CMSSMP21011 ; CERNEP2022223  
Measurement of the electroweak production of W$ \gamma $ in association with two jets in protonproton collisions at $ \sqrt{s}= $ 13 TeV  
CMS Collaboration  
23 December 2022  
Phys. Rev. D 108 (2023) 032017  
Abstract: A measurement is presented for the electroweak production of a W boson, a photon ($ \gamma $), and two jets (j) in protonproton collisions. The leptonic decay of the W boson is selected by requiring one identified electron or muon and large missing transverse momentum. The two jets are required to have large invariant dijet mass and large separation in pseudorapidity. The measurement is performed with the data collected by the CMS detector at a centerofmass energy of 13 TeV, corresponding to an integrated luminosity of 138 fb$ ^{1} $. The cross section for the electroweak W$ \gamma $jj production is 23.5 $ ^{+4.9}_{4.7} $ fb, whereas the total cross section for W$ \gamma $jj production is 113 $ \pm $ 13 fb. Differential cross sections are also measured with the distributions unfolded to the particle level. All results are in agreement with the standard model expectations. Constraints are placed on anomalous quartic gauge couplings (aQGCs) in terms of dimension8 effective field theory operators. These are the most stringent limits to date on the aQGCs parameters $f_{\mathrm{M},2{}5}/\Lambda^4$ and $f_{\mathrm{T},6{}7}/\Lambda^4$.  
Links: eprint arXiv:2212.12592 [hepex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; Physics Briefing ; CADI line (restricted) ; 
Figures  
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Figure 1:
Representative Feynman diagrams for W$ \gamma $jj production at the LHC: EW (left), EW through triple (middle left) and quartic (middle right) gauge boson couplings, and QCDinduced (right). 
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Figure 1a:
Representative Feynman diagram for W$ \gamma $jj EW production at the LHC. 
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Figure 1b:
Representative Feynman diagram for W$ \gamma $jj EW through triple gauge boson couplings production at the LHC. 
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Figure 1c:
Representative Feynman diagram for W$ \gamma $jj EW through quartic gauge boson couplings production at the LHC. 
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Figure 1d:
Representative Feynman diagram for W$ \gamma $jj QCDinduced production at the LHC. 
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Figure 2:
The $ p_{\mathrm{T}} $ distributions for photons in the barrel (left) and in the endcaps (right) in the control region for data and from background estimations before the fit to the data. The misID backgrounds are derived from data, whereas the remaining backgrounds are estimated from simulation. All events with a photon $ p_{\mathrm{T}} > $ 200 GeV are included in the last bin. The hatched bands represent the combined statistical and systematic uncertainties on the predicted yields. The vertical bars on the data points represent the statistical uncertainties of data. The bottom panels show the ratios of the data to the predicted yields. 
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Figure 2a:
The $ p_{\mathrm{T}} $ distributions for photons in the barrel in the control region for data and from background estimations before the fit to the data. The misID backgrounds are derived from data, whereas the remaining backgrounds are estimated from simulation. All events with a photon $ p_{\mathrm{T}} > $ 200 GeV are included in the last bin. The hatched bands represent the combined statistical and systematic uncertainties on the predicted yields. The vertical bars on the data points represent the statistical uncertainties of data. The bottom panel shows the ratios of the data to the predicted yields. 
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Figure 2b:
The $ p_{\mathrm{T}} $ distributions for photons in the endcaps in the control region for data and from background estimations before the fit to the data. The misID backgrounds are derived from data, whereas the remaining backgrounds are estimated from simulation. All events with a photon $ p_{\mathrm{T}} > $ 200 GeV are included in the last bin. The hatched bands represent the combined statistical and systematic uncertainties on the predicted yields. The vertical bars on the data points represent the statistical uncertainties of data. The bottom panel shows the ratios of the data to the predicted yields. 
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Figure 3:
The 2D distributions used in the fit for the total EW W$ \gamma $ cross section measurement. The hatched bands represent the combined statistical and systematic uncertainties in the predicted yields. The vertical bars on the data points represent the statistical uncertainties of data. The expectation is shown after the fit to the data. EW W$ \gamma $ in (out of) fiducial region stands for the events of EW W$ \gamma $ falling in (out of) the fiducial region defined in Sec. 9. 
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Figure 3a:
Barrel photons: The 2D distribution used in the fit for the total EW W$ \gamma $ cross section measurement. The hatched bands represent the combined statistical and systematic uncertainties in the predicted yields. The vertical bars on the data points represent the statistical uncertainties of data. The expectation is shown after the fit to the data. EW W$ \gamma $ in (out of) fiducial region stands for the events of EW W$ \gamma $ falling in (out of) the fiducial region defined in Sec. 9. 
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Figure 3b:
Endcap photons: The 2D distribution used in the fit for the total EW W$ \gamma $ cross section measurement. The hatched bands represent the combined statistical and systematic uncertainties in the predicted yields. The vertical bars on the data points represent the statistical uncertainties of data. The expectation is shown after the fit to the data. EW W$ \gamma $ in (out of) fiducial region stands for the events of EW W$ \gamma $ falling in (out of) the fiducial region defined in Sec. 9. 
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Figure 4:
Differential cross sections for the EW W$ \gamma $jj production as functions of $ p_{\mathrm{T}}^{\ell} $, $ p_{\mathrm{T}}^{\gamma} $, $ p_{\mathrm{T}}^{\mathrm{j}1} $, $ m_{\ell\gamma} $, $ m_{\text{jj}} $, and $ \Delta\eta_{\text{jj}} $. Since the ranges of some variables extend to infinity, the last bins accommodate all the events up to infinity as marked by the bin label, but the bin widths that are used as the denominator are finite and are (110, 400), (170, 200), (160, 1000), (250, 500), and (1500, 2000) GeV for $ p_{\mathrm{T}}^{\ell} $, $ p_{\mathrm{T}}^{\gamma} $, $ m_{\ell\gamma} $, $ p_{\mathrm{T}}^{\mathrm{j}1} $ and $ m_{\text{jj}} $ respectively. The blue bands stand for the systematic uncertainties and the black bands represent the total uncertainties. 
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Figure 4a:
Differential cross section for the EW W$ \gamma $jj production as functions of $ p_{\mathrm{T}}^{\ell} $. Since the range of the variable extends to infinity, the last bin accommodates all the events up to infinity as marked by the bin label, but the bin width that is used as the denominator is finite and is (110, 400) GeV.The blue bands stand for the systematic uncertainties and the black bands represent the total uncertainties. 
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Figure 4b:
Differential cross section for the EW W$ \gamma $jj production as functions of $ p_{\mathrm{T}}^{\gamma} $. Since the range of the variable extends to infinity, the last bin accommodates all the events up to infinity as marked by the bin label, but the bin width that is used as the denominator is finite and is (170 200) GeV. The blue bands stand for the systematic uncertainties and the black bands represent the total uncertainties. 
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Figure 4c:
Differential cross section for the EW W$ \gamma $jj production as functions of $ p_{\mathrm{T}}^{\mathrm{j}1} $. Since the range of the variable extends to infinity, the last bin accommodates all the events up to infinity as marked by the bin label, but the bin width that is used as the denominator is finite and is (160, 1000) GeV. The blue bands stand for the systematic uncertainties and the black bands represent the total uncertainties. 
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Figure 4d:
Differential cross section for the EW W$ \gamma $jj production as functions of $ m_{\ell\gamma} $. $ \Delta\eta_{\text{jj}} $. 
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Figure 4e:
Differential cross section for the EW W$ \gamma $jj production as functions of $ m_{\text{jj}} $. Since the range of the variable extends to infinity, the last bin accommodates all the events up to infinity as marked by the bin label, but the bin width that is used as the denominator is finite and is (1500, 2000) GeV. The blue bands stand for the systematic uncertainties and the black bands represent the total uncertainties. 
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Figure 4f:
Differential cross section for the EW W$ \gamma $jj production as functions of $ \Delta\eta_{\text{jj}} $. The blue bands stand for the systematic uncertainties and the black bands represent the total uncertainties. 
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Figure 5:
Differential cross sections for the EW+QCD W$ \gamma $jj production as functions of $ p_{\mathrm{T}}^{\ell} $, $ p_{\mathrm{T}}^{\gamma} $, $ p_{\mathrm{T}}^{\mathrm{j}1} $, $ m_{\ell\gamma} $, $ m_{\text{jj}} $, and $ \Delta\eta_{\text{jj}} $. The details of this figure are the same as for Fig. 4 
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Figure 5a:
Differential cross section for the EW+QCD W$ \gamma $jj production as functions of $ p_{\mathrm{T}}^{\ell} $. The details of this figure are the same as for Fig. 4a. 
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Figure 5b:
Differential cross section for the EW+QCD W$ \gamma $jj production as functions of $ p_{\mathrm{T}}^{\gamma} $. The details of this figure are the same as for Fig. 4b. 
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Figure 5c:
Differential cross section for the EW+QCD W$ \gamma $jj production as functions of $ p_{\mathrm{T}}^{\mathrm{j}1} $. The details of this figure are the same as for Fig. 4c. 
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Figure 5d:
Differential cross section for the EW+QCD W$ \gamma $jj production as functions of $ m_{\ell\gamma} $. The details of this figure are the same as for Fig. 4d. 
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Figure 5e:
Differential cross section for the EW+QCD W$ \gamma $jj production as functions of $ m_{\text{jj}} $. The details of this figure are the same as for Fig. 4e. 
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Figure 5f:
Differential cross section for the EW+QCD W$ \gamma $jj production as functions of $ \Delta\eta_{\text{jj}} $. The details of this figure are the same as for Fig. 4f. 
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Figure 6:
The $ m_{\mathrm{W}\gamma} $ distribution for muon events satisfying the aQGC region selection and used to set constraints on the anomalous gauge coupling parameters (left). Electron events, not shown here, are also used. The gray line represents a nonzero $ f_{\mathrm{M},2}/\Lambda^4 $ setting. Events with $ m_{\mathrm{W}\gamma} > $ 1500 GeV are included in the last bin. The hatched bands represent the combined statistical and systematic uncertainties on the predicted yields. The vertical bars on the data points represent the statistical uncertainties of data. Likelihood scan and the observed 95% CL interval for the aQGC parameter $ f_{\mathrm{M},2}/\Lambda^4 $ (right). 
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Figure 6a:
The $ m_{\mathrm{W}\gamma} $ distribution for muon events satisfying the aQGC region selection and used to set constraints on the anomalous gauge coupling parameters. Electron events, not shown here, are also used. The gray line represents a nonzero $ f_{\mathrm{M},2}/\Lambda^4 $ setting. Events with $ m_{\mathrm{W}\gamma} > $ 1500 GeV are included in the last bin. The hatched bands represent the combined statistical and systematic uncertainties on the predicted yields. The vertical bars on the data points represent the statistical uncertainties of data. 
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Figure 6b:
Likelihood scan and the observed 95% CL interval for the aQGC parameter $ f_{\mathrm{M},2}/\Lambda^4 $. 
Tables  
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Table 1:
Signal, background, and data yields for the EW W$ \gamma $ fiducial cross section measurement from the fit to the data in the signal region. Statistical and systematic uncertainties are added in quadrature. EW W$ \gamma $ in (out of) fiducial region stands for the number of events of EW W$ \gamma $ falling in (out of) the fiducial region defined in Sec. 9. 
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Table 2:
Exclusion limits at the 95% CL for each aQGC coefficient, derived from the $ m_{\mathrm{W}\gamma} $ distribution, assuming all other coefficients are set to zero. Unitarity bounds corresponding to each operator are also listed. All coupling parameter limits are in TeV$ ^{4} $, while $ U_{\text{bound}} $ values are in TeV. 
Summary 
Measurements of the electroweak (EW) production of a W boson, a photon, and two jets in protonproton collisions at a centerofmass energy of 13 TeV have been presented. The data correspond to an integrated luminosity of 138 fb$ ^{1} $ in Run 2 collected with the CMS detector. Events are selected by requiring one isolated lepton (electron or muon) with high transverse momentum ($ p_{\mathrm{T}} $), a moderate missing transverse momentum, one high$ p_{\mathrm{T}} $ isolated photon, and two jets with a large rapidity separation and a large dijet mass. The signal is observed for the first time at 13 TeV, with an observed (expected) significance of 6.0 (6.8) standard deviations, where the expectation is based on the standard model predictions. In a restricted fiducial region, the cross section for the EW W$ \gamma $jj production is 23.5 $ ^{+4.9}_{4.7} $ fb and the cross section for the total EW+QCD W$ \gamma $jj production is 113 $ \pm $ 13 fb. Both measurements are consistent with standard model predictions. For the first time, differential cross sections for EW W$ \gamma $jj and for EW+QCD W$ \gamma $jj production are measured. Constraints placed on anomalous quartic gauge couplings in terms of dimension8 effective field theory operators are extracted and are the most stringent limits to date on the aQGC parameters $f_{\mathrm{M},2{}5}/\Lambda^4$ and $f_{\mathrm{T},6{}7}/\Lambda^4$. 
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