Abstract (data abstract)

Differential cross section measurements of $\mathrm{W}^{\pm}\gamma$ production in proton-proton collisions at $\sqrt{s} = 13\,\mathrm{TeV}$ are presented. The data set used in this study was collected with the CMS detector at the CERN LHC in 2016--2018 with an integrated luminosity of $138\,\mathrm{fb}^{-1}$. Candidate events containing an electron or muon, a photon, and missing transverse momentum are selected. The measurements are compared with standard model predictions computed at next-to-leading and next-to-next-to-leading orders in perturbative quantum chromodynamics. Constraints on the presence of TeV-scale new physics affecting the $\mathrm{WW}\gamma$ vertex are determined within an effective field theory framework, focusing on the $\mathcal{O}_{3W}$ operator. A simultaneous measurement of the photon transverse momentum and the azimuthal angle of the charged lepton in a special reference frame is performed. This two-dimensional approach provides up to a factor of ten more sensitivity to the interference between the standard model and the $\mathcal{O}_{3W}$ contribution than using the transverse momentum alone.

Absolute $p_{\mathrm{T}}^{\gamma}$ cross section

Data from Figure 6 (upper left).

10.17182/hepdata.115354.v1/t1

Measured absolute differential $p_{\mathrm{T}}^{\gamma}$ cross section, compared to the MG5_aMC+PY8, GENEVA, MATRIX and MCFM predictions. The differential cross sections $\sigma_{j}(\mathrm{pp}\rightarrow\mathrm{W}^{\pm}\gamma\rightarrow\ell^{\pm}\nu\gamma)$,...
Fractional $p_{\mathrm{T}}^{\gamma}$ cross section

Data from Figure 6 (upper right).

10.17182/hepdata.115354.v1/t2

Measured fractional differential $p_{\mathrm{T}}^{\gamma}$ cross section, compared to the MG5_aMC+PY8, GENEVA, MATRIX and MCFM predictions. The differential cross sections $\sigma_{j}(\mathrm{pp}\rightarrow\mathrm{W}^{\pm}\gamma\rightarrow\ell^{\pm}\nu\gamma)$,...
Absolute $p_{\mathrm{T}}^{\gamma}$ decomposition

Data from Figure 6 (center left).

10.17182/hepdata.115354.v1/t3

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

Data from Figure 6 (center right).

10.17182/hepdata.115354.v1/t4

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

Data from Figure 6 (lower left).

10.17182/hepdata.115354.v1/t5

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

Data from Figure 6 (lower right).

10.17182/hepdata.115354.v1/t6

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

Data from supplementary Figure 2 (upper left).

10.17182/hepdata.115354.v1/t7

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

Data from Figure 7 (upper left).

10.17182/hepdata.115354.v1/t8

Measured absolute differential $\eta^{\gamma}$ cross section, compared to the MG5_aMC+PY8, GENEVA, MATRIX and MCFM predictions. The differential cross sections $\sigma_{j}(\mathrm{pp}\rightarrow\mathrm{W}^{\pm}\gamma\rightarrow\ell^{\pm}\nu\gamma)$,...
Fractional $\eta^{\gamma}$ cross section

Data from Figure 7 (upper right).

10.17182/hepdata.115354.v1/t9

Measured fractional differential $\eta^{\gamma}$ cross section, compared to the MG5_aMC+PY8, GENEVA, MATRIX and MCFM predictions. The differential cross sections $\sigma_{j}(\mathrm{pp}\rightarrow\mathrm{W}^{\pm}\gamma\rightarrow\ell^{\pm}\nu\gamma)$,...
Absolute $\eta^{\gamma}$ decomposition

Data from supplementary Figure 4 (upper left).

10.17182/hepdata.115354.v1/t10

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

Data from supplementary Figure 4 (upper right).

10.17182/hepdata.115354.v1/t11

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

Data from supplementary Figure 4 (lower left).

10.17182/hepdata.115354.v1/t12

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

Data from supplementary Figure 4 (lower right).

10.17182/hepdata.115354.v1/t13

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

Data from supplementary Figure 2 (upper right).

10.17182/hepdata.115354.v1/t14

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

Data from Figure 7 (lower left).

10.17182/hepdata.115354.v1/t15

Measured absolute differential $\Delta R(\ell,\gamma)$ cross section, compared to the MG5_aMC+PY8, GENEVA, MATRIX and MCFM predictions. The differential cross sections...
Fractional $\Delta R(\ell,\gamma)$ cross section

Data from Figure 7 (lower right).

10.17182/hepdata.115354.v1/t16

Measured fractional differential $\Delta R(\ell,\gamma)$ cross section, compared to the MG5_aMC+PY8, GENEVA, MATRIX and MCFM predictions. The differential cross sections...
Absolute $\Delta R(\ell,\gamma)$ decomposition

Data from supplementary Figure 5 (upper left).

10.17182/hepdata.115354.v1/t17

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

Data from supplementary Figure 5 (upper right).

10.17182/hepdata.115354.v1/t18

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

Data from supplementary Figure 5 (lower left).

10.17182/hepdata.115354.v1/t19

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

Data from supplementary Figure 5 (lower right).

10.17182/hepdata.115354.v1/t20

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

Data from supplementary Figure 2 (center left).

10.17182/hepdata.115354.v1/t21

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

Data from Figure 8 (upper left).

10.17182/hepdata.115354.v1/t22

Measured absolute differential $\Delta\eta(\ell,\gamma)$ cross section, compared to the MG5_aMC+PY8, GENEVA, MATRIX and MCFM predictions. The differential cross sections $\sigma_{j}(\mathrm{pp}\rightarrow\mathrm{W}^{\pm}\gamma\rightarrow\ell^{\pm}\nu\gamma)$,...
Fractional $\Delta \eta(\ell,\gamma)$ cross section

Data from Figure 8 (upper right).

10.17182/hepdata.115354.v1/t23

Measured fractional differential $\Delta\eta(\ell,\gamma)$ cross section, compared to the MG5_aMC+PY8, GENEVA, MATRIX and MCFM predictions. The differential cross sections $\sigma_{j}(\mathrm{pp}\rightarrow\mathrm{W}^{\pm}\gamma\rightarrow\ell^{\pm}\nu\gamma)$,...
Absolute $\Delta \eta(\ell,\gamma)$ decomposition

Data from supplementary Figure 6 (upper left).

10.17182/hepdata.115354.v1/t24

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

Data from supplementary Figure 6 (upper right).

10.17182/hepdata.115354.v1/t25

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

Data from supplementary Figure 6 (lower left).

10.17182/hepdata.115354.v1/t26

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

Data from supplementary Figure 6 (lower right).

10.17182/hepdata.115354.v1/t27

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

Data from supplementary Figure 2 (center right).

10.17182/hepdata.115354.v1/t28

Response matrix from the fiducial to the reconstructed bins of the differential $\Delta \eta(\ell,\gamma)$ cross section measurement.
Absolute $m_{\mathrm{T}}^{\mathrm{cluster}}$ cross section

Data from Figure 8 (lower left).

10.17182/hepdata.115354.v1/t29

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 $\sigma_{j}(\mathrm{pp}\rightarrow\mathrm{W}^{\pm}\gamma\rightarrow\ell^{\pm}\nu\gamma)$,...
Fractional $m_{\mathrm{T}}^{\mathrm{cluster}}$ cross section

Data from Figure 8 (lower right).

10.17182/hepdata.115354.v1/t30

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 $\sigma_{j}(\mathrm{pp}\rightarrow\mathrm{W}^{\pm}\gamma\rightarrow\ell^{\pm}\nu\gamma)$,...
Absolute $m_{\mathrm{T}}^{\mathrm{cluster}}$ decomposition

Data from supplementary Figure 7 (upper left).

10.17182/hepdata.115354.v1/t31

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

Data from supplementary Figure 7 (upper right).

10.17182/hepdata.115354.v1/t32

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

Data from supplementary Figure 7 (lower left).

10.17182/hepdata.115354.v1/t33

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

Data from supplementary Figure 7 (lower right).

10.17182/hepdata.115354.v1/t34

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

Data from supplementary Figure 2 (lower).

10.17182/hepdata.115354.v1/t35

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

Data from Figure 11 (left).

10.17182/hepdata.115354.v1/t36

Measured absolute differential $N_{\mathrm{jets}}$ cross section, compared to the MG5_aMC+PY8, GENEVA, MATRIX and MCFM predictions. The differential cross sections $\sigma_{j}(\mathrm{pp}\rightarrow\mathrm{W}^{\pm}\gamma\rightarrow\ell^{\pm}\nu\gamma)$,...
Absolute $N_{\mathrm{jet}}$ correlations

Data from Figure 11 (right).

10.17182/hepdata.115354.v1/t37

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...
Number of jets response matrix

Data from supplementary Figure 8 (left).

10.17182/hepdata.115354.v1/t38

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

Data from supplementary Figure 8 (right).

10.17182/hepdata.115354.v1/t39

Relative uncertainties on the measured absolute differential $N_{\mathrm{jets}}$ cross section.
Absolute $\Delta\eta(\ell,\gamma)$ cross section (RAZ)

Data from Figure 10 (left).

10.17182/hepdata.115354.v1/t40

Measured absolute differential $\Delta\eta(\ell,\gamma)$ cross section, compared to the MG5_aMC+PY8, GENEVA, MATRIX and MCFM predictions. The differential cross sections $\sigma_{j}(\mathrm{pp}\rightarrow\mathrm{W}^{\pm}\gamma\rightarrow\ell^{\pm}\nu\gamma)$,...
Fractional $\Delta \eta(\ell,\gamma)$ cross section (RAZ)

Data from Figure 10 (right).

10.17182/hepdata.115354.v1/t41

Measured fractional differential $\Delta\eta(\ell,\gamma)$ cross section, compared to the MG5_aMC+PY8, GENEVA, MATRIX and MCFM predictions. The differential cross sections $\sigma_{j}(\mathrm{pp}\rightarrow\mathrm{W}^{\pm}\gamma\rightarrow\ell^{\pm}\nu\gamma)$,...
Absolute $\Delta \eta(\ell,\gamma)$ decomposition (RAZ)

Data from supplementary Figure 10 (upper left).

10.17182/hepdata.115354.v1/t42

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...
Fractional $\Delta \eta(\ell,\gamma)$ decomposition (RAZ)

Data from supplementary Figure 10 (upper right).

10.17182/hepdata.115354.v1/t43

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...
Absolute $\Delta \eta(\ell,\gamma)$ correlations (RAZ)

Data from supplementary Figure 10 (lower left).

10.17182/hepdata.115354.v1/t44

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...
Fractional $\Delta \eta(\ell,\gamma)$ correlations (RAZ)

Data from supplementary Figure 10 (lower right).

10.17182/hepdata.115354.v1/t45

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...
$\Delta \eta(\ell,\gamma)$ response matrix (RAZ)

Data from supplementary Figure 9 (right).

10.17182/hepdata.115354.v1/t46

Response matrix from the fiducial to the reconstructed bins of the differential $\Delta \eta(\ell,\gamma)$ cross section measurement. Requirements of $m_{\mathrm{T}}^{\mathrm{cluster}}>150\,\mathrm{GeV}$...
Fiducial scaling terms vs. $C_{3W}$

Data from Table 3.

10.17182/hepdata.115354.v1/t47

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...
Scan of $q$ vs. $C_{3W}$ (SM+int. only)

Data from Figure 12.

10.17182/hepdata.115354.v1/t48

Scans of the profile likelihood test statistic $q$ as a function of $C_{3W}$, given with and without the pure BSM...
Scan of $q$ vs. $C_{3W}$ (SM+int.+BSM)

Data from Figure 12.

10.17182/hepdata.115354.v1/t49

Scans of the profile likelihood test statistic $q$ as a function of $C_{3W}$, given with and without the pure BSM...
Best-fit $C_{3W}$ and 95% CL intervals

Data from Figure 13 (left) and Table 4.

10.17182/hepdata.115354.v1/t50

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...
95% CL $C_{3W}$ intervals without $\phi$ binning

Data from Figure 13 (right).

10.17182/hepdata.115354.v1/t51

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...
$p_{\mathrm{T}}^{\gamma} \times |\phi_{f}|$ response matrix

Data from Figure 14.

10.17182/hepdata.115354.v1/t52

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

Data from Figure 15.

10.17182/hepdata.115354.v1/t53

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 $\ell$...
$p_{\mathrm{T}}^{\gamma} \times |\phi_{f}|$ $(0,\pi/6)$

Data from Figure 15.

10.17182/hepdata.115354.v1/t54

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...
$p_{\mathrm{T}}^{\gamma} \times |\phi_{f}|$ $(\pi/6,\pi/3)$

Data from Figure 15.

10.17182/hepdata.115354.v1/t55

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...
$p_{\mathrm{T}}^{\gamma} \times |\phi_{f}|$ $(\pi/3,\pi/2)$

Data from Figure 15.

10.17182/hepdata.115354.v1/t56

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...
$p_{\mathrm{T}}^{\gamma} \times |\phi_{f}|$ correlations

Data from Figure 16.

10.17182/hepdata.115354.v1/t57

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

Absolute $p_{\mathrm{T}}^{\gamma}$ cross section

Fractional $p_{\mathrm{T}}^{\gamma}$ cross section

Absolute $p_{\mathrm{T}}^{\gamma}$ decomposition

Fractional $p_{\mathrm{T}}^{\gamma}$ decomposition

Absolute $p_{\mathrm{T}}^{\gamma}$ correlations

Fractional $p_{\mathrm{T}}^{\gamma}$ correlations

$p_{\mathrm{T}}^{\gamma}$ response matrix

Absolute $\eta^{\gamma}$ cross section

Fractional $\eta^{\gamma}$ cross section

Absolute $\eta^{\gamma}$ decomposition

Fractional $\eta^{\gamma}$ decomposition

Absolute $\eta^{\gamma}$ correlations

Fractional $\eta^{\gamma}$ correlations

$\eta^{\gamma}$ response matrix

Absolute $\Delta R(\ell,\gamma)$ cross section

Fractional $\Delta R(\ell,\gamma)$ cross section

Absolute $\Delta R(\ell,\gamma)$ decomposition

Fractional $\Delta R(\ell,\gamma)$ decomposition

Absolute $\Delta R(\ell,\gamma)$ correlations

Fractional $\Delta R(\ell,\gamma)$ correlations

$\Delta R(\ell,\gamma)$ response matrix

Absolute $\Delta\eta(\ell,\gamma)$ cross section

Fractional $\Delta \eta(\ell,\gamma)$ cross section

Absolute $\Delta \eta(\ell,\gamma)$ decomposition

Fractional $\Delta \eta(\ell,\gamma)$ decomposition

Absolute $\Delta \eta(\ell,\gamma)$ correlations

Fractional $\Delta \eta(\ell,\gamma)$ correlations

$\Delta \eta(\ell,\gamma)$ response matrix

Absolute $m_{\mathrm{T}}^{\mathrm{cluster}}$ cross section

Fractional $m_{\mathrm{T}}^{\mathrm{cluster}}$ cross section

Absolute $m_{\mathrm{T}}^{\mathrm{cluster}}$ decomposition

Fractional $m_{\mathrm{T}}^{\mathrm{cluster}}$ decomposition

Absolute $m_{\mathrm{T}}^{\mathrm{cluster}}$ correlations

Fractional $m_{\mathrm{T}}^{\mathrm{cluster}}$ correlations

$m_{\mathrm{T}}^{\mathrm{cluster}}$ response matrix

Absolute $N_{\mathrm{jet}}$ cross section

Absolute $N_{\mathrm{jet}}$ correlations

Number of jets response matrix

Absolute $N_{\mathrm{jets}}$ decomposition

Absolute $\Delta\eta(\ell,\gamma)$ cross section (RAZ)

Fractional $\Delta \eta(\ell,\gamma)$ cross section (RAZ)

Absolute $\Delta \eta(\ell,\gamma)$ decomposition (RAZ)

Fractional $\Delta \eta(\ell,\gamma)$ decomposition (RAZ)

Absolute $\Delta \eta(\ell,\gamma)$ correlations (RAZ)

Fractional $\Delta \eta(\ell,\gamma)$ correlations (RAZ)

$\Delta \eta(\ell,\gamma)$ response matrix (RAZ)

Fiducial scaling terms vs. $C_{3W}$

Scan of $q$ vs. $C_{3W}$ (SM+int. only)

Scan of $q$ vs. $C_{3W}$ (SM+int.+BSM)

Best-fit $C_{3W}$ and 95% CL intervals

95% CL $C_{3W}$ intervals without $\phi$ binning

$p_{\mathrm{T}}^{\gamma} \times |\phi_{f}|$ response matrix

$p_{\mathrm{T}}^{\gamma} \times |\phi_{f}|$ cross section

$p_{\mathrm{T}}^{\gamma} \times |\phi_{f}|$ $(0,\pi/6)$

$p_{\mathrm{T}}^{\gamma} \times |\phi_{f}|$ $(\pi/6,\pi/3)$

$p_{\mathrm{T}}^{\gamma} \times |\phi_{f}|$ $(\pi/3,\pi/2)$

$p_{\mathrm{T}}^{\gamma} \times |\phi_{f}|$ correlations

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