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| CMS-SMP-22-009 ; CERN-EP-2025-206 | ||
| Measurement of the $ \mathrm{Z}\gamma $ production cross section and search for anomalous neutral triple gauge couplings in pp collisions at $ \sqrt{s}= $ 13 TeV | ||
| CMS Collaboration | ||
| 20 January 2026 | ||
| Submitted to J. High Energy Phys. | ||
| Abstract: A measurement of the fiducial cross section of the associated production of a Z boson and a high-$ p_{\mathrm{T}} $ photon, where the Z decays to two neutrinos, and a search for anomalous triple gauge couplings are reported. The results are based on data collected by the CMS experiment at the LHC in proton-proton collisions at $ \sqrt{s}= $ 13 TeV during 2016--2018, corresponding to an integrated luminosity of 138 fb$ ^{-1} $. The fiducial $ \mathrm{Z}\gamma $ cross section, where a photon with a $ p_{\mathrm{T}} $ greater than 225 GeV is produced in association with a Z, and the Z decays to a $ \nu\overline{\nu} $ pair ($ \mathrm{Z}(\nu\overline{\nu})\gamma $), is measured to be 23.3 $ ^{+1.4}_{-1.3} $ fb, in agreement, within uncertainties, with the standard model prediction. The differential cross section as a function of the photon $ p_{\mathrm{T}} $ has been measured and compared with standard model predictions computed at next-to-leading and at next-to-next-to-leading order in perturbative quantum chromodynamics. Constraints have been placed on the presence of anomalous couplings that affect the $ \mathrm{Z}\mathrm{Z}\gamma $ and $ \mathrm{Z}\gamma\gamma $ vertex using the $ p_{\mathrm{T}} $ spectrum of the photons. The observed 95% confidence level intervals for $ CP $-conserving $ h_3^{\gamma} $ and $ h_4^{\gamma} $ are determined to be (-3.4, 3.5)$ \times10^{-4} $ and (-6.8, 6.8)$ \times10^{-7} $, and for $ h_3^{\mathrm{Z}} $ and $ h_4^{\mathrm{Z}} $ they are (-2.2, 2.2)$ \times10^{-4} $ and (-4.1, 4.2)$ \times10^{-7} $, respectively. These are the strictest limits to date on $ h_3^{\gamma} $, $ h_3^{\mathrm{Z}} $ and $ h_4^{\mathrm{Z}} $. | ||
| Links: e-print arXiv:2601.14102 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
The Feynman diagram for the $ \mathrm{Z}\mathrm{V}\gamma $ vertex, where $ \mathrm{V} =\gamma^{*}/\mathrm{Z}^{*} $, in the presence of an aNTGC. |
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Figure 2:
The leading-order Feynman diagram for SM $ \mathrm{Z}\gamma $ production in the $ t $-channel (left), and (right) the additional diagram for the beyond SM \textits-channel $ \mathrm{Z}\gamma $ production due to the presence of aNTGCs. |
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Figure 2-a:
The leading-order Feynman diagram for SM $ \mathrm{Z}\gamma $ production in the $ t $-channel (left), and (right) the additional diagram for the beyond SM \textits-channel $ \mathrm{Z}\gamma $ production due to the presence of aNTGCs. |
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Figure 2-b:
The leading-order Feynman diagram for SM $ \mathrm{Z}\gamma $ production in the $ t $-channel (left), and (right) the additional diagram for the beyond SM \textits-channel $ \mathrm{Z}\gamma $ production due to the presence of aNTGCs. |
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Figure 3:
The photon $ p_{\mathrm{T}} $ spectrum for various values of aNTGC couplings and the SM predictions. |
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Figure 4:
The post-fit reconstruction-level distributions in the signal region after the combined (barrel+endcap) differential cross section fit (left: barrel region, right: endcap region). The Predicted distribution is the full model with all parameters fixed to their post-fit values. Note in particular that the free cross section parameters for the signal are also fixed to their post-fit values and then propagated through the response matrix. The bars on the black data points indicate the statistical uncertainty in the data, while the red band shows the total post-fit model uncertainty. |
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Figure 4-a:
The post-fit reconstruction-level distributions in the signal region after the combined (barrel+endcap) differential cross section fit (left: barrel region, right: endcap region). The Predicted distribution is the full model with all parameters fixed to their post-fit values. Note in particular that the free cross section parameters for the signal are also fixed to their post-fit values and then propagated through the response matrix. The bars on the black data points indicate the statistical uncertainty in the data, while the red band shows the total post-fit model uncertainty. |
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Figure 4-b:
The post-fit reconstruction-level distributions in the signal region after the combined (barrel+endcap) differential cross section fit (left: barrel region, right: endcap region). The Predicted distribution is the full model with all parameters fixed to their post-fit values. Note in particular that the free cross section parameters for the signal are also fixed to their post-fit values and then propagated through the response matrix. The bars on the black data points indicate the statistical uncertainty in the data, while the red band shows the total post-fit model uncertainty. |
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Figure 5:
Measured and predicted differential cross sections as function of $ p_{\mathrm{T}}^{\gamma} $ for the combined fiducial phase space. The colored bands associated with the predictions indicate the theoretical uncertainties associated with the MadGraph-5\_aMC@NLO and MATRIX generators. For the measured cross sections, the grey band indicates the statistical uncertainty of the fit, while the error bars on the black data points indicate the total uncertainty of the fit, including both statistical and systematic components. |
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Figure 6:
Confidence contours of the aNTGC parameters $ h_3^\gamma, h_4^\gamma $ (left) and $ h_3^\mathrm{Z}, h_4^\mathrm{Z} $ (right) with the best fit points, which are the local minima of the negative log likelihood. |
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Figure 6-a:
Confidence contours of the aNTGC parameters $ h_3^\gamma, h_4^\gamma $ (left) and $ h_3^\mathrm{Z}, h_4^\mathrm{Z} $ (right) with the best fit points, which are the local minima of the negative log likelihood. |
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Figure 6-b:
Confidence contours of the aNTGC parameters $ h_3^\gamma, h_4^\gamma $ (left) and $ h_3^\mathrm{Z}, h_4^\mathrm{Z} $ (right) with the best fit points, which are the local minima of the negative log likelihood. |
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Figure 7:
Comparison of the predicted distribution of $ p_{\mathrm{T}}^{\gamma} $ under the SM-only hypothesis in the barrel (left), and in the endcaps (right) phase space with the predictions at the upper boundaries of the observed 1D confidence intervals of the coupling parameters. The lower panels compare the SM (shown in red) and the aNTGC predictions, with the observed $ p_{\mathrm{T}}^{\gamma} $ distribution (shown in black). The error bars in both the upper and the lower panels are statistical only. |
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Figure 7-a:
Comparison of the predicted distribution of $ p_{\mathrm{T}}^{\gamma} $ under the SM-only hypothesis in the barrel (left), and in the endcaps (right) phase space with the predictions at the upper boundaries of the observed 1D confidence intervals of the coupling parameters. The lower panels compare the SM (shown in red) and the aNTGC predictions, with the observed $ p_{\mathrm{T}}^{\gamma} $ distribution (shown in black). The error bars in both the upper and the lower panels are statistical only. |
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Figure 7-b:
Comparison of the predicted distribution of $ p_{\mathrm{T}}^{\gamma} $ under the SM-only hypothesis in the barrel (left), and in the endcaps (right) phase space with the predictions at the upper boundaries of the observed 1D confidence intervals of the coupling parameters. The lower panels compare the SM (shown in red) and the aNTGC predictions, with the observed $ p_{\mathrm{T}}^{\gamma} $ distribution (shown in black). The error bars in both the upper and the lower panels are statistical only. |
| Tables | |
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Table 1:
Sources of systematic uncertainties and their estimated contributions. The $ \checkmark $ symbol indicates full correlation between the data-taking years. |
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Table 2:
Post-fit event yields in the photon-$ p_{\mathrm{T}} $ spectrum for the combined phase space. These numbers are extracted after a simultaneous fit to the data in the signal and control regions. The ``others'' background include contributions from $ \text{nonfiducial} \mathrm{Z}(\nu\overline{\nu})\gamma $, $ \mathrm{Z}/\gamma^{\ast}(\ell^+\ell^-)\gamma $, $ {\mathrm{t}\overline{\mathrm{t}}} \gamma $, $ \mathrm{W}\mathrm{V}\gamma $, single-t+$ \gamma $, VV, single-W, and jet misidentified as a photon. |
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Table 3:
Measured and predicted cross sections in femtobarns evaluated in the barrel, the endcaps, and the combined fiducial phase space. The predicted cross sections are calculated at NLO and NNLO in QCD. Due to nuisance parameters being pulled to different values in different fit configurations, the sum of the cross section in the EB and EE is not exactly equal to the combined cross section. |
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Table 4:
Measured and predicted cross sections in femtobarns in bins of $ p_{\mathrm{T}}^{\gamma} $. |
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Table 5:
Expected and observed 95% confidence level intervals of the parameters of anomalous couplings (with the other parameters fixed at zero). |
| Summary |
| We have measured the inclusive and differential cross sections of $ \mathrm{Z}(\nu\overline{\nu})\gamma $ in proton-proton collisions at $ \sqrt{s}= $ 13 TeV using data collected with the CMS detector between 2016 and 2018, corresponding to an integrated luminosity of 138 fb$ ^{-1} $. The fiducial $ \mathrm{Z}\gamma $ cross section, where a photon with a $ p_{\mathrm{T}} $ greater than 225 GeV is produced in association with a Z, and the Z decays to a $ \nu\overline{\nu} $ pair ($ \mathrm{Z}(\nu\overline{\nu})\gamma $), is measured to be 23.3 $ ^{+1.4}_{-1.3} $ fb$ ^{-1} $, in agreement, within uncertainties, with the standard model prediction, which are 26.07 $ ^{+0.96}_{-0.97} $ fb from MadGraph-5\_aMC@NLO and 25.45 $ ^{+0.41}_{-0.33} $ fb from MATRIX (NNLO). The differential $ \mathrm{Z}(\nu\overline{\nu})\gamma $ cross section as function of photon transverse momentum has been measured and compared with the standard model predictions computed at next-to-leading and next-to-next-to-leading orders in perturbative quantum chromodynamics. With these data we have probed the presence of anomalous couplings that affect the $ \mathrm{Z}\mathrm{Z}\gamma $ vertex by using the $ p_{\mathrm{T}} $ spectrum of the photons as the sensitive variable. No evidence is found for anomalous neutral trilinear gauge couplings in $ \mathrm{Z}\gamma $ production. The observed 95% confidence level intervals for $ h_3^{\gamma} $ and $ h_4^{\gamma} $ are determined to be (-3.4, 3.5)$ \times10^{-4} $ and (-6.8, 6.8)$ \times10^{-7} $; and for $ h_3^{\mathrm{Z}} $ and $ h_4^{\mathrm{Z}} $ (-2.2, 2.2)$ \times10^{-4} $ and (-4.1, 4.2)$ \times10^{-7} $, respectively. These are stricter than the earlier limits on $ h_3^{\gamma} $, $ h_3^{\mathrm{Z}} $, and $ h_4^{\mathrm{Z}} $. |
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