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| CMS-SMP-19-005 ; CERN-EP-2025-242 | ||
| Measurements of electroweak production of a photon in association with two jets in proton-proton collisions at $ \sqrt{s}= $ 13 TeV | ||
| CMS Collaboration | ||
| 29 November 2025 | ||
| Submitted to J. High Energy Phys. | ||
| Abstract: The first observation of electroweak production of a photon in association with two forward jets in proton-proton collisions is presented. The measurement uses data recorded by the CMS experiment at the LHC during 2016-2018 at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 138 fb$ ^{-1} $. The analysis is performed in a region enriched in photon production via vector boson fusion, with a requirement on the transverse momentum of the photon to exceed 200 GeV. The cross section is measured to be 202$ ^{+36}_{-32} $ fb, at a significance with respect to the null hypothesis that exceeds five standard deviations. This is in agreement with the standard model prediction of 177$ ^{+13}_{-12} $ fb. Differential cross sections are measured as a function of various observables. Limits are set on dimension-6 effective field theory operators that contribute to the WW$ \gamma $ interaction. The observed 95% confidence intervals for the corresponding Warsaw basis Wilson coefficients $ c_{\mathrm{W}} $ and $ c_{\mathrm{H}\mathrm{W}\mathrm{B}} $ are [$-$0.11, 0.16] and [$-$1.6, 1.5], respectively. | ||
| Links: e-print arXiv:2512.00502 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Representative Feynman diagram for EW $ \gamma $\text{jj} production with a photon produced via vector boson fusion. |
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Figure 2:
Representative Feynman diagrams for photons produced in FSR (left) and ISR (right). |
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Figure 2-a:
Representative Feynman diagrams for photons produced in FSR (left) and ISR (right). |
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Figure 2-b:
Representative Feynman diagrams for photons produced in FSR (left) and ISR (right). |
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Figure 3:
Representative Feynman diagrams for QCD-induced production of a photon and two jets. |
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Figure 3-a:
Representative Feynman diagrams for QCD-induced production of a photon and two jets. |
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Figure 3-b:
Representative Feynman diagrams for QCD-induced production of a photon and two jets. |
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Figure 4:
Distribution of (upper left) photon $ p_{\mathrm{T}} $, (upper right) leading jet $ p_{\mathrm{T}} $, (lower left) $ m_\mathrm{jj} $, and (lower right) $ |\Delta\eta_{\text{jj}}| $ in data and simulated processes, except the contribution of nonprompt photons that is estimated from data as discussed in Section 5. Simulted samples are normalized to their theoretical cross sections. The black points with error bars represent the data and their statistical uncertainties. The last bin includes the overflow events. The lower panels shows the ratio of the data to the expectation with the inner (outer) band representing the statistical (total) uncertainty in the combined signal and background expectations. |
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Figure 4-a:
Distribution of (upper left) photon $ p_{\mathrm{T}} $, (upper right) leading jet $ p_{\mathrm{T}} $, (lower left) $ m_\mathrm{jj} $, and (lower right) $ |\Delta\eta_{\text{jj}}| $ in data and simulated processes, except the contribution of nonprompt photons that is estimated from data as discussed in Section 5. Simulted samples are normalized to their theoretical cross sections. The black points with error bars represent the data and their statistical uncertainties. The last bin includes the overflow events. The lower panels shows the ratio of the data to the expectation with the inner (outer) band representing the statistical (total) uncertainty in the combined signal and background expectations. |
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Figure 4-b:
Distribution of (upper left) photon $ p_{\mathrm{T}} $, (upper right) leading jet $ p_{\mathrm{T}} $, (lower left) $ m_\mathrm{jj} $, and (lower right) $ |\Delta\eta_{\text{jj}}| $ in data and simulated processes, except the contribution of nonprompt photons that is estimated from data as discussed in Section 5. Simulted samples are normalized to their theoretical cross sections. The black points with error bars represent the data and their statistical uncertainties. The last bin includes the overflow events. The lower panels shows the ratio of the data to the expectation with the inner (outer) band representing the statistical (total) uncertainty in the combined signal and background expectations. |
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Figure 4-c:
Distribution of (upper left) photon $ p_{\mathrm{T}} $, (upper right) leading jet $ p_{\mathrm{T}} $, (lower left) $ m_\mathrm{jj} $, and (lower right) $ |\Delta\eta_{\text{jj}}| $ in data and simulated processes, except the contribution of nonprompt photons that is estimated from data as discussed in Section 5. Simulted samples are normalized to their theoretical cross sections. The black points with error bars represent the data and their statistical uncertainties. The last bin includes the overflow events. The lower panels shows the ratio of the data to the expectation with the inner (outer) band representing the statistical (total) uncertainty in the combined signal and background expectations. |
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Figure 4-d:
Distribution of (upper left) photon $ p_{\mathrm{T}} $, (upper right) leading jet $ p_{\mathrm{T}} $, (lower left) $ m_\mathrm{jj} $, and (lower right) $ |\Delta\eta_{\text{jj}}| $ in data and simulated processes, except the contribution of nonprompt photons that is estimated from data as discussed in Section 5. Simulted samples are normalized to their theoretical cross sections. The black points with error bars represent the data and their statistical uncertainties. The last bin includes the overflow events. The lower panels shows the ratio of the data to the expectation with the inner (outer) band representing the statistical (total) uncertainty in the combined signal and background expectations. |
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Figure 5:
Distribution of (upper left) $ C_{\gamma} $, (upper right) $ \Delta R(j_2,\gamma) $, and (lower) the Zeppenfeld variable in data and simulated processes, except the contribution of nonprompt photons that is estimated from data as discussed in Section 5. Simulted samples are normalized to their theoretical cross sections. The black points with error bars represent the data and their statistical uncertainties. The last bin includes the overflow events. The lower panels shows the ratio of the data to the expectation with the inner (outer) band representing the statistical (total) uncertainty in the combined signal and background expectations. |
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Figure 5-a:
Distribution of (upper left) $ C_{\gamma} $, (upper right) $ \Delta R(j_2,\gamma) $, and (lower) the Zeppenfeld variable in data and simulated processes, except the contribution of nonprompt photons that is estimated from data as discussed in Section 5. Simulted samples are normalized to their theoretical cross sections. The black points with error bars represent the data and their statistical uncertainties. The last bin includes the overflow events. The lower panels shows the ratio of the data to the expectation with the inner (outer) band representing the statistical (total) uncertainty in the combined signal and background expectations. |
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Figure 5-b:
Distribution of (upper left) $ C_{\gamma} $, (upper right) $ \Delta R(j_2,\gamma) $, and (lower) the Zeppenfeld variable in data and simulated processes, except the contribution of nonprompt photons that is estimated from data as discussed in Section 5. Simulted samples are normalized to their theoretical cross sections. The black points with error bars represent the data and their statistical uncertainties. The last bin includes the overflow events. The lower panels shows the ratio of the data to the expectation with the inner (outer) band representing the statistical (total) uncertainty in the combined signal and background expectations. |
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Figure 5-c:
Distribution of (upper left) $ C_{\gamma} $, (upper right) $ \Delta R(j_2,\gamma) $, and (lower) the Zeppenfeld variable in data and simulated processes, except the contribution of nonprompt photons that is estimated from data as discussed in Section 5. Simulted samples are normalized to their theoretical cross sections. The black points with error bars represent the data and their statistical uncertainties. The last bin includes the overflow events. The lower panels shows the ratio of the data to the expectation with the inner (outer) band representing the statistical (total) uncertainty in the combined signal and background expectations. |
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Figure 6:
The postfit BDT output distribution. The data are compared to the sum of the signal and the background contributions. The black points with error bars represent the data and their statistical uncertainties. The lower panel shows the ratio of the data to prediction where the inner (outer) band represents the statistical (total) uncertainty in the combined signal and background contributions after the fit. |
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Figure 7:
The rapidity gap fraction as a function of $ p_{\mathrm{T}}^{\text{veto}} $ in data and simulated samples for EW $ \gamma $\text{jj} and QCD \PGgjj. The black points with error bars represent the data and their statistical uncertainties. The theory prediction, calculated using MG5+PYTHIA, together with the MC statistical uncertainties are shown by the colored band. |
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Figure 8:
The unrolled BDT distribution in bins of the Zeppenfeld observable after the fit to the data. Signal events from different Zeppenfeld ranges at the generator level are represented by different colors, whereas different Zeppenfeld ranges at the detector level are displayed as an overlaid distribution. The different shades of green correspond to increasing ranges of the Zeppenfeld observable at the generator level ([0,0.7],[0.7,1.4],[1.4,2.1],[2.1,$ \infty $]). The label ``out'' refers to signal events outside the defined phase space. The black points with error bars represent the data and their statistical uncertainties. The lower panel shows the ratio of the data to the prediction. The inner and outer bands represent, respectively, the statistical and total uncertainties on all simulated samples after the fit. |
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Figure 9:
Normalized differential cross sections, compared with the SM predictions, as functions of (upper left) $ \eta_{\text{j}_1} $, (upper right) $ \eta_{\text{j}_2} $, (middle left) $ m_\mathrm{jj} $, (middle right) $ p_{\mathrm{T}}^\gamma $, (lower left) $ C_{\gamma} $, and (lower right) the Zeppenfeld variable. The red bars on the data points represent the statistical errors, whereas the black bars show the total uncertainties. |
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Figure 9-a:
Normalized differential cross sections, compared with the SM predictions, as functions of (upper left) $ \eta_{\text{j}_1} $, (upper right) $ \eta_{\text{j}_2} $, (middle left) $ m_\mathrm{jj} $, (middle right) $ p_{\mathrm{T}}^\gamma $, (lower left) $ C_{\gamma} $, and (lower right) the Zeppenfeld variable. The red bars on the data points represent the statistical errors, whereas the black bars show the total uncertainties. |
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Figure 9-b:
Normalized differential cross sections, compared with the SM predictions, as functions of (upper left) $ \eta_{\text{j}_1} $, (upper right) $ \eta_{\text{j}_2} $, (middle left) $ m_\mathrm{jj} $, (middle right) $ p_{\mathrm{T}}^\gamma $, (lower left) $ C_{\gamma} $, and (lower right) the Zeppenfeld variable. The red bars on the data points represent the statistical errors, whereas the black bars show the total uncertainties. |
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Figure 9-c:
Normalized differential cross sections, compared with the SM predictions, as functions of (upper left) $ \eta_{\text{j}_1} $, (upper right) $ \eta_{\text{j}_2} $, (middle left) $ m_\mathrm{jj} $, (middle right) $ p_{\mathrm{T}}^\gamma $, (lower left) $ C_{\gamma} $, and (lower right) the Zeppenfeld variable. The red bars on the data points represent the statistical errors, whereas the black bars show the total uncertainties. |
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Figure 9-d:
Normalized differential cross sections, compared with the SM predictions, as functions of (upper left) $ \eta_{\text{j}_1} $, (upper right) $ \eta_{\text{j}_2} $, (middle left) $ m_\mathrm{jj} $, (middle right) $ p_{\mathrm{T}}^\gamma $, (lower left) $ C_{\gamma} $, and (lower right) the Zeppenfeld variable. The red bars on the data points represent the statistical errors, whereas the black bars show the total uncertainties. |
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Figure 9-e:
Normalized differential cross sections, compared with the SM predictions, as functions of (upper left) $ \eta_{\text{j}_1} $, (upper right) $ \eta_{\text{j}_2} $, (middle left) $ m_\mathrm{jj} $, (middle right) $ p_{\mathrm{T}}^\gamma $, (lower left) $ C_{\gamma} $, and (lower right) the Zeppenfeld variable. The red bars on the data points represent the statistical errors, whereas the black bars show the total uncertainties. |
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Figure 9-f:
Normalized differential cross sections, compared with the SM predictions, as functions of (upper left) $ \eta_{\text{j}_1} $, (upper right) $ \eta_{\text{j}_2} $, (middle left) $ m_\mathrm{jj} $, (middle right) $ p_{\mathrm{T}}^\gamma $, (lower left) $ C_{\gamma} $, and (lower right) the Zeppenfeld variable. The red bars on the data points represent the statistical errors, whereas the black bars show the total uncertainties. |
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Figure 10:
The distribution of the DNN output trained for $ c_{\mathrm{W}} $ and $ c_{\mathrm{H}\mathrm{W}\mathrm{B}} $ coefficients in data and simulation. The simulation is corrected using the results of the inclusive $ \sigma_{\text{EW} {\gamma}\text{jj} } $ measurement. The black points with error bars represent the data and their statistical uncertainties. The purple and indigo lines show the distributions for the EW $ \gamma $\text{jj} process when $ c_{\mathrm{H}\mathrm{W}\mathrm{B}} $ and $ c_{\mathrm{W}} $, respectively, are set to one. The lower panel shows the ratio of the data to the prediction. The inner and outer bands represent, respectively, the statistical and total uncertainties on all simulated samples as evaluated in the inclusive $ \sigma_{\text{EW} {\gamma}\text{jj} } $ measurement. |
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Figure 11:
Negative of twice in the difference in the log-likelihood as a function of $ c_{\mathrm{W}} $ and $ c_{\mathrm{H}\mathrm{W}\mathrm{B}} $ based on 138 fb$ ^{-1} $ of CMS data at 13 TeV. Upper left: the one-dimensional likelihood scan for $ c_{\mathrm{W}} $, showing the observed (black solid line) and expected (red dashed line) standard values, with 68% and 95% confidence intervals indicated by horizontal dashed lines. Upper right: the one-dimensional likelihood scan for $ c_{\mathrm{H}\mathrm{W}\mathrm{B}} $, similarly presenting observed and expected limits. Lower: the two-dimensional likelihood contour for $ c_{\mathrm{W}} $ and $ c_{\mathrm{H}\mathrm{W}\mathrm{B}} $, indicating the standard model (black cross), the best fit values (red dot), and contours corresponding to one (red solid line) and two (red dashed line) standard deviations. |
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Figure 11-a:
Negative of twice in the difference in the log-likelihood as a function of $ c_{\mathrm{W}} $ and $ c_{\mathrm{H}\mathrm{W}\mathrm{B}} $ based on 138 fb$ ^{-1} $ of CMS data at 13 TeV. Upper left: the one-dimensional likelihood scan for $ c_{\mathrm{W}} $, showing the observed (black solid line) and expected (red dashed line) standard values, with 68% and 95% confidence intervals indicated by horizontal dashed lines. Upper right: the one-dimensional likelihood scan for $ c_{\mathrm{H}\mathrm{W}\mathrm{B}} $, similarly presenting observed and expected limits. Lower: the two-dimensional likelihood contour for $ c_{\mathrm{W}} $ and $ c_{\mathrm{H}\mathrm{W}\mathrm{B}} $, indicating the standard model (black cross), the best fit values (red dot), and contours corresponding to one (red solid line) and two (red dashed line) standard deviations. |
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Figure 11-b:
Negative of twice in the difference in the log-likelihood as a function of $ c_{\mathrm{W}} $ and $ c_{\mathrm{H}\mathrm{W}\mathrm{B}} $ based on 138 fb$ ^{-1} $ of CMS data at 13 TeV. Upper left: the one-dimensional likelihood scan for $ c_{\mathrm{W}} $, showing the observed (black solid line) and expected (red dashed line) standard values, with 68% and 95% confidence intervals indicated by horizontal dashed lines. Upper right: the one-dimensional likelihood scan for $ c_{\mathrm{H}\mathrm{W}\mathrm{B}} $, similarly presenting observed and expected limits. Lower: the two-dimensional likelihood contour for $ c_{\mathrm{W}} $ and $ c_{\mathrm{H}\mathrm{W}\mathrm{B}} $, indicating the standard model (black cross), the best fit values (red dot), and contours corresponding to one (red solid line) and two (red dashed line) standard deviations. |
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Figure 11-c:
Negative of twice in the difference in the log-likelihood as a function of $ c_{\mathrm{W}} $ and $ c_{\mathrm{H}\mathrm{W}\mathrm{B}} $ based on 138 fb$ ^{-1} $ of CMS data at 13 TeV. Upper left: the one-dimensional likelihood scan for $ c_{\mathrm{W}} $, showing the observed (black solid line) and expected (red dashed line) standard values, with 68% and 95% confidence intervals indicated by horizontal dashed lines. Upper right: the one-dimensional likelihood scan for $ c_{\mathrm{H}\mathrm{W}\mathrm{B}} $, similarly presenting observed and expected limits. Lower: the two-dimensional likelihood contour for $ c_{\mathrm{W}} $ and $ c_{\mathrm{H}\mathrm{W}\mathrm{B}} $, indicating the standard model (black cross), the best fit values (red dot), and contours corresponding to one (red solid line) and two (red dashed line) standard deviations. |
| Tables | |
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Table 1:
Expected event yields and their uncertainties for signal and backgrounds, including also the estimation of the nonprompt photon contribution. The number of observed data events are also included for comparison. |
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Table 2:
Summary of uncertainties affecting the measurement as extracted from the fit to data. The total uncertainty is obtained by adding individual contributions in quadrature. |
| Summary |
| The first observation has been presented of the electroweak production of a photon in association with two jets (EW $ \gamma \text{jj} $) using proton-proton collisions at $ \sqrt{s}= $ 13 TeV recorded with the CMS detector in 2016-2018 and corresponding to an integrated luminosity of 138 fb$ ^{-1} $. Events are selected by requiring a photon with transverse momentum $ p_{\mathrm{T}}^{\gamma} > $ 200 GeV and two jets separated by at least $ |\Delta \eta| > $ 2.5 with an invariant mass $ m_\mathrm{jj} > $ 500 GeV. The measured inclusive EW $ \gamma \text{jj}$ cross section is $ \sigma_{\text{EW} {\gamma}\text{jj} }= $ 202 $ \pm $ 7 (stat) $ ^{+35}_{-32} $ (syst) fb in agreement with the predicted standard model cross section of 177$ ^{+13}_{-12} $ fb. Normalized differential cross sections are also measured as functions of several observables and compared with standard model predictions at next to leading order in perturbative quantum chromodynamics. Within the uncertainties, predictions agree with measurements in all observables except the pseudorapidity of the tagging jets. In particular, measured normalized cross sections differ from prediction by about two standard deviations in the pseudorapidity distribution of the softer tagging jet. The gap fraction is measured in a signal-enriched region and is found to be in agreement with the prediction, supporting the accuracy of the modeling of hadronic activities in VBF-like processes. A deep neural network is trained to probe new WW$ \gamma $ interactions in the context of an effective field theory, described by dimension-6 operators. The observed 95% confidence intervals for the Warsaw basis Wilson coefficients $ c_{\mathrm{W}} $ and $ c_{\mathrm{H}\mathrm{W}\mathrm{B}} $ are [$-$0.11,0.16] and [$-$1.6,1.5], respectively. |
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