon candidates in the fiducial volume of the ECAL detector are reconstructed as SC 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 Ref. [28].
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 shapes of electromagnetic (EM) showers. In particular, (i) the ratio of HCAL to ECAL energies deposited within a cone of ∆R = 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 endcap, and (iii) to reduce background from misidentified electrons, photon candidates must have no associated tracks in the pixel detector.
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. The scalar sum of transverse momenta of all the tracks found in the annulus 0.05 < ∆R < 0.4 around each photon candidate is therefore required to have p TRK where A eff is the effective area used to correct each photon shower for 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 < ∆R < 0.40, excluding a rectangular strip of ∆η × ∆φ = 0.04 × 0.40 to reduce the impact of energy leakage from any converted γ → e + e − showers, is computed. The isolation in the ECAL is required to have p ECAL T < 4.2 GeV + 0.006 × p γ T + 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 1, separately for the three isolation parameters, calculated for EM showers observed in the barrel and endcap regions of the ECAL.
To estimate the efficiency of requirements on the shape and isolation of EM showers, we use the similarity between photon and electron showers and a tag-and-probe technique in which one of the electrons from Z → ee decay is required to pass more stringent electron criteria, to check whether its partner electron satisfies the photon selection criteria when the requirement   Fig. 2. The efficiencies obtained using generator-level information in Z → ee and in γ+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 efficiency in Z → ee simulation to that in the γ+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 endcap regions of the ECAL, respectively.

Muon identification and selection
Muons are reconstructed offline 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  Figure 3: Ratio of efficiencies for selecting photons in data relative to MC simulation, obtained through the tag-and-probe 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.
criteria [24], with minor changes in requirements on the distance of closest approach of the muon track to the primary vertex. We require |d z | < 0.1 cm, in the longitudinal direction, and |d T | < 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.

Reconstruction of E T /
Neutrinos from W → ν decay are not detected directly, but give rise to an imbalance in reconstructed transverse momentum in an event. This quantity is computed using objects reconstructed with the particle-flow algorithm [29], 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.

Trigger requirements
The Wγ → νγ and Zγ → γ 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 offline requirements.
For the Wγ → eνγ channel, we use an isolated, single-electron trigger, requiring electrons with |η| < 3, and a p T threshold of 32 GeV, except for the first part of Run 2011A (L = 0.2 fb −1 ), where the threshold is 27 GeV. In addition, for the last part (L = 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 M W T = √ 2p T E T / (1 − cos ∆φ( , E T / )) > 50 GeV, where ∆φ is the angle between the p T and the E T / vectors. The trigger used for the Zγ → eeγ 3.6 Wγ event selections 7 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 |η| < 2.1. The dimuon trigger used to collect Zγ → µµγ events does not require the two muons to be isolated, and has coverage for |η| < 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 = 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 = 0.8 fb −1 ), where these increase to 17 and 8 GeV, respectively.

Wγ event selections
The Wγ → νγ 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 to have p T > 15 GeV. The maximum allowed |η| 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 ∆R( , γ) > 0.7. To minimize contributions from Zγ → γ 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, |η| < 2.5, and pass looser electron selections, and for muons that have p T > 10 GeV and |η| < 2.4.
To suppress background processes without genuine E T / , we require events to have M W T > 70 GeV. We find that the simulation of the distribution in E T / 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 νγ selections yield 7470 electron and 10 809 muon candidates in the data. The selection criteria used to define the Wγ sample are summarized in Table 2.

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 to have p T > 15 GeV. The maximum |η| 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 ∆R( , γ) > 0.7 requirement. Finally, the invariant mass of the two leptons is required to satisfy m > 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 2.

Background estimates
The dominant background for both Wγ and Zγ production arises from events in which jets, originating mostly from W+jets and Z+jets events, respectively, are misidentified as photons. We estimate the background from these sources as a function of p γ T using the two methods described in Section 4.1.
For the Wγ channel, a second major background arises from Drell-Yan (qq → + − ) and EW diboson production, when one electron is misidentified as a photon. This background is estimated from data as described in Section 4.2.
Other backgrounds to Vγ processes include (i) jets misidentified as leptons in γ+jet production, (ii) Vγ events, with V decaying into τν or ττ, and subsequently τ → νν, (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+jets, and are estimated using MC simulation.

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 Section 3.2, but without the σ ηη selection, and with inverted TRK isolation requirements: GeV, for 1.566 < |η γ | < 2.5. These requirements ensure that the contributions from genuine photons are negligible, while the isolation requirements remain close to those used for 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 photon-like 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 4.1 Jets misidentified as photons 9 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 endcap, respectively. A more detailed discussion of systematic uncertainties in the background estimate is given in Section 5.4. 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): where N, N S , and N B are the total number of events and the numbers of signal and background candidates in data for any given bin of p γ T , respectively. The S(σ ηη ) and B(σ ηη ) represent the expected signal and background distributions in σ ηη . These distributions are smoothed using a kernel-density estimator [30], 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 is calculated using an unbinned extended likelihood L and minimizes − ln L as a function of the signal fraction f S = N S /N: (3)

Ratio method
We use a second method, referred to as the "ratio method," to infer the V+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+jets and multijet data to extract the misidentification rate, taking into account the quark/gluon composition of the jets in V+jets events.

4 Background estimates
The ratio method exploits a category of jets that have properties similar to electromagnetic objects in the ECAL, and are called photon-like jets. Photon-like 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 to that of passing photon-like requirements. Once R p is known, the number of jets that satisfy the final photon selection criteria (N V+jets ) can be estimated as the product of R p and the number of photon-like jets in data.  Figure 5: 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+jets and multijet data. The difference in R p values for the two processes is attributed to the fact that jets in γ+jets events are dominated by quark fragmentation, while jets in multijet events are dominated by gluon fragmentation.
We measure R p separately for each p γ T bin of the analysis both for the barrel and endcap regions of the ECAL, using "diphoton" events, defined by the presence of either two photon candidates that pass the final photon selections, or that have one photon candidate that passes the final selections and one that passes only photon-like jet selections. To reduce 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 photon-like jet yield. As only 5-10% of genuine photons in multijet events pass photon-like 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 photon-like jet originates from hadronization of a quark or a gluon. We use the simulation of the gluon-to-quark jet ratio in W+jets and Z+jets events to correct R p as a function of the p T of the photon-like jet. We find the predictions from the ratio method to be consistent with those from the template method, and consider their 4.2 Background from electrons misidentified as photons in νγ events 11 difference as an additional source of systematic uncertainty in the analysis.

Background from electrons misidentified as photons in νγ 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 having no associated track in the pixel detector. Fitting to the m distribution using a convolution of Breit-Wigner and "Crystal Ball" [31] 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 = 0.014 ± 0.003 (syst.) and 0.028 ± 0.004 (syst.) for the barrel and the endcap 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 Section 5.4.
The background in the eνγ channel is dominated by Z+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+jets and diboson processes) are estimated using MC simulation, in which a photon candidate is matched spatially to the generator-level electron.

Total background
The background from jets that are misidentified as photons is summarized as a function of p T of the photon in Table 3 for νγ events and in Table 4 for γ events, and the sums are listed as N W+jets B in Table 5 and as N Z+jets B in Table 6. The background from electrons in selected νγ events that are misidentified as photons, N eeX B , is summarized in Table 3 for both eνγ and µνγ channels. The N other B in Tables 5 and 6 indicates the rest of the background contributions estimated from simulation. For the eνγ channel, the largest contribution to N other B (53%) is from Zγ events, and the next largest is from γ+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 Sections 5.4-5.6.

The Wγ process and radiation-amplitude zero
For photon transverse momenta >15 GeV and angular separations between the charged leptons and photons of ∆R > 0.7, the Wγ production cross section at NLO for each leptonic decay channel is expected to be 31.8 ± 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 (RAZ) [32][33][34][35][36], and the effect was first observed by the D0 Collaboration [6] using the charge-signed rapidity difference Q × ∆η between the photon candidate and the charged lepton candidate from W → ν decays [37]. In the SM, the minimum is at Q × ∆η = 0 for pp collisions. Anomalous Wγ contributions can affect the distribution in Q × ∆η 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 [37], of the photon, lepton, and E T / system > 110 GeV. The three body mass M T ( γE T / ) is calculated as where M γ denotes the invariant mass of the γ system, and p T (i), i = γ, , 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.

The Zγ process
The cross section for Zγ production at NLO in the SM, for p γ T > 15 GeV, ∆R( , γ) > 0.7 between the photon and either of the charged leptons from the Z → + − decay, and m > 50 GeV, is predicted to be 5.45 ± 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 (b), respectively. Again, good agreement is found between data and the SM predictions.

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, 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 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 = data / MC obtained by measuring the efficiency in the same way for data and simulation. The product A S × S can then be replaced by the product F S × ρ eff , where F S ≡ A S × MC corresponds to the fraction of generated signal events selected in the simulation. Equation (6) 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 ∆R( , γ) > 0.7, for Wγ, and with an additional requirement, m > 50 GeV, for Zγ .

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 change the electron energy scale in data by its estimated uncertainty of 0.5% in barrel and 3% in endcaps, to gauge the contribution from the calibration of the ECAL detector. For the muon channel, the muon momentum is changed by 0.2%. For photons, we change the energy by 1% and 3% in the EB and EE region, respectively. 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 photon-like 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 × 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. [38]. To estimate the effect of electron resolution on A S × 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 Ref. [28]. The systematic effect of photon resolution on A S × 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 [39] to determine the impact on A S × 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 background and the range of the fits used in the tag-and-probe method.
The fourth category of uncertainties comprises the contributions from background. These are dominated by uncertainties in estimating the W+jets and Z+jets backgrounds from data. The difference in σ ηη distributions between data and simulated events (Section 4.1.1) 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 photon-like jets that pass 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 multijets 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+jets and Z+jets events were shown in Table 3 and 4, 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 Section 4.2 and that obtained using a simple counting method. The uncertainties for lesser contributions 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% [40].

Wγ cross section
In the summary of parameters used in the measurement of the pp → Wγ cross sections listed in Table 5, N νγ is the number of observed events, N νγ S is the number of observed signal events after background subtraction, and A S × S , ρ eff , and L are described in Section 5.3. A summary of all systematic uncertainties in the measured Wγ cross sections is given in Table 7, separately for electron and muon channels.

19
All three results are also consistent within the uncertainties with the theoretical NLO cross section of 5.45 ± 0.27 pb, computed with MCFM. The uncertainty on the prediction is obtained using the CTEQ6.6 PDF set [21].

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 ± 0.1 is consistent with the measured ratio, 6.9 ± 0.2 (stat.) ± 0.5 (syst.).

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 Vγ processes. These cross sections, predictions, and their uncertainties are summarized in Table 9 and in Fig. 10.   The most general Lorentz invariant, effective Lagrangian that describes WWγ and WWZ couplings has 14 independent parameters [42,43], 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 de-6.2 ZZγ and Zγγ couplings 21 scribing the WWγ and WWZ vertices: where V = γ or Z, W µ are the W ± fields, W µν = ∂ µ W ν − ∂ ν W µ , with the overall couplings given by g WWγ = −e, and g WWZ = −e cot θ W , where θ W is the weak mixing angle. Assuming electromagnetic gauge invariance, g γ 1 = 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 = λ γ = 0 and g Z 1 = κ Z = κ γ = 1. In this analysis, we follow the convention that describes the couplings in terms of their deviation from the SM values: Invariance under SU(2) L × U(1) Y transformations reduces these to three independent couplings: where ∆κ γ and λ γ are determined from Wγ production.

ZZγ and Zγγ couplings
The most general vertex function for ZZγ [44] can be written as with the Zγγ vertex obtained by the replacements The couplings h V i for V = Z or γ, and i = 1, 2, violate CP symmetry, while those with i = 3, 4 are CP-even. Although, at tree level, all these couplings vanish in the SM, at the higher, oneloop 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.

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 (CL) upper limits on values of ATGCs are set using the modified frequentist CL s method [45].
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+jets and Zγ+jets with up to two jets in the final state.

7 Summary
For the Wγ analysis, we set one and two-dimensional limits on each ATGC parameter ∆κ γ and λ γ , while g Z 1 is set to the SM value, assuming the "equal couplings" scenario of the LEP parameterization [46].
For the Zγ analysis, we set h V 1 and h V 2 to the SM values, and set two-dimensional limits on the h V 3 and h V 4 anomalous couplings, with V = 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 Fig. 12 for the Zγ channels, with the corresponding one-dimensional limits listed in Table 10 for Wγ, and Table 11 for Zγ.  Figure 11: Observed (solid curve) and expected (dashed curve) 95% CL exclusion contours for anomalous WWγ couplings, with ±1 and ±2 standard deviation contours from uncertainties in the measurements indicated by light and dark shaded bands, respectively.

Summary
We have presented updated measurements of the Vγ inclusive production cross sections in pp collisions at √ s = 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 ∆R > 0.7, and an additional requirement Table 11: One-dimensional 95% CL limits on ATGCs for Zγ → eeγ, Zγ → µµγ, and for the combined analyses. The intervals shown represent the allowed ranges of the coupling parameters.   of m > 50 GeV is placed on Zγ candidates. The measured cross sections for p γ T > 15 GeV, σ(pp → Wγ) × B(W → ν) = 37.0 ± 0.8 (stat.) ± 4.0 (syst.) ± 0.8 (lum.) pb and σ(pp → Zγ) × B(Z → ) = 5.33 ± 0.08 (stat.) ± 0.25 (syst.) ± 0.12 (lum.) pb, are consistent with predictions of the SM; the ratio of these measurements, 6.9 ± 0.2 (stat.) ± 0.5 (syst.), is also consistent with the SM value of 5.8 ± 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 10 and 11. and the US National Science Foundation. Individuals have received support from the Marie-Curie programme and the European Research Council and EPLANET (European Union); the Leventis Foundation; the A. P. Sloan Foundation; the Alexander von Humboldt Foundation; the Belgian Federal Science Policy Office; the Fonds pour la Formationà la Recherche dans l'Industrie et dans l'Agriculture (FRIA-Belgium); the Agentschap voor Innovatie door Wetenschap en Technologie (IWT-Belgium); the Ministry of Education, Youth and Sports (MEYS) of Czech Republic; the Council of Science and Industrial Research, India; the Compagnia di San Paolo (Torino); and the HOMING PLUS programme of Foundation for Polish Science, cofinanced from European Union, Regional Development Fund.