The measured fiducial cross section vs $E_{\mathrm{T}}^\gamma$. The central values are provided along with the statistical and systematic uncertainties together with the sign information. The statistical and "Uncor" uncertainty should be treated as uncorrelated bin-to-bin, while the rest are correlated between bins, and they are written as signed NP variations. The parton-to-particle correction factor $C_{theory}$ is the ratio of the cross-section predicted by Sherpa LO samples at particle level within the fiducial phase-space region defined in Table 4 to the predicted cross-section at parton level within the same fiducial region but with the smooth-cone isolation prescription defined above replacing the particle-level photon isolation criterion, and with Born-level leptons in place of dressed leptons. This correction should be applied on fixed order parton-level calculations. The systematic uncertainty is evaluated from a comparison with the correction factor obtained using events generated with Sherpa 2.2.2 at NLO. The uncertainty is defined as Max(stat error, systematic difference between Sherpa LO and Sherpa 2.2.2 NLO), and cannot be considered correlated bin-to-bin. In the case that the calculations are valid for dressed leptons, a modified correction factor excluding the Born-to-dressed lepton correction should be applied instead. This correction only takes into account the particle-level isolation criteria, and is provided separately here. The Sherpa 2.2.8 NLO cross-sections given below include a small contribution from EW $Z\gamma jj$ production.

The measured fiducial cross section vs $|\eta^\gamma|$. The central values are provided along with the statistical and systematic uncertainties together with the sign information. The statistical and "Uncor" uncertainty should be treated as uncorrelated bin-to-bin, while the rest are correlated between bins, and they are written as signed NP variations. The parton-to-particle correction factor $C_{theory}$ is the ratio of the cross-section predicted by Sherpa LO samples at particle level within the fiducial phase-space region defined in Table 4 to the predicted cross-section at parton level within the same fiducial region but with the smooth-cone isolation prescription defined above replacing the particle-level photon isolation criterion, and with Born-level leptons in place of dressed leptons. This correction should be applied on fixed order parton-level calculations. The systematic uncertainty is evaluated from a comparison with the correction factor obtained using events generated with SHERPA 2.2.2 at NLO. In the case that the calculations are valid for dressed leptons, a modified correction factor excluding the Born-to-dressed lepton correction should be applied instead. This correction only takes into account the particle-level isolation criteria, and is provided separately here. The Sherpa 2.2.8 NLO cross-sections given below include a small contribution from EW $Z\gamma jj$ production.

The measured fiducial cross section vs $|\eta^\gamma|$. The central values are provided along with the statistical and systematic uncertainties together with the sign information. The statistical and "Uncor" uncertainty should be treated as uncorrelated bin-to-bin, while the rest are correlated between bins, and they are written as signed NP variations. The parton-to-particle correction factor $C_{theory}$ is the ratio of the cross-section predicted by Sherpa LO samples at particle level within the fiducial phase-space region defined in Table 4 to the predicted cross-section at parton level within the same fiducial region but with the smooth-cone isolation prescription defined above replacing the particle-level photon isolation criterion, and with Born-level leptons in place of dressed leptons. This correction should be applied on fixed order parton-level calculations. The systematic uncertainty is evaluated from a comparison with the correction factor obtained using events generated with Sherpa 2.2.2 at NLO. The uncertainty is defined as Max(stat error, systematic difference between Sherpa LO and Sherpa 2.2.2 NLO), and cannot be considered correlated bin-to-bin. In the case that the calculations are valid for dressed leptons, a modified correction factor excluding the Born-to-dressed lepton correction should be applied instead. This correction only takes into account the particle-level isolation criteria, and is provided separately here. The Sherpa 2.2.8 NLO cross-sections given below include a small contribution from EW $Z\gamma jj$ production.

The measured fiducial cross section vs $m(\ell\ell\gamma)$. The central values are provided along with the statistical and systematic uncertainties together with the sign information. The statistical and "Uncor" uncertainty should be treated as uncorrelated bin-to-bin, while the rest are correlated between bins, and they are written as signed NP variations. The parton-to-particle correction factor $C_{theory}$ is the ratio of the cross-section predicted by Sherpa LO samples at particle level within the fiducial phase-space region defined in Table 4 to the predicted cross-section at parton level within the same fiducial region but with the smooth-cone isolation prescription defined above replacing the particle-level photon isolation criterion, and with Born-level leptons in place of dressed leptons. This correction should be applied on fixed order parton-level calculations. The systematic uncertainty is evaluated from a comparison with the correction factor obtained using events generated with SHERPA 2.2.2 at NLO. In the case that the calculations are valid for dressed leptons, a modified correction factor excluding the Born-to-dressed lepton correction should be applied instead. This correction only takes into account the particle-level isolation criteria, and is provided separately here. The Sherpa 2.2.8 NLO cross-sections given below include a small contribution from EW $Z\gamma jj$ production.

The measured fiducial cross section vs $m(\ell\ell\gamma)$. The central values are provided along with the statistical and systematic uncertainties together with the sign information. The statistical and "Uncor" uncertainty should be treated as uncorrelated bin-to-bin, while the rest are correlated between bins, and they are written as signed NP variations. The parton-to-particle correction factor $C_{theory}$ is the ratio of the cross-section predicted by Sherpa LO samples at particle level within the fiducial phase-space region defined in Table 4 to the predicted cross-section at parton level within the same fiducial region but with the smooth-cone isolation prescription defined above replacing the particle-level photon isolation criterion, and with Born-level leptons in place of dressed leptons. This correction should be applied on fixed order parton-level calculations. The systematic uncertainty is evaluated from a comparison with the correction factor obtained using events generated with Sherpa 2.2.2 at NLO. The uncertainty is defined as Max(stat error, systematic difference between Sherpa LO and Sherpa 2.2.2 NLO), and cannot be considered correlated bin-to-bin. In the case that the calculations are valid for dressed leptons, a modified correction factor excluding the Born-to-dressed lepton correction should be applied instead. This correction only takes into account the particle-level isolation criteria, and is provided separately here. The Sherpa 2.2.8 NLO cross-sections given below include a small contribution from EW $Z\gamma jj$ production.

The measured fiducial cross section vs $p_{\mathrm{T}}^{\ell\ell\gamma}$. The central values are provided along with the statistical and systematic uncertainties together with the sign information. The statistical and "Uncor" uncertainty should be treated as uncorrelated bin-to-bin, while the rest are correlated between bins, and they are written as signed NP variations. The parton-to-particle correction factor $C_{theory}$ is the ratio of the cross-section predicted by Sherpa LO samples at particle level within the fiducial phase-space region defined in Table 4 to the predicted cross-section at parton level within the same fiducial region but with the smooth-cone isolation prescription defined above replacing the particle-level photon isolation criterion, and with Born-level leptons in place of dressed leptons. This correction should be applied on fixed order parton-level calculations. The systematic uncertainty is evaluated from a comparison with the correction factor obtained using events generated with SHERPA 2.2.2 at NLO. In the case that the calculations are valid for dressed leptons, a modified correction factor excluding the Born-to-dressed lepton correction should be applied instead. This correction only takes into account the particle-level isolation criteria, and is provided separately here. The Sherpa 2.2.8 NLO cross-sections given below include a small contribution from EW $Z\gamma jj$ production.

The measured fiducial cross section vs $p_{\mathrm{T}}^{\ell\ell\gamma}$. The central values are provided along with the statistical and systematic uncertainties together with the sign information. The statistical and "Uncor" uncertainty should be treated as uncorrelated bin-to-bin, while the rest are correlated between bins, and they are written as signed NP variations. The parton-to-particle correction factor $C_{theory}$ is the ratio of the cross-section predicted by Sherpa LO samples at particle level within the fiducial phase-space region defined in Table 4 to the predicted cross-section at parton level within the same fiducial region but with the smooth-cone isolation prescription defined above replacing the particle-level photon isolation criterion, and with Born-level leptons in place of dressed leptons. This correction should be applied on fixed order parton-level calculations. The systematic uncertainty is evaluated from a comparison with the correction factor obtained using events generated with Sherpa 2.2.2 at NLO. The uncertainty is defined as Max(stat error, systematic difference between Sherpa LO and Sherpa 2.2.2 NLO), and cannot be considered correlated bin-to-bin. In the case that the calculations are valid for dressed leptons, a modified correction factor excluding the Born-to-dressed lepton correction should be applied instead. This correction only takes into account the particle-level isolation criteria, and is provided separately here. The Sherpa 2.2.8 NLO cross-sections given below include a small contribution from EW $Z\gamma jj$ production.

The measured fiducial cross section vs $\Delta\phi(ll,\gamma)$. The central values are provided along with the statistical and systematic uncertainties together with the sign information. The statistical and "Uncor" uncertainty should be treated as uncorrelated bin-to-bin, while the rest are correlated between bins, and they are written as signed NP variations. The parton-to-particle correction factor $C_{theory}$ is the ratio of the cross-section predicted by Sherpa LO samples at particle level within the fiducial phase-space region defined in Table 4 to the predicted cross-section at parton level within the same fiducial region but with the smooth-cone isolation prescription defined above replacing the particle-level photon isolation criterion, and with Born-level leptons in place of dressed leptons. This correction should be applied on fixed order parton-level calculations. The systematic uncertainty is evaluated from a comparison with the correction factor obtained using events generated with SHERPA 2.2.2 at NLO. In the case that the calculations are valid for dressed leptons, a modified correction factor excluding the Born-to-dressed lepton correction should be applied instead. This correction only takes into account the particle-level isolation criteria, and is provided separately here. The Sherpa 2.2.8 NLO cross-sections given below include a small contribution from EW $Z\gamma jj$ production.

The measured fiducial cross section vs $\Delta\phi(ll,\gamma)$. The central values are provided along with the statistical and systematic uncertainties together with the sign information. The statistical and "Uncor" uncertainty should be treated as uncorrelated bin-to-bin, while the rest are correlated between bins, and they are written as signed NP variations. The parton-to-particle correction factor $C_{theory}$ is the ratio of the cross-section predicted by Sherpa LO samples at particle level within the fiducial phase-space region defined in Table 4 to the predicted cross-section at parton level within the same fiducial region but with the smooth-cone isolation prescription defined above replacing the particle-level photon isolation criterion, and with Born-level leptons in place of dressed leptons. This correction should be applied on fixed order parton-level calculations. The systematic uncertainty is evaluated from a comparison with the correction factor obtained using events generated with Sherpa 2.2.2 at NLO. The uncertainty is defined as Max(stat error, systematic difference between Sherpa LO and Sherpa 2.2.2 NLO), and cannot be considered correlated bin-to-bin. In the case that the calculations are valid for dressed leptons, a modified correction factor excluding the Born-to-dressed lepton correction should be applied instead. This correction only takes into account the particle-level isolation criteria, and is provided separately here. The Sherpa 2.2.8 NLO cross-sections given below include a small contribution from EW $Z\gamma jj$ production.

The measured fiducial cross section vs $p_{\mathrm{T}}^{\ell\ell\gamma}/m(\ell\ell\gamma)$. The central values are provided along with the statistical and systematic uncertainties together with the sign information. The statistical and "Uncor" uncertainty should be treated as uncorrelated bin-to-bin, while the rest are correlated between bins, and they are written as signed NP variations. The parton-to-particle correction factor $C_{theory}$ is the ratio of the cross-section predicted by Sherpa LO samples at particle level within the fiducial phase-space region defined in Table 4 to the predicted cross-section at parton level within the same fiducial region but with the smooth-cone isolation prescription defined above replacing the particle-level photon isolation criterion, and with Born-level leptons in place of dressed leptons. This correction should be applied on fixed order parton-level calculations. The systematic uncertainty is evaluated from a comparison with the correction factor obtained using events generated with SHERPA 2.2.2 at NLO. In the case that the calculations are valid for dressed leptons, a modified correction factor excluding the Born-to-dressed lepton correction should be applied instead. This correction only takes into account the particle-level isolation criteria, and is provided separately here. The Sherpa 2.2.8 NLO cross-sections given below include a small contribution from EW $Z\gamma jj$ production.

The measured fiducial cross section vs $p_{\mathrm{T}}^{\ell\ell\gamma}/m(\ell\ell\gamma)$. The central values are provided along with the statistical and systematic uncertainties together with the sign information. The statistical and "Uncor" uncertainty should be treated as uncorrelated bin-to-bin, while the rest are correlated between bins, and they are written as signed NP variations. The parton-to-particle correction factor $C_{theory}$ is the ratio of the cross-section predicted by Sherpa LO samples at particle level within the fiducial phase-space region defined in Table 4 to the predicted cross-section at parton level within the same fiducial region but with the smooth-cone isolation prescription defined above replacing the particle-level photon isolation criterion, and with Born-level leptons in place of dressed leptons. This correction should be applied on fixed order parton-level calculations. The systematic uncertainty is evaluated from a comparison with the correction factor obtained using events generated with Sherpa 2.2.2 at NLO. The uncertainty is defined as Max(stat error, systematic difference between Sherpa LO and Sherpa 2.2.2 NLO), and cannot be considered correlated bin-to-bin. In the case that the calculations are valid for dressed leptons, a modified correction factor excluding the Born-to-dressed lepton correction should be applied instead. This correction only takes into account the particle-level isolation criteria, and is provided separately here. The Sherpa 2.2.8 NLO cross-sections given below include a small contribution from EW $Z\gamma jj$ production.

Measured differential cross sections for the $pp \rightarrow \nu\bar{\nu}\gamma$ process as a function of $p_{T}^{\nu\bar{\nu}}$ in the inclusive $N_{jets} \geq 0$ extended fiducial region defined in the paper.

Measured differential cross sections for the $pp \rightarrow \nu\bar{\nu}\gamma$ process as a function of $p_{T}^{\nu\bar{\nu}}$ in the exclusive $N_{jets} = 0$ extended fiducial region defined in the paper.

Measured differential cross sections as a function of $N_{jets}$ in the extended fiducial region defined in the paper.

Observed and expected one dimensional 95% C.L. limits on vertex function parameters for the $ZZ\gamma$ and $Z\gamma\gamma$ vertices.

Observed and expected one dimensional 95% C.L. limits on EFT parameters for the $ZZ\gamma$ and $Z\gamma\gamma$ vertices.

Measured integrated cross sections for the $Z\gamma\gamma$ process for neutrino final state at $\sqrt{s} = 8$ TeV in the extended fiducial regions defined in the paper, table 5. The parton-to-particle correction factors are also shown, which are defined as the ratio of the cross sections at parton-level to the cross sections at particle-level.

The differential cross sections as a function of $E_{\mathrm{T}}^{\gamma}$ for the $pp \rightarrow \ell^{+}\ell^{-}\gamma$ process in the inclusive $N_{\mathrm{jets}} \geq 0$ extended fiducial region. The parton-to-particle correction factors are also shown, which are defined as the ratio of the cross sections at parton-level to the cross sections at particle-level.

The differential cross sections as a function of $E_{\mathrm{T}}^{\gamma}$ for the $pp \rightarrow \ell^{+}\ell^{-}\gamma$ process in the exclusive $N_{\mathrm{jets}} = 0$ extended fiducial region. The parton-to-particle correction factors are also shown, which are defined as the ratio of the cross sections at parton-level to the cross sections at particle-level.

The differential cross sections as a function of $E_{\mathrm{T}}^{\gamma}$ for the $pp \rightarrow \nu\bar{\nu}\gamma$ process in the inclusive $N_{\mathrm{jets}} \geq 0$ extended fiducial region. The parton-to-particle correction factors are also shown, which are defined as the ratio of the cross sections at parton-level to the cross sections at particle-level.

The differential cross sections as a function of $E_{\mathrm{T}}^{\gamma}$ for the $pp \rightarrow \nu\bar{\nu}\gamma$ process in the exclusive $N_{\mathrm{jets}} = 0$ extended fiducial region. The parton-to-particle correction factors are also shown, which are defined as the ratio of the cross sections at parton-level to the cross sections at particle-level.

The differential cross sections as a function of $m_{\ell^{+}\ell^{-}\gamma}$ for the $pp \rightarrow \ell^{+}\ell^{-}\gamma$ process in the inclusive $N_{\mathrm{jets}} \geq 0$ extended fiducial region. The parton-to-particle correction factors are also shown, which are defined as the ratio of the cross sections at parton-level to the cross sections at particle-level.

The differential cross sections as a function of $m_{\ell^{+}\ell^{-}\gamma}$ for the $pp \rightarrow \ell^{+}\ell^{-}\gamma$ process in the exclusive $N_{\mathrm{jets}} = 0$ extended fiducial region. The parton-to-particle correction factors are also shown, which are defined as the ratio of the cross sections at parton-level to the cross sections at particle-level.

The cross sections as a function of $N_{\mathrm{jets}}$ for the $pp \rightarrow \ell^{+}\ell^{-}\gamma$ process in the extended fiducial region. The parton-to-particle correction factors are also shown, which are defined as the ratio of the cross sections at parton-level to the cross sections at particle-level.

Fiducial cross sections for pT(gamma) > 15 GeV with statistical, systematic, and luminosity uncertainties, respectively. Combined result of electron and muon channels.