Measurement of the cross section for electroweak production of Z γ in association with two jets and constraints on anomalous quartic gauge couplings in proton-proton collisions at √ s = 8 TeV

A measurement is presented of the cross section for the electroweak production of a Z boson and a photon in association with two jets in proton-proton collisions at √ s = 8 TeV. The Z bosons are identiﬁed through their decays to electron or muon pairs. The measurement is based on data collected with the CMS detector corresponding to an integrated luminosity of 19.7 fb − 1 . The electroweak contribution has a signiﬁcance of 3.0 standard deviations, and the measured ﬁducial cross section is 1.86 + 0.90 − 0.75 (stat) + 0.34 − 0.26 (syst) ± 0.05 (lumi) fb, while the summed electroweak and quantum chromodynamic total cross section in the same region is observed to be 5.94 + 1.53 − 1.35 (stat) + 0.43 − 0.37 (syst) ± 0.13 (lumi) fb. Both measurements are consistent with the leading-order standard model predictions. Limits on anomalous quartic gauge couplings are set based on the Z γ mass distribution.

tially compatible with originating from the electron track. The energy of muons is obtained from the curvature of the corresponding track. The energy of charged hadrons is determined from a combination of their momentum measured in the tracker and the matching ECAL and HCAL energy deposits, corrected for zero-suppression effects and for the response function of the calorimeters to hadronic showers. Finally, the energy of neutral hadrons is obtained from the corresponding corrected ECAL and HCAL energy.
In the barrel section of the ECAL, an energy resolution of about 1% is achieved for unconverted or late-converting photons in the tens of GeV energy range. The resolution for other photons in the barrel section is about 1.3% up to |η| = 1, rising to about 2.5% at |η| = 1.4. In the endcaps, the resolution for unconverted or late-converting photons is about 2.5%, and the resolution for the remaining photons in the endcap is between 3% and 4% [19]. When combining information from the entire detector, the jet energy resolution is typically 15% at 10 GeV, 8% at 100 GeV, and 4% at 1 TeV.
Muons are measured in the range of |η| < 2.4, with detection planes utilizing three technologies: drift tubes, cathode strip chambers, and resistive-plate chambers. Matching muons to tracks measured in the silicon tracker results in a p T resolution for muons with 20 < p T < 100 GeV of 1.3-2.0% in the barrel and better than 6% in the endcaps.
The electron momentum is estimated by combining the energy measurement in the ECAL with the momentum measurement in the tracker. The momentum resolution for electrons with transverse momentum p T ≈ 45 GeV from Z → ee decays ranges from 1.7% for nonshowering electrons in the barrel region to 4.5% for showering electrons in the endcaps. The dielectron mass resolution for Z → ee decays is 1.9% when both electrons are in the ECAL barrel, and 2.9% when both electrons are in the endcaps.
A more detailed description of the CMS detector, together with a definition of the coordinate system used and the relevant kinematic variables, can be found in Ref. [20].

Event reconstruction and selection
Candidate events are selected online with triggers that require two muons or electrons, where the leading and subleading leptons have p T > 17 and 8 GeV respectively, with |η| < 2.4 (muons) or |η| < 2.5 (electrons). The overall trigger efficiency is about 94% and 90% for muons and electrons, respectively, with a small dependence on p T and η.
Muons are reconstructed with a global fit using both the inner tracking system and the muon spectrometer. An isolation requirement is applied in order to suppress the background from multijet events [21,22]. Electron candidates are reconstructed by matching energy deposits in the ECAL with reconstructed tracks; they must pass stringent quality criteria and an isolation requirement [23]. Charged leptons must originate from the primary vertex, which is defined as the vertex whose tracks have the highest sum of p 2 T . We require that each event has exactly two oppositely charged muons (electrons) with p T > 20 GeV and |η| < 2.4 (2.5) and that the invariant mass of the dilepton system must satisfy 70 < M < 110 GeV. The selection efficiencies for leptons are measured using the tag-and-probe method [24] and are approximately 96% for the muons [25] and 80% for the electrons [21].
Photon candidates are reconstructed from energy deposits in the ECAL with no associated track. Quality selection criteria [19] are applied to the reconstructed photons to suppress the background from hadrons misidentified as photons. The observables used in the photon selection are: (1) PF-based isolation variables that are corrected for the contribution from additional proton-proton collisions in the same bunch crossing (pileup); (2) a small ratio of hadronic energy in the HCAL to electromagnetic energy in the ECAL matched in (η, φ) (where φ is azimuthal angle in radians); (3) the transverse width of the electromagnetic shower along the η direction [19]; and (4) an electron track veto. We consider only photons in the ECAL barrel region (|η| < 1.44) with p T > 25 GeV. Events with the photon candidate in one of the endcaps (|η| > 1.57) are excluded from the selection because their signal purity is lower and systematic uncertainties are large.
Hadronic jets are formed from the particles reconstructed by the PF algorithm, using the FAST-JET software package [26] and the anti-k T jet clustering algorithm [27] with a distance parameter of 0.5. To reduce the contamination from pileup, charged PF candidates in the tracker acceptance region |η| < 2.4, are excluded from the jet clustering procedure if associated with pileup vertices. The contribution of neutral particles from pileup events to the jet energy is taken into account by means of a correction based on the projected area of the jet on the front face of the calorimeter. Jet energy corrections are derived from a measurement of the p T balance in dijet and photon+jet events in data [28]. Further residual corrections as functions of p T and η are applied to the data to correct for the small differences between data and simulation. Additional quality criteria are applied to the jets in order to remove spurious jet-like features originating from isolated noise patterns in the calorimeters or in the tracker [29]. The two jets with the highest p T are tagged as the signal jets and are required to have p T > 30 GeV and |η| < 4.7. Since we are primarily interested in the VBS topologies, we require that the invariant mass of the two jets, M jj > 150 GeV. Table 1 presents a summary of the three different section criteria that are used for (1) the SM EW signal search, (2) the SM fiducial cross section measurement, and (3) the aQGC searches. The criteria isolate events consistent with the VBS topology of two high-energy scattered jets separated by a large rapidity gap. The cross section measurement adds two variables sensitive to the VBS process: |y Zγ − (y j1 + y j2 )/2|, which ensures the Zγ systems is located between the scattered jets in eta; and ∆φ Zγ,jj , which requires the Zγ system transverse momentum is consistent with recoiling against the transverse momentum of the two combined jets. The fiducial cross section criteria constrain the VBS topology with only basic kinematic cuts that define the acceptance of the CMS detector and a simple two dimensional requirement on the rapidity separation and invariant mass of the jets. A tight p γ T selection is applied to reach a higher expected significance in a search for a possible aQGC signal in the EW Zγjj process. (2) the cross section measurement; and (3) the selection for the aQGC search. "j1" and "j2" represent the jets that have the largest and second-largest p T , " 1" and " 2" denote the lepton and antilepton from the decay of the Z boson, y is the rapidity, ∆φ Zγ,jj is the absolute difference between φ Zγ and φ j1j2 , and the angular separation ∆R = √ (∆η) 2 + (∆φ) 2 .

Data and simulation
We use data collected with the CMS detector, corresponding to an integrated luminosity of 19.7 fb −1 , at proton-proton center-of-mass energy of 8 TeV.
The EW signal, Zγjj, at leading-order (LO), and the main background, QCD Zγ with 0-3 additional jets, for which the next-to-leading-order (NLO) QCD prediction has been taken from Ref.
[30], matched with parton shower based on the so-called "MLM prescription" [31,32], are simulated using MADGRAPH v5.1.3.30 [33] interfaced with PYTHIA v6.424 [34] for hadronization and showering, using a CTEQ6L1 parton distribution function (PDF) set [35]. The second significant background contribution comes from processes where a jet is misidentified as a photon (fake photon), and this contribution is estimated from data. Other background contributions come from diboson processes (WW/WZ/ZZ) simulated by PYTHIA, single top processes simulated by POWHEG, and ttγ simulated using MADGRAPH interfaced with PYTHIA. The next-to-leading-order QCD cross sections are used to normalize these simulated samples, except for ttγ where an LO prediction is taken.
All the simulated events are processed through a GEANT4 [36] simulation of the CMS detector. The tag-and-probe technique is used to correct for data-Monte Carlo (MC) differences in the trigger efficiency, as well as the reconstruction and selection efficiencies. Additional protonproton interactions are superimposed over the hard scattering interaction with the distribution of primary vertices matching that obtained from the collision data.

Background modeling
The dominant source of background to the EW signal is QCD Zγ + jets production. The shape of this background is taken from MC simulation and the normalization is evaluated from data in a control region, defined as 150 < M jj < 400 GeV, where the signal contribution is below 1%. The simulated MC events correctly reproduce the yield of these events with a correction factor of 1.00 ± 0.22 for the combined Z → µ + µ − and Z → e + e − channels. The value is comparable with the NLO QCD K factor from Ref.
The background from fake photons arises mainly from Z+jets events where one jet satisfies the photon ID criteria. The estimation is based on events similar to the ones selected with the baseline selection described in Table 1, except that the photon must fail the tight photon ID and satisfy a looser ID requirement based on the charged isolation variable. This selection ensures that the photon arises from a jet, but still has kinematic properties similar to a genuine photon satisfying the tight photon ID. Considering the difference between the σ ηη distributions for fake photons and genuine photons, a fit is made to normalize the number of events with fake photons to the number of events with genuine photons and obtain the probability to have a fake photon. The fake photon probability is calculated based on different p γ T regions in a manner similar to that described in Ref. [37].
Other backgrounds, including top quark and diboson production processes are estimated from MC simulations and normalized to the integrated luminosity of the data sample. The contribution from these backgrounds is less than 10% after applying the kinematic selection (Section 3) and is negligible once the final EW and aQGC selection criteria (Sections 7 and 8) are applied.
The M jj distributions for the Z → µ + µ − and e + e − channels after the selection requirements described in Section 3 are shown in Fig. 2. The observed distributions are compared to the combined prediction of the backgrounds and of the EW Zγjj signal.  Figure 2: The M jj distributions measured in (left) muon and (right) electron channels. The data (solid symbols with error bars representing the statistical uncertainties) are compared to a datadriven background estimate, combined with MC predictions for the signal contribution. The hashed bands represent the full uncertainty in the predictions, as described in Section 6. The last bin includes overflow events.

Measurement of the signal significance and fiducial cross section 6 Systematic uncertainties
The systematic uncertainty in the QCD Zγ+jets background estimation is 22% for both Z → µ + µ − and Z → e + e − ; it is dominated by the large statistical uncertainty in the control region used for normalization. The shape uncertainties that are related to the extrapolation of the normalization factor to the signal region (M jj > 400 GeV) are determined by varying the renormalization and factorization scales as well as the MLM matching scale [31,32] up and down by a factor of two. Finally, we combine both the normalization factor uncertainty and the shape uncertainty to obtain the total uncertainty.
The systematic uncertainty in the background estimation from fake photons arises from the variation in the choice of the charged isolation sideband and the σ ηη distribution used for estimating the fake photon probability. The total uncertainties in the fake photon background estimation can be found in Table 2. The theoretical uncertainty in the top quark background is The systematic uncertainties in the estimation of the trigger efficiency, measured using the tag-and-probe technique, are 1.2% and 1.7% for the Z → µ + µ − and Z → e + e − channels, respectively. Using similar methods, the systematic uncertainties in the efficiencies for lepton reconstruction and identification in the two channels are 1.9% and 1.0%, respectively. The systematic uncertainty in the jet energy scale and resolution is estimated by varying the jet energy scale and resolution up and down within their p T -and η-dependent uncertainties [28]. The uncertainty is 14% for M jj > 400 GeV. Another source of uncertainty is the modelling of the pileup. The inelastic cross section is varied by ±5% in order to evaluate this contribution. The uncertainty in the integrated luminosity is 2.6% [38].
There are also three sources of theoretical uncertainties applied to the signal only. The PDF uncertainty for the signal is estimated with the CT10 [39] PDF set, following the asymmetric Hessian method introduced in Refs. [40,41]. The scale uncertainty is evaluated by varying the renormalization and factorization scales independently by a factor of two. The magnitude of the interference between QCD and EW Zγjj processes is assigned as systematic uncertainties in the two M jj ranges.
All the systematic uncertainties described are applied to both the signal significance measurement and the aQGC search. They are also propagated to the uncertainty in the measured fiducial cross section, with the exception of the theoretical uncertainty associated with the signal cross section.
All the uncertainties in our analysis are summarized in Table 2.

Measurement of the signal significance and fiducial cross section
As shown in Table 1, in addition to the common selection, we apply three further requirements to isolate the EW signal: |y Zγ − (y j1 + y j2 )/2| < 1.2, |∆η jj | > 1.6, and ∆φ Zγ,jj > 2.0 radians. The selection requirements are chosen by optimizing the expected significance. We apply the CL s criterion described in Ref. [42,43] to assess the signal significance, based on the binned M jj distribution, using only the two rightmost bins corresponding to 400 < M jj < 800 GeV and M jj > 800 GeV. We consider QCD Zγjj production and events without Zγ as background and EW Zγjj production as signal. Table 3 summarizes the number of events predicted for each process with the number of events observed. For EW Zγjj production, the observations are found to be compatible with expectations in the different channels. By combining both channels, we find evidence for EW Zγjj production with an observed and expected significance of 3.0 and 2.1 standard deviations, respectively. We determine the ratio of the observed signal to that expected from the SM for LO EW Zγjj production asμ = 1.5 +0.9 −0.6 using a binned likelihood fit over the two ranges of the M jj distribution.
Applying the same criteria, we can also measure the significance of the combined EW and QCD Zγjj process. As shown in Table 3, with the two decay channels combined in the search region, of the signal events 7.0 (38.4%) are estimated to come from EW production and the remaining 11.3 from QCD production. As a result, the observed (expected) significance for the combined EW and QCD Zγjj process is 5.7 (5.5) standard deviations.
To determine the cross section for EW Zγjj production we use a fiducial kinematic region based on the acceptance of the CMS detector with a minimal selection on the M jj and ∆η jj variables to select the VBS topology. The fiducial region is defined as described in Table 1. We define the cross section in the fiducial region as σ f = σ gμ α g f where σ g is the cross section for generated signal events,μ is the signal strength, and α g f is the acceptance for the generated events in the fiducial region, evaluated through simulation. The fiducial cross section for EW Zγjj production is 1.86 +0.90 −0.75 (stat) +0.34 −0.26 (syst) ± 0.05 (lumi) fb, consistent with the theoretical prediction at LO of 1.27 ± 0.11 (scale) ± 0.05 (PDF) fb calculated using MADGRAPH.
The cross section for all processes that produce the Zγjj final state can be compared to theoretical predictions. The fiducial region studied here lies in a particularly interesting region of phase space because of the substantial contribution to Zγjj from EW production. By restricting the phase space to the fiducial region for the EW process as defined before, the expected fraction of EW events in the combined sample of EW and QCD signal events is 26%, and the cross section of the combined process is 5.94 +1.53 −1.35 (stat) +0.43 −0.37 (syst) ± 0.13 (lumi) fb, which is consistent with the theoretical prediction at LO calculated using MADGRAPH: 5.05 ± 1.22 (scale) ± 0.31 (PDF) fb.

Search for anomalous quartic gauge couplings
The effects of any new physics between the TeV and the Planck scale might be significant in the high energy tails of measurements at the LHC and can be parameterized via effective anomalous couplings. With the discovery of the Higgs boson, higher-dimensional operators can be introduced in a linear way [44]: where f M0,1,2,3 and f T0,2,8,9 are coefficients of relevant effective operators, and Λ represents the scale of new physics responsible for anomalous couplings. The Lagrangian of the aQGCs is implemented within the MADGRAPH package.
We study the distribution of the mass of the dilepton and photon system, M Zγ , to search for contributions from aQGCs. The effects of new physics would be seen at higher energy and modify the interference of VBS diagrams. To select the region sensitive to new physics, we require p γ T > 60 GeV. The selection for the aQGC analysis is described in Table 1. The Zγ mass distribution is shown in Fig. 3, where the last bin includes all events with M Zγ > 420 GeV. Because no significant excess is seen in the M Zγ distribution, we use the shape of the M Zγ distribution to extract limits on aQGC contributions.
With the parameterization of signals and related systematic uncertainties, for each aQGC parameter, we reweight the SM signal shape to the aQGC shape. The following test statistic is used: where the likelihood function (L) is constructed for both lepton channels and combined, using a bin-wise Poisson distribution with profiled nuisance parameters (θ). α test represents the aQGC point being tested. The symbolθ represents the values corresponding to the maximum of the likelihood at the point α test , whileα andθ correspond to the global maximum of the likelihood. This test statistic is assumed to follow a χ 2 distribution [45], from which one can extract limits. Exclusion limits are shown in Table 4. Each coupling parameter is varied over a set of discrete values, keeping the other parameters fixed to zero.
An effective theory is only valid at energies lower than the scale of new physics, and highdimensional operators with nonzero aQGC values can lead to unitarity violation at sufficiently high energies. For each aQGC listed in Table 4, we checked the stated upper limit against the unitary bound [46] obtained with VBFNLO [47]. In general, we find the limits on all aQGC parameters are set in the unitary unsafe region, except for f T9 where the unitarity bound is up to 6 TeV. Form factors can be introduced to unitarize the high energy contribution, however it is difficult to compare results from different experiments and it is not theoretically well motivated. In this study all of the aQGC limits shown are evaluated without a form factor, and can be directly compared to limits set in references [3-7, 9-12].

Conclusions
The measurement of the cross section for the electroweak production of a Z boson and a photon in association with two jets, where the Z boson decays into electron or muon pairs, was pre- sented. The measurement is based on a sample of proton-proton collisions collected with the CMS detector at a center-of-mass energy of 8 TeV, corresponding to an integrated luminosity of 19.7 fb −1 . We find evidence for EW Zγjj production with an observed (expected) significance of 3.0 (2.1) standard deviations. The fiducial cross section for EW Zγjj production is measured to be 1.86 +0.90 −0.75 (stat) +0.34 −0.26 (syst) ± 0.05 (lumi) fb, consistent with the theoretical prediction. The fiducial cross section for combined EW and QCD Zγjj production is 5.94 +1.53 −1.35 (stat) +0.43 −0.37 (syst) ± 0.13 (lumi) fb, which is also consistent with the leading-order theoretical prediction.
In the framework of dimension-eight effective field theory operators, limits on the aQGC parameters f M0,1,2,3 and f T0,1,2,8,9 are set at 95% confidence level. This is the first constraints on the neutral aQGC parameters f T8 .

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, we acknowledge the enduring support for the construction and operation of the LHC and the CMS detector provided by the following funding agencies: BMWFW and FWF (Aus  [10] CMS Collaboration, "Evidence for exclusive γγ to W + W − production and constraints on anomalous quartic gauge couplings at √ s = 7 and 8 TeV", JHEP 08 (2016) 119, doi:10.1007/JHEP08(2016)119, arXiv:1604.04464.

References
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