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CMS-SMP-20-016 ; CERN-EP-2021-095
Measurement of the electroweak production of Z$\gamma$ and two jets in proton-proton collisions at $\sqrt{s} = $ 13 TeV and constraints on anomalous quartic gauge couplings
Phys. Rev. D 104 (2021) 072001
Abstract: The first observation of the electroweak (EW) production of a Z boson, a photon, and two forward jets (Z$ \gamma $jj) in proton-proton collisions at a center-of-mass energy of 13 TeV is presented. A data set corresponding to an integrated luminosity of 137 fb$^{-1}$, collected by the CMS experiment at the LHC in 2016-2018 is used. The measured fiducial cross section for EW Z$ \gamma $jj is $\sigma_{\mathrm{EW}}=$ 5.21 $\pm$ 0.52 (stat) $\pm$ 0.56 (syst) fb $ = $ 5.21 $\pm$ 0.76 fb. Single-differential cross sections in photon, leading lepton, and leading jet transverse momenta, and double-differential cross sections in $m_{\mathrm{jj}}$ and $|{\Delta\eta_{\mathrm{jj}}}|$ are also measured. Exclusion limits on anomalous quartic gauge couplings are derived at 95% confidence level in terms of the effective field theory operators M$_{0}$ to M$_{5}$, M$_{7}$, T$_{0}$ to T$_{2}$, and T$_{5}$ to T$_{9}$.
Figures & Tables Summary References CMS Publications
Figures

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Figure 1:
Representative Feynman diagrams for Z$ \gamma $jj production. With the exception of the upper right one, the diagrams involve only EW vertices: VBS via W boson (upper left), VBS with QGC (upper center), vector boson fusion with TGCs (lower left), bremsstrahlung (lower center), multiperipheral (lower right), whereas the diagram (upper right) represents a QCD-induced contribution.

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Figure 1-a:
Representative Feynman diagram for Z$ \gamma $jj production. The diagram involves VBS via W bosons.

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Figure 1-b:
Representative Feynman diagram for Z$ \gamma $jj production. The diagram involves VBS with a QGC.

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Figure 1-c:
Representative Feynman diagram for Z$ \gamma $jj production. The diagram represents a QCD-induced contribution.

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Figure 1-d:
Representative Feynman diagram for Z$ \gamma $jj production. The diagram involves vector boson fusion with a TGC.

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Figure 1-e:
Representative Feynman diagram for Z$ \gamma $jj production. The diagram involves bremsstrahlung vertices.

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Figure 1-f:
Representative Feynman diagram for Z$ \gamma $jj production. The diagram involves multiperipheral vertices.

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Figure 2:
The pre-fit $m_{\mathrm {jj}}$ distributions for the dilepton+$\gamma _{\text {barrel}}$ events are shown for the dielectron (left) and the dimuon (right) categories with data collected from 2016 to 2018. 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, whereas the hatched bands represent the statistical uncertainty in the combined signal and background expectations. The last bin includes overflow events. The lower panel shows the ratio of the data to the expectation.

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Figure 2-a:
The pre-fit $m_{\mathrm {jj}}$ distributions for the dilepton+$\gamma _{\text {barrel}}$ events are shown for the dielectron category with data collected from 2016 to 2018. 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, whereas the hatched bands represent the statistical uncertainty in the combined signal and background expectations. The last bin includes overflow events. The lower panel shows the ratio of the data to the expectation.

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Figure 2-b:
The pre-fit $m_{\mathrm {jj}}$ distributions for the dilepton+$\gamma _{\text {barrel}}$ events are shown for the dimuon category with data collected from 2016 to 2018. 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, whereas the hatched bands represent the statistical uncertainty in the combined signal and background expectations. The last bin includes overflow events. The lower panel shows the ratio of the data to the expectation.

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Figure 3:
The pre-fit $m_{\mathrm {jj}}$ distributions for the dilepton+$\gamma _{\text {endcap}}$ events are shown for the dielectron (left) and the dimuon (right) categories with data collected from 2016 to 2018. 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, whereas the hatched bands represent the statistical uncertainty in the combined signal and background expectations. The last bin includes overflow events. The lower panel shows the ratio of the data to the expectation.

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Figure 3-a:
The pre-fit $m_{\mathrm {jj}}$ distributions for the dilepton+$\gamma _{\text {endcap}}$ events are shown for the dielectron category with data collected from 2016 to 2018. 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, whereas the hatched bands represent the statistical uncertainty in the combined signal and background expectations. The last bin includes overflow events. The lower panel shows the ratio of the data to the expectation.

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Figure 3-b:
The pre-fit $m_{\mathrm {jj}}$ distributions for the dilepton+$\gamma _{\text {endcap}}$ events are shown for the dimuon category with data collected from 2016 to 2018. 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, whereas the hatched bands represent the statistical uncertainty in the combined signal and background expectations. The last bin includes overflow events. The lower panel shows the ratio of the data to the expectation.

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Figure 4:
The post-fit 2D distributions of the dielectron (left) and dimuon (right) for the $\gamma _{\text {barrel}}$ categories, as functions of $m_\mathrm {jj}$ in bins of $ {| \Delta \eta _{\mathrm {jj}} |}$. The horizontal axis is split into bins of $ {| \Delta \eta _{\mathrm {jj}} |}$ of [2.5, 4.5], [4.5, 6.0], and $ > $6.0. The data are compared to the signal and background in the predictions. The black points with error bars represent the data and their statistical uncertainties, whereas the hatched bands represent the total uncertainties of the predictions.

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Figure 4-a:
The post-fit 2D distributions of the dielectron for the $\gamma _{\text {barrel}}$ categories, as functions of $m_\mathrm {jj}$ in bins of $ {| \Delta \eta _{\mathrm {jj}} |}$. The horizontal axis is split into bins of $ {| \Delta \eta _{\mathrm {jj}} |}$ of [2.5, 4.5], [4.5, 6.0], and $ > $6.0. The data are compared to the signal and background in the predictions. The black points with error bars represent the data and their statistical uncertainties, whereas the hatched bands represent the total uncertainties of the predictions.

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Figure 4-b:
The post-fit 2D distributions of the dimuon for the $\gamma _{\text {barrel}}$ categories, as functions of $m_\mathrm {jj}$ in bins of $ {| \Delta \eta _{\mathrm {jj}} |}$. The horizontal axis is split into bins of $ {| \Delta \eta _{\mathrm {jj}} |}$ of [2.5, 4.5], [4.5, 6.0], and $ > $6.0. The data are compared to the signal and background in the predictions. The black points with error bars represent the data and their statistical uncertainties, whereas the hatched bands represent the total uncertainties of the predictions.

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Figure 5:
The post-fit 2D distributions of the dielectron (left) and dimuon (right) for the $\gamma _{\text {endcap}}$ categories, as functions of $m_\mathrm {jj}$ in bins of $ {| \Delta \eta _{\mathrm {jj}} |}$. The horizontal axis is split into bins of $ {| \Delta \eta _{\mathrm {jj}} |}$ of [2.5, 4.5], [4.5, 6.0], and $ > $6.0. The data are compared to the signal and background in the predictions. The black points with error bars represent the data and their statistical uncertainties, whereas the hatched bands represent the total uncertainties of the predictions.

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Figure 5-a:
The post-fit 2D distributions of the dielectron for the $\gamma _{\text {endcap}}$ categories, as functions of $m_\mathrm {jj}$ in bins of $ {| \Delta \eta _{\mathrm {jj}} |}$. The horizontal axis is split into bins of $ {| \Delta \eta _{\mathrm {jj}} |}$ of [2.5, 4.5], [4.5, 6.0], and $ > $6.0. The data are compared to the signal and background in the predictions. The black points with error bars represent the data and their statistical uncertainties, whereas the hatched bands represent the total uncertainties of the predictions.

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Figure 5-b:
The post-fit 2D distributions of the dimuon for the $\gamma _{\text {endcap}}$ categories, as functions of $m_\mathrm {jj}$ in bins of $ {| \Delta \eta _{\mathrm {jj}} |}$. The horizontal axis is split into bins of $ {| \Delta \eta _{\mathrm {jj}} |}$ of [2.5, 4.5], [4.5, 6.0], and $ > $6.0. The data are compared to the signal and background in the predictions. The black points with error bars represent the data and their statistical uncertainties, whereas the hatched bands represent the total uncertainties of the predictions.

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Figure 6:
The post-fit distributions in the control region for the dielectron (left) and dimuon (right) for the $\gamma _{\text {barrel}}$ categories as a function of $m_\mathrm {jj}$. The horizontal axis is split into bins of $m_{\mathrm {jj}}$ of [150, 300], [300, 400], and [400,500]. The black points with error bars represent the data and their statistical uncertainties, whereas the hatched bands represent the total uncertainties of the predictions.

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Figure 6-a:
The post-fit distributions in the control region for the dielectron for the $\gamma _{\text {barrel}}$ categories as a function of $m_\mathrm {jj}$. The horizontal axis is split into bins of $m_{\mathrm {jj}}$ of [150, 300], [300, 400], and [400,500]. The black points with error bars represent the data and their statistical uncertainties, whereas the hatched bands represent the total uncertainties of the predictions.

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Figure 6-b:
The post-fit distributions in the control region for the dimuon for the $\gamma _{\text {barrel}}$ categories as a function of $m_\mathrm {jj}$. The horizontal axis is split into bins of $m_{\mathrm {jj}}$ of [150, 300], [300, 400], and [400,500]. The black points with error bars represent the data and their statistical uncertainties, whereas the hatched bands represent the total uncertainties of the predictions.

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Figure 7:
The post-fit distributions in the control region for the dielectron (left) and dimuon (right) for the $\gamma _{\text {endcap}}$ categories as a function of $m_\mathrm {jj}$. The horizontal axis is split into bins of $m_{\mathrm {jj}}$ of [150, 300], [300, 400], and [400,500]. The black points with error bars represent the data and their statistical uncertainties, whereas the hatched bands represent the total uncertainties of the predictions.

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Figure 7-a:
The post-fit distributions in the control region for the dielectron for the $\gamma _{\text {endcap}}$ categories as a function of $m_\mathrm {jj}$. The horizontal axis is split into bins of $m_{\mathrm {jj}}$ of [150, 300], [300, 400], and [400,500]. The black points with error bars represent the data and their statistical uncertainties, whereas the hatched bands represent the total uncertainties of the predictions.

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Figure 7-b:
The post-fit distributions in the control region for the dimuon for the $\gamma _{\text {endcap}}$ categories as a function of $m_\mathrm {jj}$. The horizontal axis is split into bins of $m_{\mathrm {jj}}$ of [150, 300], [300, 400], and [400,500]. The black points with error bars represent the data and their statistical uncertainties, whereas the hatched bands represent the total uncertainties of the predictions.

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Figure 8:
Unfolded differential cross section as a function of the leading lepton ${p_{\mathrm {T}}}$, leading jet ${p_{\mathrm {T}}}$, leading photon ${p_{\mathrm {T}}}$, and $m_{\mathrm {jj}}$-$ {| \Delta \eta _{\mathrm {jj}} |}$ for EW Z$ \gamma $jj. The black points with error bars represent the data and their statistical uncertainties, whereas the red bands represent the total theoretical uncertainties from the MG5 simulation. The last bin includes overflow events.

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Figure 8-a:
Unfolded differential cross section as a function of the leading lepton ${p_{\mathrm {T}}}$ for EW Z$ \gamma $jj. The black points with error bars represent the data and their statistical uncertainties, whereas the red bands represent the total theoretical uncertainties from the MG5 simulation. The last bin includes overflow events.

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Figure 8-b:
Unfolded differential cross section as a function of leading jet ${p_{\mathrm {T}}}$ for EW Z$ \gamma $jj. The black points with error bars represent the data and their statistical uncertainties, whereas the red bands represent the total theoretical uncertainties from the MG5 simulation. The last bin includes overflow events.

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Figure 8-c:
Unfolded differential cross section as a function of leading photon ${p_{\mathrm {T}}}$ for EW Z$ \gamma $jj. The black points with error bars represent the data and their statistical uncertainties, whereas the red bands represent the total theoretical uncertainties from the MG5 simulation. The last bin includes overflow events.

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Figure 8-d:
Unfolded differential cross section as a function of $m_{\mathrm {jj}}$-$ {| \Delta \eta _{\mathrm {jj}} |}$ for EW Z$ \gamma $jj. The black points with error bars represent the data and their statistical uncertainties, whereas the red bands represent the total theoretical uncertainties from the MG5 simulation. The last bin includes overflow events.

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Figure 9:
Unfolded differential cross section as a function of the leading lepton ${p_{\mathrm {T}}}$, leading photon ${p_{\mathrm {T}}}$, leading jet ${p_{\mathrm {T}}}$, and $m_{\mathrm {jj}}$-$ {| \Delta \eta _{\mathrm {jj}} |}$ for EW+QCD Z$ \gamma $jj. The black points with error bars represent the data and their statistical uncertainties, whereas the red bands represent the total theoretical uncertainties from the MG5 simulation. The last bin includes overflow events.

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Figure 9-a:
Unfolded differential cross section as a function of the leading lepton ${p_{\mathrm {T}}}$ for EW+QCD Z$ \gamma $jj. The black points with error bars represent the data and their statistical uncertainties, whereas the red bands represent the total theoretical uncertainties from the MG5 simulation. The last bin includes overflow events.

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Figure 9-b:
Unfolded differential cross section as a function of the leading photon ${p_{\mathrm {T}}}$ for EW+QCD Z$ \gamma $jj. The black points with error bars represent the data and their statistical uncertainties, whereas the red bands represent the total theoretical uncertainties from the MG5 simulation. The last bin includes overflow events.

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Figure 9-c:
Unfolded differential cross section as a function of the leading jet ${p_{\mathrm {T}}}$ for EW+QCD Z$ \gamma $jj. The black points with error bars represent the data and their statistical uncertainties, whereas the red bands represent the total theoretical uncertainties from the MG5 simulation. The last bin includes overflow events.

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Figure 9-d:
Unfolded differential cross section as a function of the $m_{\mathrm {jj}}$-$ {| \Delta \eta _{\mathrm {jj}} |}$ for EW+QCD Z$ \gamma $jj. The black points with error bars represent the data and their statistical uncertainties, whereas the red bands represent the total theoretical uncertainties from the MG5 simulation. The last bin includes overflow events.

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Figure 10:
The $m_{\mathrm{Z} \gamma}$ distribution for events satisfying the aQGC region selection, which is used to set constraints on the anomalous coupling parameters. The bins of $m_{\mathrm{Z} \gamma}$ are [150, 400, 600, 800, 1000, 1200, 2000] GeV, where the last bin includes overflow events. The red line represents a nonzero $F_{\mathrm {T8}}$ value and the blue line represents a nonzero $F_{\mathrm {T9}}$ value, which would significantly enhance the yields at high $m_{\mathrm{Z} \gamma}$. The black points with error bars represent the data and their statistical uncertainties, whereas the hatched bands represent the statistical uncertainties in the SM predictions.
Tables

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Table 1:
Summary of the five sets of event selection criteria used to define events in the fiducial cross section measurement region, control region, EW signal extraction region, and the region used to search for aQGC contributions.

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Table 2:
The impact of the systematic uncertainties on the EW signal strength measurement.

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Table 3:
Post-fit yields of predicted signal and background with total uncertainties, and observed event counts after the selection in the EW signal region. The $\gamma _{\text {barrel}}$ and $\gamma _{\text {endcap}}$ columns represent events with photons in the ECAL barrel and endcaps, respectively.

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Table 4:
The signal strengths and differential cross sections from SM expectation and fit calculated as part of the unfolding of $ {p_{\mathrm {T}}} ^{\gamma}$, $ {p_{\mathrm {T}}} ^{\mathrm {j}_1}$, and $ {p_{\mathrm {T}}} ^{\ell _1}$ observables for EW Z$ \gamma $jj. The last bin includes overflow events.

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Table 5:
The signal strengths and differential cross sections from SM expectation and fit calculated as part of the unfolding of 2D $m_{\mathrm {jj}}$-$ {| \Delta \eta _{\mathrm {jj}} |}$ observables for EW Z$ \gamma $jj. The last bin includes overflow events.

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Table 6:
The signal strengths and differential cross sections from SM expectation and fit calculated as part of the unfolding of $ {p_{\mathrm {T}}} ^{\gamma}$, $ {p_{\mathrm {T}}} ^{\mathrm {j}_1}$, and $ {p_{\mathrm {T}}} ^{\ell _1}$ observables for EW+QCD Z$ \gamma $jj. The last bin includes overflow events.

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Table 7:
The signal strengths and differential cross sections from SM expectation and fit calculated as part of the unfolding of 2D $m_{\mathrm {jj}}$-$ {| \Delta \eta _{\mathrm {jj}} |}$ observables for EW+QCD Z$ \gamma $jj. The last bin includes overflow events.

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Table 8:
The expected and observed limits on the aQGC parameters at 95% confidence level. The last column presents the scattering energy values for which the amplitude would violate unitarity for the observed value of the aQGC parameter. All coupling parameter limits are set in $ TeV ^{-4}$, whereas the unitarity bounds are in TeV.
Summary
This paper presents the first observation of the electroweak (EW) production of a Z boson, a photon, and two jets (Z$ \gamma $jj) in $\sqrt{s} = $ 13 TeV proton-proton collisions recorded with the CMS detector in 2016-2018 corresponding to an integrated luminosity of 137 fb$^{-1}$. Events were selected by requiring two opposite-sign leptons with the same flavor from the decay of a Z boson, one identified photon, and two jets that have a large separation in pseudorapidity and a large dijet mass. The measured cross section in the fiducial volume defined in Table 1 for EW Z$ \gamma $jj production is 5.21 $\pm$ 0.52 (stat) $\pm$ 0.56 (syst) fb $ = $ 5.21 $\pm$ 0.76 fb, and the fiducial cross section of EW and QCD-induced production is 14.7 $\pm$ 0.80 (stat) $\pm$ 1.26 (syst) fb $ = $ 14.7 $\pm$ 1.53 fb. Both the observed and expected signal significances are well in excess of 5 standard deviations. Differential cross sections for EW and EW+QCD are measured for several observables and compared to standard model predictions computed at leading order. Within the uncertainties, the measurements agree with the predictions. Constraints are set on the effective field theory dimension-8 operators M$_{0}$ to M$_{5}$, M$_{7}$, T$_{0}$ to T$_{2}$, and T$_{5}$ to T$_{9}$, giving rise to anomalous quartic gauge couplings. These constraints are either competitive with or more stringent than those previously obtained.
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Compact Muon Solenoid
LHC, CERN