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CMS-SMP-19-013 ; CERN-EP-2021-073
Measurements of the ${\mathrm{p}}{\mathrm{p}}\to\mathrm{W^{\pm}}\gamma\gamma$ and ${\mathrm{p}}{\mathrm{p}}\to\mathrm{Z}\gamma\gamma$ cross sections at $\sqrt s = $ 13 TeV and limits on anomalous quartic gauge couplings
JHEP 10 (2021) 174
Abstract: The cross section for W or Z boson production in association with two photons is measured in proton-proton collisions at a centre-of-mass energy of 13 TeV. The data set corresponds to an integrated luminosity of 137 fb$^{-1}$ collected by the CMS experiment at the LHC. The $\mathrm{W}\to\ell\nu$ and $\mathrm{Z}\to\ell\ell$ decay modes (where $\ell=$ e, $\mu$) are used to extract the W$\gamma\gamma$ and Z$\gamma\gamma$ cross sections in a phase space defined by electron (muon) with transverse momentum larger than 35 (30) GeV and photon transverse momentum larger than 20 GeV. The measured cross sections in this phase space are $\sigma(\mathrm{W}\gamma\gamma)=$ 13.6$^{+1.9}_{-1.9}$ (stat)$^{+4.0}_{-4.0}$ (syst) $\pm$ 0.08 (PDF+scale) fb and $\sigma(\mathrm{Z}\gamma\gamma)=$ 5.41$^{+0.58}_{-0.55}$ (stat)$^{+0.64}_{-0.70}$ (syst) $\pm$ 0.06 (PDF+scale) fb. Limits on anomalous quartic gauge couplings are set in the framework of an effective field theory with dimension-8 operators.
Figures & Tables Summary References CMS Publications
Figures

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Figure 1:
Representative Feynman diagrams for the V$\gamma \gamma $ production in the SM (left and centre) and beyond the SM (right).

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Figure 1-a:
Representative Feynman diagram for the V$\gamma \gamma $ production in the SM.

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Figure 1-b:
Representative Feynman diagram for the V$\gamma \gamma $ production in the SM.

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Figure 1-c:
Representative Feynman diagram for the V$\gamma \gamma $ production in the SM.

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Figure 1-d:
Representative Feynman diagram for the V$\gamma \gamma $ production beyond the SM.

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Figure 2:
Distribution of the transverse momentum of the diphoton system for the W$\gamma \gamma $ electron (upper left) and muon (upper right) channels and for the Z$\gamma \gamma $ electron (lower left) and muon (lower right) channels. The predicted yields are shown with their pre-fit normalisations. The black points represent the data with error bars showing the statistical uncertainties. The hatched histogram shows the expected signal contribution. The background estimate for electron (jet) misidentified as photons, obtained from control samples in data, is shown in light brown (purple). The remaining background, derived from MC simulation, is shown in green. In the ratio plots, the grey hashed area is the statistical uncertainty on the sum of signal and backgrounds, while the uncertainty in the black dots is the statistical uncertainty of the data. In blue, the expected distribution for an example value of the anomalous coupling parameters $f_{\mathrm {M}3}/\Lambda ^4$ and $f_{\mathrm {T}0}/\Lambda ^4$ is also shown (see Section 8 for the details).

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Figure 2-a:
Distribution of the transverse momentum of the diphoton system for the W$\gamma \gamma $ electron channel. The predicted yields are shown with their pre-fit normalisations. The black points represent the data with error bars showing the statistical uncertainties. The hatched histogram shows the expected signal contribution. The background estimate for electron (jet) misidentified as photons, obtained from control samples in data, is shown in light brown (purple). The remaining background, derived from MC simulation, is shown in green. In the ratio plot, the grey hashed area is the statistical uncertainty on the sum of signal and backgrounds, while the uncertainty in the black dots is the statistical uncertainty of the data. In blue, the expected distribution for an example value of the anomalous coupling parameters $f_{\mathrm {M}3}/\Lambda ^4$ and $f_{\mathrm {T}0}/\Lambda ^4$ is also shown (see Section 8 for the details).

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Figure 2-b:
Distribution of the transverse momentum of the diphoton system for the W$\gamma \gamma $ muon channel. The predicted yields are shown with their pre-fit normalisations. The black points represent the data with error bars showing the statistical uncertainties. The hatched histogram shows the expected signal contribution. The background estimate for electron (jet) misidentified as photons, obtained from control samples in data, is shown in light brown (purple). The remaining background, derived from MC simulation, is shown in green. In the ratio plot, the grey hashed area is the statistical uncertainty on the sum of signal and backgrounds, while the uncertainty in the black dots is the statistical uncertainty of the data. In blue, the expected distribution for an example value of the anomalous coupling parameters $f_{\mathrm {M}3}/\Lambda ^4$ and $f_{\mathrm {T}0}/\Lambda ^4$ is also shown (see Section 8 for the details).

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Figure 2-c:
Distribution of the transverse momentum of the diphoton system for the Z$\gamma \gamma $ electron channel. The predicted yields are shown with their pre-fit normalisations. The black points represent the data with error bars showing the statistical uncertainties. The hatched histogram shows the expected signal contribution. The background estimate for electron (jet) misidentified as photons, obtained from control samples in data, is shown in light brown (purple). The remaining background, derived from MC simulation, is shown in green. In the ratio plot, the grey hashed area is the statistical uncertainty on the sum of signal and backgrounds, while the uncertainty in the black dots is the statistical uncertainty of the data. In blue, the expected distribution for an example value of the anomalous coupling parameters $f_{\mathrm {M}3}/\Lambda ^4$ and $f_{\mathrm {T}0}/\Lambda ^4$ is also shown (see Section 8 for the details).

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Figure 2-d:
Distribution of the transverse momentum of the diphoton system for the Z$\gamma \gamma $ muon channel. The predicted yields are shown with their pre-fit normalisations. The black points represent the data with error bars showing the statistical uncertainties. The hatched histogram shows the expected signal contribution. The background estimate for electron (jet) misidentified as photons, obtained from control samples in data, is shown in light brown (purple). The remaining background, derived from MC simulation, is shown in green. In the ratio plot, the grey hashed area is the statistical uncertainty on the sum of signal and backgrounds, while the uncertainty in the black dots is the statistical uncertainty of the data. In blue, the expected distribution for an example value of the anomalous coupling parameters $f_{\mathrm {M}3}/\Lambda ^4$ and $f_{\mathrm {T}0}/\Lambda ^4$ is also shown (see Section 8 for the details).

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Figure 3:
Distribution of the transverse momentum of the diphoton system, obtained in the control region enriched in misidentified photons, for the W$\gamma \gamma $ and for the Z$\gamma \gamma $ electron channels. The black points represent the data with error bars showing the statistical uncertainties. The hatched histogram shows the expected negligible signal contribution. The background estimate for electron (jet) misidentified as photons, obtained from control samples in data, is shown in light brown (purple). The remaining backgrounds, derived from MC simulation, are shown in green. In the ratio plots, the grey hashed area is the statistical uncertainty on the sum of signal and backgrounds, while the uncertainty in the black dots is the statistical uncertainty of the data.

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Figure 3-a:
Distribution of the transverse momentum of the diphoton system, obtained in the control region enriched in misidentified photons, for the W$\gamma \gamma $ electron channel. The black points represent the data with error bars showing the statistical uncertainties. The hatched histogram shows the expected negligible signal contribution. The background estimate for electron (jet) misidentified as photons, obtained from control samples in data, is shown in light brown (purple). The remaining backgrounds, derived from MC simulation, are shown in green. In the ratio plot, the grey hashed area is the statistical uncertainty on the sum of signal and backgrounds, while the uncertainty in the black dots is the statistical uncertainty of the data.

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Figure 3-b:
Distribution of the transverse momentum of the diphoton system, obtained in the control region enriched in misidentified photons, for the Z$\gamma \gamma $ electron channel. The black points represent the data with error bars showing the statistical uncertainties. The hatched histogram shows the expected negligible signal contribution. The background estimate for electron (jet) misidentified as photons, obtained from control samples in data, is shown in light brown (purple). The remaining backgrounds, derived from MC simulation, are shown in green. In the ratio plot, the grey hashed area is the statistical uncertainty on the sum of signal and backgrounds, while the uncertainty in the black dots is the statistical uncertainty of the data.

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Figure 4:
Best fit values of the signal strengths for the W$\gamma \gamma $ (left) and Z$\gamma \gamma $ (right) channels. The error bars represent the total uncertainty while the magenta bands represent the theoretical uncertainty in the MadGraph 5_aMC@NLO cross section.

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Figure 4-a:
Best fit values of the signal strengths for the W$\gamma \gamma $ channel. The error bars represent the total uncertainty while the magenta bands represent the theoretical uncertainty in the MadGraph 5_aMC@NLO cross section.

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Figure 4-b:
Best fit values of the signal strengths for the Z$\gamma \gamma $ channel. The error bars represent the total uncertainty while the magenta bands represent the theoretical uncertainty in the MadGraph 5_aMC@NLO cross section.
Tables

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Table 1:
Summary of the systematic uncertainties (in percent) for the W$\gamma \gamma $ and Z$\gamma \gamma $ cross section measurements. The numbers indicate the impact of each systematic uncertainty in the value of the measured cross section in the corresponding channel.

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Table 2:
Summary of the pre-fit predicted and observed numbers of events for 137 fb$^{-1}$ for the W$\gamma \gamma $ (upper Table) and Z$\gamma \gamma $ (lower Table) selections in the electron and muon channels. The systematic uncertainties of the individual backgrounds and the total background are obtained by summing the contributions of different systematic uncertainties in quadrature. The statistical uncertainties are those related to the MC event samples and control region statistical uncertainties.

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Table 3:
Expected and observed 95% confidence level intervals for the different anomalous couplings in both the W$\gamma \gamma $ and Z$\gamma \gamma $ channels.
Summary
The cross sections for both the W$\gamma\gamma$ and Z$\gamma\gamma$ processes are measured in proton-proton collisions by the CMS experiment at a centre-of-mass energy of 13 TeV corresponding to an integrated luminosity of 137 fb$^{-1}$.

The cross sections are measured in a fiducial region where simulated signal events are selected at generator level in the W$\gamma\gamma$ channel by requiring exactly one electron or muon with transverse momentum ${p_{\mathrm{T}}} > $ 30 GeV and at least two photons, each with ${p_{\mathrm{T}}} > $ 20 GeV. Events are selected in the Z$\gamma\gamma$ channel by requiring two oppositely charged electrons or muons, at least one of them with ${p_{\mathrm{T}}} > $ 30 GeV, and at least two photons, each with ${p_{\mathrm{T}}} > $ 20 GeV. All leptons and photons are required to have pseudorapidity $|\eta| < $ 2.5. Additionally, the invariant mass of the dilepton system is required to exceed $m_{\ell\ell} > $ 55 GeV.

The measured cross sections are 13.6$^{+1.9}_{-1.9}$ (stat)$^{+4.0}_{-4.0}$ (syst) $\pm$ 0.08 (PDF+scale) fb for the W$\gamma\gamma$ channel and 5.41$^{+0.58}_{-0.55}$ (stat)$^{+0.64}_{-0.70}$ (syst) $\pm$ 0.06 (PDF+scale) fb for the Z$\gamma\gamma$ channel. These results are in agreement with the theoretical cross sections computed at next-to-leading order. The corresponding signal significances are 3.1 and 4.8 standard deviations. Limits on anomalous quartic gauge couplings are set using both channels.
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Compact Muon Solenoid
LHC, CERN