Upper limits on the production cross section times branching fraction of the b* RH hypothesis at a 95% CL. Dashed colored lines show the expected limits from the l+jets and all-hadronic channels, where the latter start at resonance masses of 1.4 TeV. The observed and expected limits from the combination are shown as solid and dashed black lines, respectively. The green and yellow bands show the 68 and 95% confidence intervals on the combined expected limits.

Upper limits on the production cross section times branching fraction of the b* VL hypothesis at a 95% CL. Dashed colored lines show the expected limits from the l+jets and all-hadronic channels, where the latter start at resonance masses of 1.4 TeV. The observed and expected limits from the combination are shown as solid and dashed black lines, respectively. The green and yellow bands show the 68 and 95% confidence intervals on the combined expected limits.

Upper limits on the production cross section times branching fraction of the B+b hypothesis at a 95% CL. Dashed colored lines show the expected limits from the l+jets and all-hadronic channels, where the latter start at resonance masses of 1.4 TeV. The observed and expected limits from the combination are shown as solid and dashed black lines, respectively. The green and yellow bands show the 68 and 95% confidence intervals on the combined expected limits.

Upper limits on the production cross section times branching fraction of the B+t hypothesis at a 95% CL. Dashed colored lines show the expected limits from the l+jets and all-hadronic channels, where the latter start at resonance masses of 1.4 TeV. The observed and expected limits from the combination are shown as solid and dashed black lines, respectively. The green and yellow bands show the 68 and 95% confidence intervals on the combined expected limits.

Bayesian upper exclusion limits on the ratio $g_{W'}/g_{W}$ for an SSM-like W$\prime$ boson are shown. The unity coupling ratio (blue dotted curve) corresponds to the SSM common benchmark. The 68 and 95% quantiles of the limits are represented by the green and yellow bands, respectively.

Bayesian lower exclusion limits on the NUGIM G(221) mixing angle $\cot(\theta_{E})$ are shown as a function of the W$\prime$ boson mass. The theoretically excluded region is shaded in grey. The 68 and 95% quantiles of the limits are represented by the green and yellow bands, respectively.

Bayesian upper exclusion limits at 95% CL on the product of the production cross section and branching fraction of a QBH in an associated $ au$ lepton and neutrino final state. Minimum threshold masses $m_{th}$ of up to 6.6 TeV are excluded at 95% CL. The observed limit (solid line) is obtained from the intersection with the LO QBH cross section (blue dotted curve). The 68 and 95% quantiles of the limits are represented by the green and yellow bands, respectively.

Bayesian upper limits at 95% CL on the cross section of the process $pp\rightarrow\tau\nu$ mediated via LQ exchange in the t-channel. The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis. The predicted LQ cross section at LO in the three coupling benchmark scenarios is depicted in different colors for $g_{U}=1$. The uncertainty bandy correspond to the sum in quadrature of PDF and scale variations. The first benchmark scenario considers only couplings to left-handed SM fermions (i.e. $\beta_{\text{R}}^{ij}=0$) and is referred to as "best fit LH". The second benchmark, referred to as "best fit LH+RH", considers $|\beta_{\text{R}}^{\text{b}\tau}|=1$ and all other $\beta_{\text{R}}^{ij}=0$. In the third "democratic" benchmark, equal couplings only to LH fermions are assumed, i.e. $\beta_{\text{L}}^{ij}=1$ and $\beta_{\text{R}}^{ij}=0$ for all $i$ and $j$.

Expected and observed lower limits of the LQ mass as a function of the coupling $g_{U}$ in the LH scenario. The blue band shows the 68% and 95% regions of $g_{U}$ preferred by the fit to the b anomalies data.

Expected and observed lower limits of the LQ mass as a function of the coupling $g_{U}$ in the LH+RH scenario. The blue band shows the 68% and 95% regions of $g_{U}$ preferred by the fit to the b anomalies data.

Expected and observed lower limits of the LQ mass as a function of the coupling $g_{U}$ in the democratic scenario. The blue band shows the 68% and 95% regions of $g_{U}$ preferred by the fit to the b anomalies data.

Bayesian upper exclusion limits at 95% CL on each of the Wilson coefficients described by the EFT model based on 2016-2018 data. The three different coupling types represent a left-handed vector coupling ($\epsilon^{cb}_{L}$), tensor-like coupling ($\epsilon^{cb}_{T}$), and scalar-tensor-like coupling ($\epsilon^{cb}_{S_{L}}$). The 68 and 95% quantiles of the limits are represented by the green and yellow bands, respectively.

Summary of exclusion limits (expected and observed) calculated at 95% CL for full Run-2 CMS data.

Background prediction and observed data yields in the signal region bins. The background yields are obtained from the background-only fit and serve as input to the simplified likelihood reinterpretation scheme. The naming of the bins is "year_binnumber", following the binning from Figure 4.

Matrix of covariance coefficients between signal region bins. The coefficients are obtained from the background-only fit and serve as input to the simplified likelihood reinterpretation scheme. The naming of the bins is "year_binnumber", following the binning used in Figure 4.

Predicted signal yields for the 2017 data-taking period, corresponding to 41.3 fb$^{-1}$, after the application of each search requirement (cumulative) for various signal hypothesis. The requirements listed are presented as total efficiencies w.r.t. the previous selection step.

Observed upper limits at 90% CL on the square of the kinetic mixing coefficient $\epsilon$ in the minimal model of a dark photon

Observed upper limits at 90% CL on the mixing angle $\theta_H$ for the type IV 2HDM+S scenario with fixed $tan\beta=0.5$

The combined efficiency of the dimuon scouting trigger and the MVA muon selection, averaged between 2017 and 2018, weighted by the integrated luminosity of each year. The trigger and selection efficiencies are also included in the table.

Theory cross-section times branching fraction to muons times acceptance for the dark photon and 2HDM+S models.

Number of predicted signal events in the $\mu\mu X$ final states, for several benchmark signal hypotheses for Majorana HNL. The quoted uncertainties include statistical and systematic uncertainties.

The 95% CL limits on $|V_{Ne}|^2$ as a function of the HNL mass for a Majorana HNL. Values of $-1$ indicate that no limit is available for the mass point.

The 95% CL limits on $|V_{N\mu}|^2$ as a function of the HNL mass for a Majorana HNL. Values of $-1$ indicate that no limit is available for the mass point.

The 95% CL limits on $|V_{Ne}|^2$ as a function of the HNL mass for a Dirac HNL. Values of $-1$ indicate that no limit is available for the mass point.

The 95% CL limits on $|V_{N\mu}|^2$ as a function of the HNL mass for a Dirac HNL. Values of $-1$ indicate that no limit is available for the mass point.

Covariance matrix for the background prediction in the signal region bins for the $eeX$ final states. The bin labels specify the channel, the $m(\ell_2,\ell_3)$ bin, and the $\Delta_{\mathrm{2D}}$ bin.

Covariance matrix for the background prediction in the signal region bins for the $\mu\mu X$ final states. The bin labels specify the channel, the $m(\ell_2,\ell_3)$ bin, and the $\Delta_{\mathrm{2D}}$ bin.

Correlation matrix for the background prediction the signal region bins for the $eeX$ final states. The bin labels specify the channel, the $m(\ell_2,\ell_3)$ bin, and the $\Delta_{\mathrm{2D}}$ bin.

Correlation matrix for the background prediction the signal region bins for the $\mu\mu X$ final states. The bin labels specify the channel, the $m(\ell_2,\ell_3)$ bin, and the $\Delta_{\mathrm{2D}}$ bin.

Mean lifetime and production cross section for HNLs of Majorana nature, assuming the decay to three charged leptons and coupling to only electrons or muons, as evaluated from simulated event samples.

The $m_{lJ}$ distribution in the boosted DY control region, muon channel.

The $m_{lljj}$ distribution in the resolved flavor control region.

The $m_{lJ}$ distribution in the boosted flavor control region, with electron jet.

The $m_{lJ}$ distribution in the boosted flavor control region, with muon jet

The $m_{lljj}$ distribution in the resolved signal region, electron channel.

The $m_{lljj}$ distribution in the resolved signal region, muon channel.

The $m_{lJ}$ distribution in the boosted signal region, electron channel.

The $m_{lJ}$ distribution in the boosted signal region, muon channel.

The expected and observed $95\%$ CL upper limits on the production cross section times the branching fraction $\sigma (\mathrm{p}\mathrm{p} \rightarrow W_{R}) \mathcal{B}(W_{R} \rightarrow \mathrm{e}\mathrm{e}\mathrm{q}\overline{\mathrm{q}'})$ for $m_{N} = m_{W_{R}}/2$ GeV in the electron channel. The red solid lines represent the values expected from the theory.

The expected and observed $95\%$ CL upper limits on the production cross section times the branching fraction $\sigma (\mathrm{p}\mathrm{p} \rightarrow W_{R}) \mathcal{B}(W_{R} \rightarrow \mathrm{e}\mathrm{e}\mathrm{q}\overline{\mathrm{q}'})$ for $m_{N} = m_{W_{R}}/2$ GeV in the muon channel. The red solid lines represent the values expected from the theory.

The expected and observed $95\%$ CL upper limits on the production cross section times the branching fraction $\sigma (\mathrm{p}\mathrm{p} \rightarrow W_{R}) \mathcal{B}(W_{R} \rightarrow \mathrm{e}\mathrm{e}\mathrm{q}\overline{\mathrm{q}'})$ for $m_{N} = 200$ GeV in the electron channel. The red solid lines represent the values expected from the theory.

The expected and observed $95\%$ CL upper limits on the production cross section times the branching fraction $\sigma (\mathrm{p}\mathrm{p} \rightarrow W_{R}) \mathcal{B}(W_{R} \rightarrow \mathrm{e}\mathrm{e}\mathrm{q}\overline{\mathrm{q}'})$ for $m_{N} = 200$ GeV in the muon channel. The red solid lines represent the values expected from the theory.

The observed $95\%$ CL upper limits on the production cross section times the branching fraction $\sigma (\mathrm{p}\mathrm{p} \rightarrow W_{R}) \mathcal{B}(W_{R} \rightarrow \mathrm{e}\mathrm{e}\mathrm{q}\overline{\mathrm{q}'})$ divided by the theory cross sections in the electron channel. The observed exclusions are shown for the resolved (solid green), boosted (solid blue), and combined (solid black) channels, along with the expected exclusion for the combined result (dotted black). The dash-dotted lines represent the one standard deviation of the expected exclusion. The observed exclusions from the previous search performed by the CMS Collaboration (arXiv:1803.11116) is also shown in magenta.

The observed $95\%$ CL upper limits on the production cross section times the branching fraction $\sigma (\mathrm{p}\mathrm{p} \rightarrow W_{R}) \mathcal{B}(W_{R} \rightarrow \mathrm{e}\mathrm{e}\mathrm{q}\overline{\mathrm{q}'})$ divided by the theory cross sections in the muon channel. The observed exclusions are shown for the resolved (solid green), boosted (solid blue), and combined (solid black) channels, along with the expected exclusion for the combined result (dotted black). The dash-dotted lines represent the one standard deviation of the expected exclusion. The observed exclusions from the previous search performed by the CMS Collaboration (arXiv:1803.11116) is also shown in magenta.

Relative uncertainties in the total yields of the signal and background predictions.

Covariance matrix for all bins used in the background-only fit of the electron channel of this analysis. There are 243 bins in total, 81 for every data-taking year. For every year, each region has nine bins and the bins are grouped by rergion in the following order: ee boosted DY CR, #mu-jet flavor CR, ee resolved DY CR, resolved flavor CR, ee boosted SR, ee resolved SR, #mu#mu boosted DY CR, e-jet flavor CR, and #mu#mu resolved DY CR.

Covariance matrix for all bins used in the background-only fit of the muon channel of this analysis. There are 243 bins in total, 81 for every data-taking year. For every year, each region has nine bins and the bins are grouped by rergion in the following order: ee boosted DY CR, #mu-jet flavor CR, ee resolved DY CR, #mu#mu boosted DY CR, e-jet flavor CR, $#mu#mu$ resolved DY CR, resolved flavor CR, #mu#mu boosted SR, and the #mu#mu resolved SR.

Predicted signal yields for the 2016 data-taking period, corresponding to $35.9\,\text{fb}^{-1}$, after the application of each search requirement for the $m_{W_{R}} = 0.3$, 0.4, and 0.5 TeV and $m_{N} = 0.2$ TeV signal hypotheses for the boosted , dielectron channel.The requirements listed are cumulative such that only the events and objects passing a given requirement are considered in subsequent requirements.

Predicted signal yields for the 2016 data-taking period, corresponding to $35.9\,\text{fb}^{-1}$, after the application of each search requirement for the $(m_{W_{R}},m_{N}) = (3.0,1.4)$ TeV signal hypothesis for the resolved , dielectron channel.The requirements listed are cumulative such that only the events and objects passing a given requirement are considered in subsequent requirements.

Predicted signal yields for the 2016 data-taking period, corresponding to $35.9\,\text{fb}^{-1}$, after the application of each search requirement for the $(m_{W_{R}},m_{N}) = (4.0,2.0)$ TeV signal hypothesis for the resolved , dielectron channel.The requirements listed are cumulative such that only the events and objects passing a given requirement are considered in subsequent requirements.

Predicted signal yields for the 2016 data-taking period, corresponding to $35.9\,\text{fb}^{-1}$, after the application of each search requirement for the $(m_{W_{R}},m_{N}) = (5.0,3.0)$ TeV signal hypothesis for the resolved , dielectron channel.The requirements listed are cumulative such that only the events and objects passing a given requirement are considered in subsequent requirements.

Predicted signal yields for the 2016 data-taking period, corresponding to $35.9\,\text{fb}^{-1}$, after the application of each search requirement for the $m_{W_{R}} = 0.3$, 0.4, and 0.5 TeV and $m_{N} = 0.2$ TeV signal hypotheses for the boosted , dimuon channel.The requirements listed are cumulative such that only the events and objects passing a given requirement are considered in subsequent requirements.

Predicted signal yields for the 2016 data-taking period, corresponding to $35.9\,\text{fb}^{-1}$, after the application of each search requirement for the $(m_{W_{R}},m_{N}) = (3.0,1.4)$ TeV signal hypothesis for the resolved , dimuon channel.The requirements listed are cumulative such that only the events and objects passing a given requirement are considered in subsequent requirements.

Predicted signal yields for the 2016 data-taking period, corresponding to $35.9\,\text{fb}^{-1}$, after the application of each search requirement for the $(m_{W_{R}},m_{N}) = (4.0,2.0)$ TeV signal hypothesis for the resolved , dimuon channel.The requirements listed are cumulative such that only the events and objects passing a given requirement are considered in subsequent requirements.

Predicted signal yields for the 2016 data-taking period, corresponding to $35.9\,\text{fb}^{-1}$, after the application of each search requirement for the $(m_{W_{R}},m_{N}) = (5.0,3.0)$ TeV signal hypothesis for the resolved , dimuon channel.The requirements listed are cumulative such that only the events and objects passing a given requirement are considered in subsequent requirements.

Predicted signal yields for the 2017 data-taking period, corresponding to $41.5\,\text{fb}^{-1}$, after the application of each search requirement for the $m_{W_{R}} = 0.3$, 0.4, and 0.5 TeV and $m_{N} = 0.2$ TeV signal hypotheses for the boosted , dielectron channel.The requirements listed are cumulative such that only the events and objects passing a given requirement are considered in subsequent requirements.

Predicted signal yields for the 2017 data-taking period, corresponding to $41.5\,\text{fb}^{-1}$, after the application of each search requirement for the $(m_{W_{R}},m_{N}) = (3.0,1.4)$ TeV signal hypothesis for the resolved , dielectron channel.The requirements listed are cumulative such that only the events and objects passing a given requirement are considered in subsequent requirements.

Predicted signal yields for the 2017 data-taking period, corresponding to $41.5\,\text{fb}^{-1}$, after the application of each search requirement for the $(m_{W_{R}},m_{N}) = (4.0,2.0)$ TeV signal hypothesis for the resolved , dielectron channel.The requirements listed are cumulative such that only the events and objects passing a given requirement are considered in subsequent requirements.

Predicted signal yields for the 2017 data-taking period, corresponding to $41.5\,\text{fb}^{-1}$, after the application of each search requirement for the $(m_{W_{R}},m_{N}) = (5.0,3.0)$ TeV signal hypothesis for the resolved , dielectron channel.The requirements listed are cumulative such that only the events and objects passing a given requirement are considered in subsequent requirements.

Predicted signal yields for the 2017 data-taking period, corresponding to $41.5\,\text{fb}^{-1}$, after the application of each search requirement for the $m_{W_{R}} = 0.3$, 0.4, and 0.5 TeV and $m_{N} = 0.2$ TeV signal hypotheses for the boosted , dimuon channel.The requirements listed are cumulative such that only the events and objects passing a given requirement are considered in subsequent requirements.

Predicted signal yields for the 2017 data-taking period, corresponding to $41.5\,\text{fb}^{-1}$, after the application of each search requirement for the $(m_{W_{R}},m_{N}) = (3.0,1.4)$ TeV signal hypothesis for the resolved , dimuon channel.The requirements listed are cumulative such that only the events and objects passing a given requirement are considered in subsequent requirements.

Predicted signal yields for the 2017 data-taking period, corresponding to $41.5\,\text{fb}^{-1}$, after the application of each search requirement for the $(m_{W_{R}},m_{N}) = (4.0,2.0)$ TeV signal hypothesis for the resolved , dimuon channel.The requirements listed are cumulative such that only the events and objects passing a given requirement are considered in subsequent requirements.

Predicted signal yields for the 2017 data-taking period, corresponding to $41.5\,\text{fb}^{-1}$, after the application of each search requirement for the $(m_{W_{R}},m_{N}) = (5.0,3.0)$ TeV signal hypothesis for the resolved , dimuon channel.The requirements listed are cumulative such that only the events and objects passing a given requirement are considered in subsequent requirements.

Predicted signal yields for the 2018 data-taking period, corresponding to $59.7\,\text{fb}^{-1}$, after the application of each search requirement for the $m_{W_{R}} = 0.3$, 0.4, and 0.5 TeV and $m_{N} = 0.2$ TeV signal hypotheses for the boosted , dielectron channel.The requirements listed are cumulative such that only the events and objects passing a given requirement are considered in subsequent requirements.

Predicted signal yields for the 2018 data-taking period, corresponding to $59.7\,\text{fb}^{-1}$, after the application of each search requirement for the $(m_{W_{R}},m_{N}) = (3.0,1.4)$ TeV signal hypothesis for the resolved , dielectron channel.The requirements listed are cumulative such that only the events and objects passing a given requirement are considered in subsequent requirements.

Predicted signal yields for the 2018 data-taking period, corresponding to $59.7\,\text{fb}^{-1}$, after the application of each search requirement for the $(m_{W_{R}},m_{N}) = (4.0,2.0)$ TeV signal hypothesis for the resolved , dielectron channel.The requirements listed are cumulative such that only the events and objects passing a given requirement are considered in subsequent requirements.

Predicted signal yields for the 2018 data-taking period, corresponding to $59.7\,\text{fb}^{-1}$, after the application of each search requirement for the $(m_{W_{R}},m_{N}) = (5.0,3.0)$ TeV signal hypothesis for the resolved , dielectron channel.The requirements listed are cumulative such that only the events and objects passing a given requirement are considered in subsequent requirements.

Predicted signal yields for the 2018 data-taking period, corresponding to $59.7\,\text{fb}^{-1}$, after the application of each search requirement for the $m_{W_{R}} = 0.3$, 0.4, and 0.5 TeV and $m_{N} = 0.2$ TeV signal hypotheses for the boosted , dimuon channel.The requirements listed are cumulative such that only the events and objects passing a given requirement are considered in subsequent requirements.

Predicted signal yields for the 2018 data-taking period, corresponding to $59.7\,\text{fb}^{-1}$, after the application of each search requirement for the $(m_{W_{R}},m_{N}) = (3.0,1.4)$ TeV signal hypothesis for the resolved , dimuon channel.The requirements listed are cumulative such that only the events and objects passing a given requirement are considered in subsequent requirements.

Predicted signal yields for the 2018 data-taking period, corresponding to $59.7\,\text{fb}^{-1}$, after the application of each search requirement for the $(m_{W_{R}},m_{N}) = (4.0,2.0)$ TeV signal hypothesis for the resolved , dimuon channel.The requirements listed are cumulative such that only the events and objects passing a given requirement are considered in subsequent requirements.

Predicted signal yields for the 2018 data-taking period, corresponding to $59.7\,\text{fb}^{-1}$, after the application of each search requirement for the $(m_{W_{R}},m_{N}) = (5.0,3.0)$ TeV signal hypothesis for the resolved , dimuon channel.The requirements listed are cumulative such that only the events and objects passing a given requirement are considered in subsequent requirements.

Cross sections calculated to next-to-leading (NLO) accuracy

Normalized differential cross section distribution as a function of the leading b jet transverse momentum for the Z + >= 1 b jet events

Differential cross section distribution as a function of the leading b jet absolute pseudorapidity for the Z + >= 1 b jet events

Normalized differential cross section distribution as a function of the leading b jet absolute pseudorapidity for the Z + >= 1 b jet events

Differential cross section distribution as a function of the leading b jet transverse momentum for Z +>= 1 b jet events

Normalized differential cross section distribution as a function of azimuthal difference between Z boson and the leading b jet for the Z + >= 1 b jet events

Differential cross section distribution as a function of the rapidity difference between Z boson and the leading b jet for the Z + >= 1 b jet events

Normalized differential cross section distribution as a function of the rapidity difference between Z boson and the leading b jet for the Z + >= 1 b jet events

Differential cross section distribution as a function of the angular separation between the Z boson and the leading b jet for the Z + >= 1 b jet events

Normalized differential cross section distribution as a function of the angular separation between the Z boson and the leading b jet for the Z + >= 1 b jet events

Differential cross section distribution as a function of the leading b jet transverse momentum for the Z + >= 2 b jet events

Normalized differential cross section distribution as a function of the leading b jet transverse momentum for the Z + >= 2 b jet events

Differential cross section distribution as a function of the leading b jet absolute pseudorapidity

Normalized differential cross section distribution as a function of the leading b jet absolute pseudorapidity

Differential cross section distribution as a function of the subleading b jet transverse momentum for the Z + >= 2 b jet events

Normalized differential cross section distribution as a function of the subleading b jet transverse momentum for the Z + >= 2 b jet events

Differential cross section distribution as a function of the Z boson transverse momentum for the Z + >= 2 b jet events

Normalized differential cross section distribution as a function of the Z boson transverse momentum for the Z + >= 2 b jet events

Differential cross section as a function of the angular separation between two b jets for the Z + >= 2 b jet events

Normalized differential cross section as a function of the angular separtion between two b jets for the Z + >= 2 b jet events

Differential cross section as a function of the minimum angular separation between the Z boson and two b jets for the Z + >= 2 b jet events

Normalized differential cross section as a function of the minimum angular separation between the Z boson and two b jets for the Z + >= 2 b jet events

Differential cross section as a function of the asymmetry of the Z + >= 2 b jets system

Normalized differential cross section as a function of the asymmetry of the Z + >= 2 b jets system

Differential cross section as a function of the invariant mass of two b jets for the Z + >= 2 b jet events

Normalized differential cross section as a function of the invariant mass of two b jets for the Z + >= 2 b jet events

Differential cross section as a function of the invariant mass of the Z boson and two b jets for the Z + >= 2 b jet events

Normalized differential cross section as a function of invariant mass of the Z boson and two b jets for the Z + >= 2 b jet events

Distributions of the cross section ratios as a function of the leading b jet transverse momentum

Distributions of the cross section ratios as a function of the leading b jet absolute pseudorapidity

Relative uncertainties on the measured fractional differential $p_{\mathrm{T}}^{\gamma}$ cross section.

Correlation matrix for the measured absolute differential $p_{\mathrm{T}}^{\gamma}$ cross section.

Correlation matrix for the measured fractional differential $p_{\mathrm{T}}^{\gamma}$ cross section.

Response matrix from the fiducial to the reconstructed bins of the differential $p_{\mathrm{T}}^{\gamma}$ cross section measurement.

Measured absolute differential $\eta^{\gamma}$ cross section, compared to the MG5_aMC+PY8, GENEVA, MATRIX and MCFM predictions. The differential cross sections $\sigma_{j}(\mathrm{pp}\rightarrow\mathrm{W}^{\pm}\gamma\rightarrow\ell^{\pm}\nu\gamma)$, where $\ell$ denotes all three lepton flavors, are measured in the following fiducial region: $p_{\mathrm{T}}^{\ell} > 30\,\mathrm{GeV}$, $|\eta^{\ell}| < 2.5$, $p_{\mathrm{T}}^{\gamma} > 30\,\mathrm{GeV}$, $|\eta^{\gamma}| < 2.5$, $p_{\mathrm{T}}^{\mathrm{miss}} > 40\,\mathrm{GeV}$, and $\Delta R(\ell, \gamma) > 0.7$. The leptons are dressed by adding the four-momenta of any photons with $\Delta R(\ell, \gamma) < 0.1$ to the four-momentum of the lepton. A smooth-cone photon isolation is also applied, with parameters $\delta_{0}=0.4$, $\epsilon=1.0$, and $n=1$.

Measured fractional differential $\eta^{\gamma}$ cross section, compared to the MG5_aMC+PY8, GENEVA, MATRIX and MCFM predictions. The differential cross sections $\sigma_{j}(\mathrm{pp}\rightarrow\mathrm{W}^{\pm}\gamma\rightarrow\ell^{\pm}\nu\gamma)$, where $\ell$ denotes all three lepton flavors, are measured in the following fiducial region: $p_{\mathrm{T}}^{\ell} > 30\,\mathrm{GeV}$, $|\eta^{\ell}| < 2.5$, $p_{\mathrm{T}}^{\gamma} > 30\,\mathrm{GeV}$, $|\eta^{\gamma}| < 2.5$, $p_{\mathrm{T}}^{\mathrm{miss}} > 40\,\mathrm{GeV}$, and $\Delta R(\ell, \gamma) > 0.7$. The leptons are dressed by adding the four-momenta of any photons with $\Delta R(\ell, \gamma) < 0.1$ to the four-momentum of the lepton. A smooth-cone photon isolation is also applied, with parameters $\delta_{0}=0.4$, $\epsilon=1.0$, and $n=1$.

Relative uncertainties on the measured absolute differential $\eta^{\gamma}$ cross section.

Relative uncertainties on the measured fractional differential $\eta^{\gamma}$ cross section.

Correlation matrix for the measured absolute differential $\eta^{\gamma}$ cross section.

Correlation matrix for the measured fractional differential $\eta^{\gamma}$ cross section.

Response matrix from the fiducial to the reconstructed bins of the differential $\eta^{\gamma}$ cross section measurement.

Measured absolute differential $\Delta R(\ell,\gamma)$ cross section, compared to the MG5_aMC+PY8, GENEVA, MATRIX and MCFM predictions. The differential cross sections $\sigma_{j}(\mathrm{pp}\rightarrow\mathrm{W}^{\pm}\gamma\rightarrow\ell^{\pm}\nu\gamma)$, where $\ell$ denotes all three lepton flavors, are measured in the following fiducial region: $p_{\mathrm{T}}^{\ell} > 30\,\mathrm{GeV}$, $|\eta^{\ell}| < 2.5$, $p_{\mathrm{T}}^{\gamma} > 30\,\mathrm{GeV}$, $|\eta^{\gamma}| < 2.5$, $p_{\mathrm{T}}^{\mathrm{miss}} > 40\,\mathrm{GeV}$, and $\Delta R(\ell, \gamma) > 0.7$. The leptons are dressed by adding the four-momenta of any photons with $\Delta R(\ell, \gamma) < 0.1$ to the four-momentum of the lepton. A smooth-cone photon isolation is also applied, with parameters $\delta_{0}=0.4$, $\epsilon=1.0$, and $n=1$.

Measured fractional differential $\Delta R(\ell,\gamma)$ cross section, compared to the MG5_aMC+PY8, GENEVA, MATRIX and MCFM predictions. The differential cross sections $\sigma_{j}(\mathrm{pp}\rightarrow\mathrm{W}^{\pm}\gamma\rightarrow\ell^{\pm}\nu\gamma)$, where $\ell$ denotes all three lepton flavors, are measured in the following fiducial region: $p_{\mathrm{T}}^{\ell} > 30\,\mathrm{GeV}$, $|\eta^{\ell}| < 2.5$, $p_{\mathrm{T}}^{\gamma} > 30\,\mathrm{GeV}$, $|\eta^{\gamma}| < 2.5$, $p_{\mathrm{T}}^{\mathrm{miss}} > 40\,\mathrm{GeV}$, and $\Delta R(\ell, \gamma) > 0.7$. The leptons are dressed by adding the four-momenta of any photons with $\Delta R(\ell, \gamma) < 0.1$ to the four-momentum of the lepton. A smooth-cone photon isolation is also applied, with parameters $\delta_{0}=0.4$, $\epsilon=1.0$, and $n=1$.

Relative uncertainties on the measured absolute differential $\Delta R(\ell,\gamma)$ cross section.

Relative uncertainties on the measured fractional differential $\Delta R(\ell,\gamma)$ cross section.

Correlation matrix for the measured absolute differential $\Delta R(\ell,\gamma)$ cross section.

Correlation matrix for the measured fractional differential $\Delta R(\ell,\gamma)$ cross section.

Response matrix from the fiducial to the reconstructed bins of the differential $\Delta R(\ell,\gamma)$ cross section measurement.

Measured absolute differential $\Delta\eta(\ell,\gamma)$ cross section, compared to the MG5_aMC+PY8, GENEVA, MATRIX and MCFM predictions. The differential cross sections $\sigma_{j}(\mathrm{pp}\rightarrow\mathrm{W}^{\pm}\gamma\rightarrow\ell^{\pm}\nu\gamma)$, where $\ell$ denotes all three lepton flavors, are measured in the following fiducial region: $p_{\mathrm{T}}^{\ell} > 30\,\mathrm{GeV}$, $|\eta^{\ell}| < 2.5$, $p_{\mathrm{T}}^{\gamma} > 30\,\mathrm{GeV}$, $|\eta^{\gamma}| < 2.5$, $p_{\mathrm{T}}^{\mathrm{miss}} > 40\,\mathrm{GeV}$, and $\Delta R(\ell, \gamma) > 0.7$. The leptons are dressed by adding the four-momenta of any photons with $\Delta R(\ell, \gamma) < 0.1$ to the four-momentum of the lepton. A smooth-cone photon isolation is also applied, with parameters $\delta_{0}=0.4$, $\epsilon=1.0$, and $n=1$.

Measured fractional differential $\Delta\eta(\ell,\gamma)$ cross section, compared to the MG5_aMC+PY8, GENEVA, MATRIX and MCFM predictions. The differential cross sections $\sigma_{j}(\mathrm{pp}\rightarrow\mathrm{W}^{\pm}\gamma\rightarrow\ell^{\pm}\nu\gamma)$, where $\ell$ denotes all three lepton flavors, are measured in the following fiducial region: $p_{\mathrm{T}}^{\ell} > 30\,\mathrm{GeV}$, $|\eta^{\ell}| < 2.5$, $p_{\mathrm{T}}^{\gamma} > 30\,\mathrm{GeV}$, $|\eta^{\gamma}| < 2.5$, $p_{\mathrm{T}}^{\mathrm{miss}} > 40\,\mathrm{GeV}$, and $\Delta R(\ell, \gamma) > 0.7$. The leptons are dressed by adding the four-momenta of any photons with $\Delta R(\ell, \gamma) < 0.1$ to the four-momentum of the lepton. A smooth-cone photon isolation is also applied, with parameters $\delta_{0}=0.4$, $\epsilon=1.0$, and $n=1$.

Relative uncertainties on the measured absolute differential $\Delta \eta(\ell,\gamma)$ cross section.

Relative uncertainties on the measured fractional differential $\Delta \eta(\ell,\gamma)$ cross section.

Correlation matrix for the measured absolute differential $\Delta \eta(\ell,\gamma)$ cross section.

Correlation matrix for the measured fractional differential $\Delta \eta(\ell,\gamma)$ cross section.

Response matrix from the fiducial to the reconstructed bins of the differential $\Delta \eta(\ell,\gamma)$ cross section measurement.

Measured absolute differential $m_{\mathrm{T}}^{\mathrm{cluster}}$ cross section, compared to the MG5_aMC+PY8, GENEVA, MATRIX and MCFM predictions. The differential cross sections $\sigma_{j}(\mathrm{pp}\rightarrow\mathrm{W}^{\pm}\gamma\rightarrow\ell^{\pm}\nu\gamma)$, where $\ell$ denotes all three lepton flavors, are measured in the following fiducial region: $p_{\mathrm{T}}^{\ell} > 30\,\mathrm{GeV}$, $|\eta^{\ell}| < 2.5$, $p_{\mathrm{T}}^{\gamma} > 30\,\mathrm{GeV}$, $|\eta^{\gamma}| < 2.5$, $p_{\mathrm{T}}^{\mathrm{miss}} > 40\,\mathrm{GeV}$, and $\Delta R(\ell, \gamma) > 0.7$. The leptons are dressed by adding the four-momenta of any photons with $\Delta R(\ell, \gamma) < 0.1$ to the four-momentum of the lepton. A smooth-cone photon isolation is also applied, with parameters $\delta_{0}=0.4$, $\epsilon=1.0$, and $n=1$.

Measured fractional differential $m_{\mathrm{T}}^{\mathrm{cluster}}$ cross section, compared to the MG5_aMC+PY8, GENEVA, MATRIX and MCFM predictions. The differential cross sections $\sigma_{j}(\mathrm{pp}\rightarrow\mathrm{W}^{\pm}\gamma\rightarrow\ell^{\pm}\nu\gamma)$, where $\ell$ denotes all three lepton flavors, are measured in the following fiducial region: $p_{\mathrm{T}}^{\ell} > 30\,\mathrm{GeV}$, $|\eta^{\ell}| < 2.5$, $p_{\mathrm{T}}^{\gamma} > 30\,\mathrm{GeV}$, $|\eta^{\gamma}| < 2.5$, $p_{\mathrm{T}}^{\mathrm{miss}} > 40\,\mathrm{GeV}$, and $\Delta R(\ell, \gamma) > 0.7$. The leptons are dressed by adding the four-momenta of any photons with $\Delta R(\ell, \gamma) < 0.1$ to the four-momentum of the lepton. A smooth-cone photon isolation is also applied, with parameters $\delta_{0}=0.4$, $\epsilon=1.0$, and $n=1$.

Relative uncertainties on the measured absolute differential $m_{\mathrm{T}}^{\mathrm{cluster}}$ cross section.

Relative uncertainties on the measured fractional differential $m_{\mathrm{T}}^{\mathrm{cluster}}$ cross section.

Correlation matrix for the measured absolute differential $m_{\mathrm{T}}^{\mathrm{cluster}}$ cross section.

Correlation matrix for the measured fractional differential $m_{\mathrm{T}}^{\mathrm{cluster}}$ cross section.

Response matrix from the fiducial to the reconstructed bins of the differential $m_{\mathrm{T}}^{\mathrm{cluster}}$ cross section measurement.

Measured absolute differential $N_{\mathrm{jets}}$ cross section, compared to the MG5_aMC+PY8, GENEVA, MATRIX and MCFM predictions. The differential cross sections $\sigma_{j}(\mathrm{pp}\rightarrow\mathrm{W}^{\pm}\gamma\rightarrow\ell^{\pm}\nu\gamma)$, where $\ell$ denotes all three lepton flavors, are measured in the following fiducial region: $p_{\mathrm{T}}^{\ell} > 30\,\mathrm{GeV}$, $|\eta^{\ell}| < 2.5$, $p_{\mathrm{T}}^{\gamma} > 30\,\mathrm{GeV}$, $|\eta^{\gamma}| < 2.5$, $p_{\mathrm{T}}^{\mathrm{miss}} > 40\,\mathrm{GeV}$, and $\Delta R(\ell, \gamma) > 0.7$. The leptons are dressed by adding the four-momenta of any photons with $\Delta R(\ell, \gamma) < 0.1$ to the four-momentum of the lepton. A smooth-cone photon isolation is also applied, with parameters $\delta_{0}=0.4$, $\epsilon=1.0$, and $n=1$.

Correlation matrix for the measured absolute differential $N_{\mathrm{jets}}$ cross section. The differential cross sections $\sigma_{j}(\mathrm{pp}\rightarrow\mathrm{W}^{\pm}\gamma\rightarrow\ell^{\pm}\nu\gamma)$, where $\ell$ denotes all three lepton flavors, are measured in the following fiducial region: $p_{\mathrm{T}}^{\ell} > 30\,\mathrm{GeV}$, $|\eta^{\ell}| < 2.5$, $p_{\mathrm{T}}^{\gamma} > 30\,\mathrm{GeV}$, $|\eta^{\gamma}| < 2.5$, $p_{\mathrm{T}}^{\mathrm{miss}} > 40\,\mathrm{GeV}$, and $\Delta R(\ell, \gamma) > 0.7$. The leptons are dressed by adding the four-momenta of any photons with $\Delta R(\ell, \gamma) < 0.1$ to the four-momentum of the lepton. A smooth-cone photon isolation is also applied, with parameters $\delta_{0}=0.4$, $\epsilon=1.0$, and $n=1$.

Response matrix from the fiducial to the reconstructed bins of the differential $N_{\mathrm{jets}}$ cross section measurement.

Relative uncertainties on the measured absolute differential $N_{\mathrm{jets}}$ cross section.

Measured absolute differential $\Delta\eta(\ell,\gamma)$ cross section, compared to the MG5_aMC+PY8, GENEVA, MATRIX and MCFM predictions. The differential cross sections $\sigma_{j}(\mathrm{pp}\rightarrow\mathrm{W}^{\pm}\gamma\rightarrow\ell^{\pm}\nu\gamma)$, where $\ell$ denotes all three lepton flavors, are measured in the following fiducial region: $p_{\mathrm{T}}^{\ell} > 30\,\mathrm{GeV}$, $|\eta^{\ell}| < 2.5$, $p_{\mathrm{T}}^{\gamma} > 30\,\mathrm{GeV}$, $|\eta^{\gamma}| < 2.5$, $p_{\mathrm{T}}^{\mathrm{miss}} > 40\,\mathrm{GeV}$, and $\Delta R(\ell, \gamma) > 0.7$. The leptons are dressed by adding the four-momenta of any photons with $\Delta R(\ell, \gamma) < 0.1$ to the four-momentum of the lepton. A smooth-cone photon isolation is also applied, with parameters $\delta_{0}=0.4$, $\epsilon=1.0$, and $n=1$. Requirements of $m_{\mathrm{T}}^{\mathrm{cluster}}>150\,\mathrm{GeV}$ and a veto on the presence of any jet with $p_{\mathrm{T}} > 30\,\mathrm{GeV}$ and $|\eta| < 2.5$ are applied in addition to the baseline selection.

Measured fractional differential $\Delta\eta(\ell,\gamma)$ cross section, compared to the MG5_aMC+PY8, GENEVA, MATRIX and MCFM predictions. The differential cross sections $\sigma_{j}(\mathrm{pp}\rightarrow\mathrm{W}^{\pm}\gamma\rightarrow\ell^{\pm}\nu\gamma)$, where $\ell$ denotes all three lepton flavors, are measured in the following fiducial region: $p_{\mathrm{T}}^{\ell} > 30\,\mathrm{GeV}$, $|\eta^{\ell}| < 2.5$, $p_{\mathrm{T}}^{\gamma} > 30\,\mathrm{GeV}$, $|\eta^{\gamma}| < 2.5$, $p_{\mathrm{T}}^{\mathrm{miss}} > 40\,\mathrm{GeV}$, and $\Delta R(\ell, \gamma) > 0.7$. The leptons are dressed by adding the four-momenta of any photons with $\Delta R(\ell, \gamma) < 0.1$ to the four-momentum of the lepton. A smooth-cone photon isolation is also applied, with parameters $\delta_{0}=0.4$, $\epsilon=1.0$, and $n=1$. Requirements of $m_{\mathrm{T}}^{\mathrm{cluster}}>150\,\mathrm{GeV}$ and a veto on the presence of any jet with $p_{\mathrm{T}} > 30\,\mathrm{GeV}$ and $|\eta| < 2.5$ are applied in addition to the baseline selection.

Relative uncertainties on the measured absolute differential $\Delta \eta(\ell,\gamma)$ cross section. Requirements of $m_{\mathrm{T}}^{\mathrm{cluster}}>150\,\mathrm{GeV}$ and a veto on the presence of any jet with $p_{\mathrm{T}} > 30\,\mathrm{GeV}$ and $|\eta| < 2.5$ are applied in addition to the baseline selection.

Relative uncertainties on the measured fractional differential $\Delta \eta(\ell,\gamma)$ cross section. Requirements of $m_{\mathrm{T}}^{\mathrm{cluster}}>150\,\mathrm{GeV}$ and a veto on the presence of any jet with $p_{\mathrm{T}} > 30\,\mathrm{GeV}$ and $|\eta| < 2.5$ are applied in addition to the baseline selection.

Correlation matrix for the measured absolute differential $\Delta \eta(\ell,\gamma)$ cross section. Requirements of $m_{\mathrm{T}}^{\mathrm{cluster}}>150\,\mathrm{GeV}$ and a veto on the presence of any jet with $p_{\mathrm{T}} > 30\,\mathrm{GeV}$ and $|\eta| < 2.5$ are applied in addition to the baseline selection.

Correlation matrix for the measured fractional differential $\Delta \eta(\ell,\gamma)$ cross section. Requirements of $m_{\mathrm{T}}^{\mathrm{cluster}}>150\,\mathrm{GeV}$ and a veto on the presence of any jet with $p_{\mathrm{T}} > 30\,\mathrm{GeV}$ and $|\eta| < 2.5$ are applied in addition to the baseline selection.

Response matrix from the fiducial to the reconstructed bins of the differential $\Delta \eta(\ell,\gamma)$ cross section measurement. Requirements of $m_{\mathrm{T}}^{\mathrm{cluster}}>150\,\mathrm{GeV}$ and a veto on the presence of any jet with $p_{\mathrm{T}} > 30\,\mathrm{GeV}$ and $|\eta| < 2.5$ are applied in addition to the baseline selection.

Fiducial cross section scaling terms as a function of $C_{3W}$ in all $p_{\mathrm{T}}^{\gamma} \times |\phi_{f}|$ bins. Values are given relative to the SM prediction.

Scans of the profile likelihood test statistic $q$ as a function of $C_{3W}$, given with and without the pure BSM term.

Scans of the profile likelihood test statistic $q$ as a function of $C_{3W}$, given with and without the pure BSM term.

Best-fit values of $C_{3W}$ and corresponding 95% CL confidence intervals as a function of the maximum $p_{\mathrm{T}}^{\gamma}$ bin included in the fit, with and without the pure BSM term.

Best-fit values of $C_{3W}$ and corresponding 95% CL confidence intervals as a function of the maximum $p_{\mathrm{T}}^{\gamma}$ bin included in the fit, with and without the binning in $|\phi_{f}|$.

Response matrix from the fiducial to the reconstructed bins of the differential $p_{\mathrm{T}}^{\gamma} \times |\phi_{f}|$ cross section measurement.

Measured double-differential $p_{\mathrm{T}}^{\gamma} \times |\phi_{f}|$ cross section, compared to the MG5_aMC+PY8 NLO prediction. The differential cross sections $\sigma_{j}(\mathrm{pp}\rightarrow\mathrm{W}^{\pm}\gamma\rightarrow\ell^{\pm}\nu\gamma)$, where $\ell$ denotes all three lepton flavors, are measured in the following fiducial region: $p_{\mathrm{T}}^{\ell} > 80\,\mathrm{GeV}$, $|\eta^{\ell}| < 2.5$, $p_{\mathrm{T}}^{\gamma} > 150\,\mathrm{GeV}$, $|\eta^{\gamma}| < 2.5$, $p_{\mathrm{T}}^{\mathrm{miss}} > 40\,\mathrm{GeV}$, and $\Delta R(\ell, \gamma) > 0.7$. The leptons are dressed by adding the four-momenta of any photons with $\Delta R(\ell, \gamma) < 0.1$ to the four-momentum of the lepton. A smooth-cone photon isolation is also applied, with parameters $\delta_{0}=0.4$, $\epsilon=1.0$, and $n=1$. A veto on the presence of any jet with $p_{\mathrm{T}} > 30\,\mathrm{GeV}$ and $|\eta| < 2.5$ is also applied for this result.

Measured double-differential $p_{\mathrm{T}}^{\gamma} \times |\phi_{f}|$ cross section, compared to the MG5_aMC+PY8 NLO prediction. This table gives the entries for the $(0,\pi/6)$ slice. The differential cross sections $\sigma_{j}(\mathrm{pp}\rightarrow\mathrm{W}^{\pm}\gamma\rightarrow\ell^{\pm}\nu\gamma)$, where $\ell$ denotes all three lepton flavors, are measured in the following fiducial region: $p_{\mathrm{T}}^{\ell} > 80\,\mathrm{GeV}$, $|\eta^{\ell}| < 2.5$, $p_{\mathrm{T}}^{\gamma} > 150\,\mathrm{GeV}$, $|\eta^{\gamma}| < 2.5$, $p_{\mathrm{T}}^{\mathrm{miss}} > 40\,\mathrm{GeV}$, and $\Delta R(\ell, \gamma) > 0.7$. The leptons are dressed by adding the four-momenta of any photons with $\Delta R(\ell, \gamma) < 0.1$ to the four-momentum of the lepton. A smooth-cone photon isolation is also applied, with parameters $\delta_{0}=0.4$, $\epsilon=1.0$, and $n=1$. A veto on the presence of any jet with $p_{\mathrm{T}} > 30\,\mathrm{GeV}$ and $|\eta| < 2.5$ is also applied for this result.

Measured double-differential $p_{\mathrm{T}}^{\gamma} \times |\phi_{f}|$ cross section, compared to the MG5_aMC+PY8 NLO prediction. This table gives the entries for the $(\pi/6,\pi/3)$ slice. The differential cross sections $\sigma_{j}(\mathrm{pp}\rightarrow\mathrm{W}^{\pm}\gamma\rightarrow\ell^{\pm}\nu\gamma)$, where $\ell$ denotes all three lepton flavors, are measured in the following fiducial region: $p_{\mathrm{T}}^{\ell} > 80\,\mathrm{GeV}$, $|\eta^{\ell}| < 2.5$, $p_{\mathrm{T}}^{\gamma} > 150\,\mathrm{GeV}$, $|\eta^{\gamma}| < 2.5$, $p_{\mathrm{T}}^{\mathrm{miss}} > 40\,\mathrm{GeV}$, and $\Delta R(\ell, \gamma) > 0.7$. The leptons are dressed by adding the four-momenta of any photons with $\Delta R(\ell, \gamma) < 0.1$ to the four-momentum of the lepton. A smooth-cone photon isolation is also applied, with parameters $\delta_{0}=0.4$, $\epsilon=1.0$, and $n=1$. A veto on the presence of any jet with $p_{\mathrm{T}} > 30\,\mathrm{GeV}$ and $|\eta| < 2.5$ is also applied for this result.

Measured double-differential $p_{\mathrm{T}}^{\gamma} \times |\phi_{f}|$ cross section, compared to the MG5_aMC+PY8 NLO prediction. This table gives the entries for the $(\pi/3,\pi/2)$ slice. The differential cross sections $\sigma_{j}(\mathrm{pp}\rightarrow\mathrm{W}^{\pm}\gamma\rightarrow\ell^{\pm}\nu\gamma)$, where $\ell$ denotes all three lepton flavors, are measured in the following fiducial region: $p_{\mathrm{T}}^{\ell} > 80\,\mathrm{GeV}$, $|\eta^{\ell}| < 2.5$, $p_{\mathrm{T}}^{\gamma} > 150\,\mathrm{GeV}$, $|\eta^{\gamma}| < 2.5$, $p_{\mathrm{T}}^{\mathrm{miss}} > 40\,\mathrm{GeV}$, and $\Delta R(\ell, \gamma) > 0.7$. The leptons are dressed by adding the four-momenta of any photons with $\Delta R(\ell, \gamma) < 0.1$ to the four-momentum of the lepton. A smooth-cone photon isolation is also applied, with parameters $\delta_{0}=0.4$, $\epsilon=1.0$, and $n=1$. A veto on the presence of any jet with $p_{\mathrm{T}} > 30\,\mathrm{GeV}$ and $|\eta| < 2.5$ is also applied for this result.

Correlation matrix for the measured absolute differential $p_{\mathrm{T}}^{\gamma} \times |\phi_{f}|$ cross section.