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| CMS-SMP-20-005 ; CERN-EP-2021-219 | ||
| Measurement of ${\mathrm{W^{\pm}}\gamma}$ differential cross sections in proton-proton collisions at $\sqrt{s} = $ 13 TeV and effective field theory constraints | ||
| CMS Collaboration | ||
| 27 November 2021 | ||
| Phys. Rev. D 105 (2022) 052003 | ||
| Abstract: Differential cross section measurements of ${\mathrm{W^{\pm}}\gamma}$ production in proton-proton collisions at $\sqrt{s} = $ 13 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 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 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. | ||
| Links: e-print arXiv:2111.13948 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; | ||
| Figures & Tables | Summary | Additional Figures | References | CMS Publications |
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| Figures | |
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Figure 1:
LO Feynman diagrams for ${\mathrm{W^{+}} \gamma}$ production showing initial-state (left) and final-state (center) radiation of the photon, and the WW$ \gamma$ TGC process (right). |
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Figure 1-a:
LO Feynman diagrams for ${\mathrm{W^{+}} \gamma}$ production showing initial-state (left) and final-state (center) radiation of the photon, and the WW$ \gamma$ TGC process (right). |
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Figure 1-b:
LO Feynman diagrams for ${\mathrm{W^{+}} \gamma}$ production showing initial-state (left) and final-state (center) radiation of the photon, and the WW$ \gamma$ TGC process (right). |
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Figure 1-c:
LO Feynman diagrams for ${\mathrm{W^{+}} \gamma}$ production showing initial-state (left) and final-state (center) radiation of the photon, and the WW$ \gamma$ TGC process (right). |
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Figure 2:
Scheme of the special coordinate system for ${\mathrm{W^{\pm}} \gamma}$ production, defined by a Lorentz boost to the center-of-mass frame along the direction $\hat{r}$. The $z$ axis is chosen as the $\mathrm{W^{\pm}}$ boson direction in this frame, and $y$ is given by $\hat{z} \times \hat{r}$. The $\mathrm{W^{\pm}}$ boson decay plane is indicated in blue, where the labels ${f_{+}}$ and ${f_{-}}$ refer to positive and negative helicity final-state fermions. The angles $\phi $ and $\theta $ are the azimuthal and polar angles of ${f_{+}}$. |
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Figure 3:
Particle-level distributions (in arbitrary units) of the decay angle $\phi $, comparing the LO 2 $\to$ 2 process (left) to the LO MLM-merged prediction with up to two additional jets in the matrix element calculations (right). The black line gives the SM prediction ($ {C_{3W}} = $ 0) and the red, green, and blue lines correspond to different nonzero values of ${C_{3W}}$, for which only the interference contribution is shown. The black and blue dashed lines in the right figure give the distributions in the presence of a jet veto, as described in the text. |
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Figure 3-a:
Particle-level distributions (in arbitrary units) of the decay angle $\phi $, comparing the LO 2 $\to$ 2 process (left) to the LO MLM-merged prediction with up to two additional jets in the matrix element calculations (right). The black line gives the SM prediction ($ {C_{3W}} = $ 0) and the red, green, and blue lines correspond to different nonzero values of ${C_{3W}}$, for which only the interference contribution is shown. The black and blue dashed lines in the right figure give the distributions in the presence of a jet veto, as described in the text. |
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Figure 3-b:
Particle-level distributions (in arbitrary units) of the decay angle $\phi $, comparing the LO 2 $\to$ 2 process (left) to the LO MLM-merged prediction with up to two additional jets in the matrix element calculations (right). The black line gives the SM prediction ($ {C_{3W}} = $ 0) and the red, green, and blue lines correspond to different nonzero values of ${C_{3W}}$, for which only the interference contribution is shown. The black and blue dashed lines in the right figure give the distributions in the presence of a jet veto, as described in the text. |
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Figure 4:
Distributions of the lepton ${p_{\mathrm {T}}}$ (upper left), the photon ${p_{\mathrm {T}}}$ (upper right), ${{m_{\mathrm {T}}} (\ell, {{p_{\mathrm {T}}} ^\text {miss}})}$ (lower left), and ${m_{\mathrm {T}}^{\text {cluster}}}$ (lower right), combining the electron and muon channels. The horizontal and vertical bars associated to the data points correspond to the bin widths and statistical uncertainties, respectively. The shaded band represents the total statistical and systematic uncertainty in the signal plus background expectation. |
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Figure 4-a:
Distributions of the lepton ${p_{\mathrm {T}}}$ (upper left), the photon ${p_{\mathrm {T}}}$ (upper right), ${{m_{\mathrm {T}}} (\ell, {{p_{\mathrm {T}}} ^\text {miss}})}$ (lower left), and ${m_{\mathrm {T}}^{\text {cluster}}}$ (lower right), combining the electron and muon channels. The horizontal and vertical bars associated to the data points correspond to the bin widths and statistical uncertainties, respectively. The shaded band represents the total statistical and systematic uncertainty in the signal plus background expectation. |
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Figure 4-b:
Distributions of the lepton ${p_{\mathrm {T}}}$ (upper left), the photon ${p_{\mathrm {T}}}$ (upper right), ${{m_{\mathrm {T}}} (\ell, {{p_{\mathrm {T}}} ^\text {miss}})}$ (lower left), and ${m_{\mathrm {T}}^{\text {cluster}}}$ (lower right), combining the electron and muon channels. The horizontal and vertical bars associated to the data points correspond to the bin widths and statistical uncertainties, respectively. The shaded band represents the total statistical and systematic uncertainty in the signal plus background expectation. |
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Figure 4-c:
Distributions of the lepton ${p_{\mathrm {T}}}$ (upper left), the photon ${p_{\mathrm {T}}}$ (upper right), ${{m_{\mathrm {T}}} (\ell, {{p_{\mathrm {T}}} ^\text {miss}})}$ (lower left), and ${m_{\mathrm {T}}^{\text {cluster}}}$ (lower right), combining the electron and muon channels. The horizontal and vertical bars associated to the data points correspond to the bin widths and statistical uncertainties, respectively. The shaded band represents the total statistical and systematic uncertainty in the signal plus background expectation. |
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Figure 4-d:
Distributions of the lepton ${p_{\mathrm {T}}}$ (upper left), the photon ${p_{\mathrm {T}}}$ (upper right), ${{m_{\mathrm {T}}} (\ell, {{p_{\mathrm {T}}} ^\text {miss}})}$ (lower left), and ${m_{\mathrm {T}}^{\text {cluster}}}$ (lower right), combining the electron and muon channels. The horizontal and vertical bars associated to the data points correspond to the bin widths and statistical uncertainties, respectively. The shaded band represents the total statistical and systematic uncertainty in the signal plus background expectation. |
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Figure 5:
The two-dimensional distribution of ${\phi ^{\text {gen}}}$ versus ${\phi ^{\text {true}}}$, where the former is reconstructed using the particle-level lepton and photon momenta and ${{\vec{p}}_{\mathrm {T}}^{\, \text {miss}}}$. The off-diagonal components correspond to events where the incorrect solution for ${\eta ^{\nu}}$ is chosen, as described in the text. |
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Figure 6:
The measured ${{p_{\mathrm {T}}} ^{\gamma}}$ absolute (left) and fractional (right) differential cross sections (upper), compared with the MG5\_aMC+PY8, GENEVA, MATRIX and MCFM predictions, and corresponding uncertainty decomposition (center) and correlation matrices (lower). In the upper figures, the black vertical bars give the total uncertainty on each measurement. The predictions are offset horizontally in each bin to improve visibility, and the corresponding vertical bars show the missing higher order correction uncertainties. |
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Figure 6-a:
The measured ${{p_{\mathrm {T}}} ^{\gamma}}$ absolute (left) and fractional (right) differential cross sections (upper), compared with the MG5\_aMC+PY8, GENEVA, MATRIX and MCFM predictions, and corresponding uncertainty decomposition (center) and correlation matrices (lower). In the upper figures, the black vertical bars give the total uncertainty on each measurement. The predictions are offset horizontally in each bin to improve visibility, and the corresponding vertical bars show the missing higher order correction uncertainties. |
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Figure 6-b:
The measured ${{p_{\mathrm {T}}} ^{\gamma}}$ absolute (left) and fractional (right) differential cross sections (upper), compared with the MG5\_aMC+PY8, GENEVA, MATRIX and MCFM predictions, and corresponding uncertainty decomposition (center) and correlation matrices (lower). In the upper figures, the black vertical bars give the total uncertainty on each measurement. The predictions are offset horizontally in each bin to improve visibility, and the corresponding vertical bars show the missing higher order correction uncertainties. |
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Figure 6-c:
The measured ${{p_{\mathrm {T}}} ^{\gamma}}$ absolute (left) and fractional (right) differential cross sections (upper), compared with the MG5\_aMC+PY8, GENEVA, MATRIX and MCFM predictions, and corresponding uncertainty decomposition (center) and correlation matrices (lower). In the upper figures, the black vertical bars give the total uncertainty on each measurement. The predictions are offset horizontally in each bin to improve visibility, and the corresponding vertical bars show the missing higher order correction uncertainties. |
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Figure 6-d:
The measured ${{p_{\mathrm {T}}} ^{\gamma}}$ absolute (left) and fractional (right) differential cross sections (upper), compared with the MG5\_aMC+PY8, GENEVA, MATRIX and MCFM predictions, and corresponding uncertainty decomposition (center) and correlation matrices (lower). In the upper figures, the black vertical bars give the total uncertainty on each measurement. The predictions are offset horizontally in each bin to improve visibility, and the corresponding vertical bars show the missing higher order correction uncertainties. |
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Figure 6-e:
The measured ${{p_{\mathrm {T}}} ^{\gamma}}$ absolute (left) and fractional (right) differential cross sections (upper), compared with the MG5\_aMC+PY8, GENEVA, MATRIX and MCFM predictions, and corresponding uncertainty decomposition (center) and correlation matrices (lower). In the upper figures, the black vertical bars give the total uncertainty on each measurement. The predictions are offset horizontally in each bin to improve visibility, and the corresponding vertical bars show the missing higher order correction uncertainties. |
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Figure 6-f:
The measured ${{p_{\mathrm {T}}} ^{\gamma}}$ absolute (left) and fractional (right) differential cross sections (upper), compared with the MG5\_aMC+PY8, GENEVA, MATRIX and MCFM predictions, and corresponding uncertainty decomposition (center) and correlation matrices (lower). In the upper figures, the black vertical bars give the total uncertainty on each measurement. The predictions are offset horizontally in each bin to improve visibility, and the corresponding vertical bars show the missing higher order correction uncertainties. |
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Figure 7:
The measured absolute (left) and fractional (right) differential cross sections for ${\eta ^{\gamma}}$ (upper) and ${{\Delta R}(\ell,\gamma)}$ (lower), compared with the MG5\_aMC+PY8, GENEVA, MATRIX and MCFM predictions. The shaded bands give the corresponding missing higher order correction uncertainties. The black vertical bars give the total uncertainty on each measurement. The predictions are offset horizontally in each bin to improve visibility, and the corresponding vertical bars show the missing higher order correction uncertainties. |
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Figure 7-a:
The measured absolute (left) and fractional (right) differential cross sections for ${\eta ^{\gamma}}$ (upper) and ${{\Delta R}(\ell,\gamma)}$ (lower), compared with the MG5\_aMC+PY8, GENEVA, MATRIX and MCFM predictions. The shaded bands give the corresponding missing higher order correction uncertainties. The black vertical bars give the total uncertainty on each measurement. The predictions are offset horizontally in each bin to improve visibility, and the corresponding vertical bars show the missing higher order correction uncertainties. |
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Figure 7-b:
The measured absolute (left) and fractional (right) differential cross sections for ${\eta ^{\gamma}}$ (upper) and ${{\Delta R}(\ell,\gamma)}$ (lower), compared with the MG5\_aMC+PY8, GENEVA, MATRIX and MCFM predictions. The shaded bands give the corresponding missing higher order correction uncertainties. The black vertical bars give the total uncertainty on each measurement. The predictions are offset horizontally in each bin to improve visibility, and the corresponding vertical bars show the missing higher order correction uncertainties. |
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Figure 7-c:
The measured absolute (left) and fractional (right) differential cross sections for ${\eta ^{\gamma}}$ (upper) and ${{\Delta R}(\ell,\gamma)}$ (lower), compared with the MG5\_aMC+PY8, GENEVA, MATRIX and MCFM predictions. The shaded bands give the corresponding missing higher order correction uncertainties. The black vertical bars give the total uncertainty on each measurement. The predictions are offset horizontally in each bin to improve visibility, and the corresponding vertical bars show the missing higher order correction uncertainties. |
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Figure 7-d:
The measured absolute (left) and fractional (right) differential cross sections for ${\eta ^{\gamma}}$ (upper) and ${{\Delta R}(\ell,\gamma)}$ (lower), compared with the MG5\_aMC+PY8, GENEVA, MATRIX and MCFM predictions. The shaded bands give the corresponding missing higher order correction uncertainties. The black vertical bars give the total uncertainty on each measurement. The predictions are offset horizontally in each bin to improve visibility, and the corresponding vertical bars show the missing higher order correction uncertainties. |
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Figure 8:
The measured absolute (left) and fractional (right) differential cross sections for ${{\Delta \eta} (\ell,\gamma)}$ (upper) and ${m_{\mathrm {T}}^{\text {cluster}}}$ (lower), compared with the MG5\_aMC+PY8, GENEVA, MATRIX and MCFM predictions. The shaded bands give the corresponding missing higher order correction uncertainties. The black vertical bars give the total uncertainty on each measurement. The predictions are offset horizontally in each bin to improve visibility, and the corresponding vertical bars show the missing higher order correction uncertainties. |
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Figure 8-a:
The measured absolute (left) and fractional (right) differential cross sections for ${{\Delta \eta} (\ell,\gamma)}$ (upper) and ${m_{\mathrm {T}}^{\text {cluster}}}$ (lower), compared with the MG5\_aMC+PY8, GENEVA, MATRIX and MCFM predictions. The shaded bands give the corresponding missing higher order correction uncertainties. The black vertical bars give the total uncertainty on each measurement. The predictions are offset horizontally in each bin to improve visibility, and the corresponding vertical bars show the missing higher order correction uncertainties. |
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Figure 8-b:
The measured absolute (left) and fractional (right) differential cross sections for ${{\Delta \eta} (\ell,\gamma)}$ (upper) and ${m_{\mathrm {T}}^{\text {cluster}}}$ (lower), compared with the MG5\_aMC+PY8, GENEVA, MATRIX and MCFM predictions. The shaded bands give the corresponding missing higher order correction uncertainties. The black vertical bars give the total uncertainty on each measurement. The predictions are offset horizontally in each bin to improve visibility, and the corresponding vertical bars show the missing higher order correction uncertainties. |
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Figure 8-c:
The measured absolute (left) and fractional (right) differential cross sections for ${{\Delta \eta} (\ell,\gamma)}$ (upper) and ${m_{\mathrm {T}}^{\text {cluster}}}$ (lower), compared with the MG5\_aMC+PY8, GENEVA, MATRIX and MCFM predictions. The shaded bands give the corresponding missing higher order correction uncertainties. The black vertical bars give the total uncertainty on each measurement. The predictions are offset horizontally in each bin to improve visibility, and the corresponding vertical bars show the missing higher order correction uncertainties. |
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Figure 8-d:
The measured absolute (left) and fractional (right) differential cross sections for ${{\Delta \eta} (\ell,\gamma)}$ (upper) and ${m_{\mathrm {T}}^{\text {cluster}}}$ (lower), compared with the MG5\_aMC+PY8, GENEVA, MATRIX and MCFM predictions. The shaded bands give the corresponding missing higher order correction uncertainties. The black vertical bars give the total uncertainty on each measurement. The predictions are offset horizontally in each bin to improve visibility, and the corresponding vertical bars show the missing higher order correction uncertainties. |
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Figure 9:
The measured jet multiplicity cross sections (left) and corresponding correlation matrix (right). In the left figure, the black vertical bars give the total uncertainty on each measurement. The predictions are offset horizontally in each bin to improve visibility, and the corresponding vertical bars show the missing higher order correction uncertainties. |
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Figure 9-a:
The measured jet multiplicity cross sections (left) and corresponding correlation matrix (right). In the left figure, the black vertical bars give the total uncertainty on each measurement. The predictions are offset horizontally in each bin to improve visibility, and the corresponding vertical bars show the missing higher order correction uncertainties. |
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Figure 9-b:
The measured jet multiplicity cross sections (left) and corresponding correlation matrix (right). In the left figure, the black vertical bars give the total uncertainty on each measurement. The predictions are offset horizontally in each bin to improve visibility, and the corresponding vertical bars show the missing higher order correction uncertainties. |
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Figure 10:
The measured ${{\Delta \eta} (\ell,\gamma)}$ absolute (left) and fractional (right) differential cross sections, compared with the MG5\_aMC+PY8, GENEVA, MATRIX and MCFM predictions. The black vertical bars give the total uncertainty on each measurement. The predictions are offset horizontally in each bin to improve visibility, and the corresponding vertical bars show the missing higher order correction uncertainties. |
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Figure 10-a:
The measured ${{\Delta \eta} (\ell,\gamma)}$ absolute (left) and fractional (right) differential cross sections, compared with the MG5\_aMC+PY8, GENEVA, MATRIX and MCFM predictions. The black vertical bars give the total uncertainty on each measurement. The predictions are offset horizontally in each bin to improve visibility, and the corresponding vertical bars show the missing higher order correction uncertainties. |
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Figure 10-b:
The measured ${{\Delta \eta} (\ell,\gamma)}$ absolute (left) and fractional (right) differential cross sections, compared with the MG5\_aMC+PY8, GENEVA, MATRIX and MCFM predictions. The black vertical bars give the total uncertainty on each measurement. The predictions are offset horizontally in each bin to improve visibility, and the corresponding vertical bars show the missing higher order correction uncertainties. |
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Figure 11:
The expected and observed ${{p_{\mathrm {T}}} ^{\gamma}}$ distribution in each ${| {\phi _{f}} |}$ region before the maximum likelihood fit is performed. The horizontal and vertical bars associated to the data points correspond to the bin widths and statistical uncertainties, respectively. The shaded uncertainty band incorporates all statistical and systematic uncertainties. The red and blue lines show how the total expectation changes when ${C_{3W}}$ is set to $-$0.2 and 0.2 TeV$ ^{-2}$, respectively. Only the SM and interference terms are included in this example. |
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Figure 12:
Scans of the profile likelihood test statistic $q$ as a function of ${C_{3W}}$, given with and without the pure BSM term by the dashed red and solid black lines, respectively. The full set of ${{p_{\mathrm {T}}} ^{\gamma}}$ and ${| {\phi _{f}} |}$ bins, described in the text, are included for these scans. |
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Figure 13:
Best-fit values of ${C_{3W}}$ and the corresponding 95% CL confidence intervals as a function of the maximum ${{p_{\mathrm {T}}} ^{\gamma}}$ bin included in the fit (left). Measurements with and without the pure BSM term are given by the black and red lines, respectively. The limits without the pure BSM term given with and without the binning in ${| {\phi _{f}} |}$ are also shown (right), with black and blue lines, respectively. Please note the different vertical scales; the black lines in both figures correspond to the same limits. |
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Figure 13-a:
Best-fit values of ${C_{3W}}$ and the corresponding 95% CL confidence intervals as a function of the maximum ${{p_{\mathrm {T}}} ^{\gamma}}$ bin included in the fit (left). Measurements with and without the pure BSM term are given by the black and red lines, respectively. The limits without the pure BSM term given with and without the binning in ${| {\phi _{f}} |}$ are also shown (right), with black and blue lines, respectively. Please note the different vertical scales; the black lines in both figures correspond to the same limits. |
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Figure 13-b:
Best-fit values of ${C_{3W}}$ and the corresponding 95% CL confidence intervals as a function of the maximum ${{p_{\mathrm {T}}} ^{\gamma}}$ bin included in the fit (left). Measurements with and without the pure BSM term are given by the black and red lines, respectively. The limits without the pure BSM term given with and without the binning in ${| {\phi _{f}} |}$ are also shown (right), with black and blue lines, respectively. Please note the different vertical scales; the black lines in both figures correspond to the same limits. |
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Figure 14:
Response matrix for the differential $ {{p_{\mathrm {T}}} ^{\gamma}} {\times} {{| {\phi _{f}} |}} $ cross section measurement. The entry in each bin gives the probability for an event of a given particle-level fiducial bin to be reconstructed in one of the corresponding reconstruction-level bins. The inner labels give the ${| {\phi _{f}} |}$ bin and the outer labels indicate the ${{p_{\mathrm {T}}} ^{\gamma}}$ bin. |
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Figure 15:
Measured double-differential $ {{p_{\mathrm {T}}} ^{\gamma}} {\times} {{| {\phi _{f}} |}} $ cross section and comparison to the MG5\_aMC+PY8 NLO prediction. The black vertical bars give the total uncertainty on each measurement. The red shaded bands give the missing higher order correction uncertainties in the prediction. |
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Figure 16:
Correlation matrix for the measured $ {{p_{\mathrm {T}}} ^{\gamma}} {\times} {{| {\phi _{f}} |}} $ cross sections. |
| Tables | |
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Table 1:
Summary of the systematic uncertainties affecting the signal and background predictions. The table notes whether each uncertainty affects the shape of the measured observable or just the normalization, and whether the effect is correlated between the data-taking years. The normalization effect on the expected yield of the applicable processes is also given. For some shape uncertainties the values vary significantly across the observable distribution. In these cases the typical range and maximum values are given, where the former is the central 68% interval considering all bins. |
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Table 2:
Cross sections measured in bins of jet multiplicity and comparison with the MG5\_aMC+PY8, GENEVA, MATRIX and MCFM predictions. The MCFM column marked (EW) is the NNLO QCD prediction combined with NLO electroweak corrections, as described in the text. |
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Table 3:
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: $ {\mu ^{\text {int}}} = {\sigma ^{\text {int}}} / {\sigma ^{\text {SM}}} $ and $ {\mu ^{\text {BSM}}} = {\sigma ^{\text {BSM}}} / {\sigma ^{\text {SM}}} $. |
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Table 4:
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. |
| Summary |
|
This paper has presented an analysis of ${\mathrm{W^{\pm}}\gamma}$ production in $\sqrt{s} = $ 13 TeV proton-proton collisions using data recorded with the CMS detector at the LHC, corresponding to an integrated luminosity of 138 fb$^{-1}$. Differential cross sections have been measured for several observables and compared with standard model (SM) predictions computed at next-to-leading and next-to-next-to-leading orders in perturbative quantum chromodynamics. The radiation amplitude zero effect, caused by interference between ${\mathrm{W^{\pm}}\gamma}$ production diagrams, has been studied via a measurement of the pseudorapidity difference between the lepton and the photon. Constraints on the presence of TeVns-scale new physics affecting the WW$\gamma$ vertex have been determined using an effective field theory framework. Confidence intervals on the Wilson coefficient ${C_{3W}} $, determined at the 95% confidence level, are [$-$0.062, 0.052] TeV$^{-2}$ with the inclusion of the interference and pure beyond the SM contributions, and [$-$0.38, 0.17] TeV$^{-2}$ when only the interference is considered. A novel two-dimensional approach is used with the simultaneous measurement of the photon transverse momentum and the azimuthal angle of the charged lepton in a special reference frame. With this method, the sensitivity to the interference between the SM and the ${\mathcal{O}_{3W}}$ operator is enhanced by up to a factor of ten compared to a measurement using the transverse momentum alone. This improves the validity of the result, as the dependence on the missing higher-order contributions in the EFT expansion is reduced. The technique will also be valuable in the future when sufficiently small values of ${C_{3W}}$ are probed such that the interference contribution will be dominant. |
| Additional Figures | |
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Additional Figure 1:
Particle-level distributions of the photon $ {p_{\mathrm {T}}} $, considering only the LO 2 $\rightarrow $ 2 process, comparing the inclusion of the interference and BSM components (left) to the inclusion of only the interference (right). The markers give the SM prediction ($C_{3W} = $ 0) and lines correspond to different values of $C_{3W}$. |
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Additional Figure 1-a:
Particle-level distributions of the photon $ {p_{\mathrm {T}}} $, considering only the LO 2 $\rightarrow $ 2 process, with the inclusion of the interference and BSM components. The markers give the SM prediction ($C_{3W} = $ 0) and lines correspond to different values of $C_{3W}$. |
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Additional Figure 1-b:
Particle-level distributions of the photon $ {p_{\mathrm {T}}} $, considering only the LO 2 $\rightarrow $ 2 process, with the inclusion of only the interference. The markers give the SM prediction ($C_{3W} = $ 0) and lines correspond to different values of $C_{3W}$. |
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Additional Figure 2:
Response matrices for the $ {p_{\mathrm {T}}^{{\gamma}}} $, $\eta ^{{\gamma}}$, $ {\Delta R}(\ell,\gamma)$, $\Delta \eta (\ell,\gamma)$, and $ {m_{\mathrm {T}}^{\text {cluster}}} $ differential cross section measurements under the baseline selection. |
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Additional Figure 2-a:
Response matrice for the $ {p_{\mathrm {T}}^{{\gamma}}} $ differential cross section measurement under the baseline selection. |
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Additional Figure 2-b:
Response matrice for the $\eta ^{{\gamma}}$ differential cross section measurement under the baseline selection. |
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Additional Figure 2-c:
Response matrice for the $ {\Delta R}(\ell,\gamma)$ differential cross section measurement under the baseline selection. |
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Additional Figure 2-d:
Response matrice for the $\Delta \eta (\ell,\gamma)$ differential cross section measurement under the baseline selection. |
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Additional Figure 2-e:
Response matrice for the $ {m_{\mathrm {T}}^{\text {cluster}}} $ differential cross section measurement under the baseline selection. |
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Additional Figure 3:
Expected and observed distributions of $\eta ^{{\gamma}}$, $ {\Delta R}(\ell,\gamma)$ and $\Delta \eta (\ell,\gamma)$ under the baseline selection before the maximum likelihood is performed. |
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Additional Figure 3-a:
Expected and observed distributions of $\eta ^{{\gamma}}$ under the baseline selection before the maximum likelihood is performed. |
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Additional Figure 3-b:
Expected and observed distributions of $ {\Delta R}(\ell,\gamma)$ under the baseline selection before the maximum likelihood is performed. |
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Additional Figure 3-c:
Expected and observed distributions of $\Delta \eta (\ell,\gamma)$ under the baseline selection before the maximum likelihood is performed. |
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Additional Figure 4:
The uncertainty compositions and correlation matrices for the $\eta ^{\gamma}$ absolute (left) and fractional (right) differential cross sections. |
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Additional Figure 4-a:
The uncertainty composition for the $\eta ^{\gamma}$ absolute differential cross section. |
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Additional Figure 4-b:
The uncertainty composition for the $\eta ^{\gamma}$ fractional differential cross section. |
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Additional Figure 4-c:
The correlation matrice for the $\eta ^{\gamma}$ absolute differential cross section. |
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Additional Figure 4-d:
The correlation matrice for the $\eta ^{\gamma}$ fractional differential cross section. |
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Additional Figure 5:
The uncertainty compositions and correlation matrices for the $\Delta R(\ell,\gamma)$ absolute (left) and fractional (right) differential cross sections. |
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Additional Figure 5-a:
The uncertainty composition for the $\Delta R(\ell,\gamma)$ absolute differential cross section. |
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Additional Figure 5-b:
The uncertainty composition for the $\Delta R(\ell,\gamma)$ fractional differential cross section. |
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Additional Figure 5-c:
The correlation matrice for the $\Delta R(\ell,\gamma)$ absolute differential cross section. |
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Additional Figure 5-d:
The correlation matrice for the $\Delta R(\ell,\gamma)$ fractional differential cross section. |
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Additional Figure 6:
The uncertainty compositions and correlation matrices for the $\Delta \eta (\ell,\gamma)$ absolute (left) and fractional (right) differential cross sections. |
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Additional Figure 6-a:
The uncertainty composition for the $\Delta \eta (\ell,\gamma)$ absolute differential cross section. |
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Additional Figure 6-b:
The uncertainty composition for the $\Delta \eta (\ell,\gamma)$ fractional differential cross section. |
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Additional Figure 6-c:
The correlation matrice for the $\Delta \eta (\ell,\gamma)$ absolute differential cross section. |
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Additional Figure 6-d:
The correlation matrice for the $\Delta \eta (\ell,\gamma)$ fractional differential cross section. |
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Additional Figure 7:
The uncertainty compositions and correlation matrices for the $ {m_{\mathrm {T}}^{\text {cluster}}} $ absolute (left) and fractional (right) differential cross sections. |
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Additional Figure 7-a:
The uncertainty composition for the $ {m_{\mathrm {T}}^{\text {cluster}}} $ absolute differential cross sections. |
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Additional Figure 7-b:
The uncertainty composition for the $ {m_{\mathrm {T}}^{\text {cluster}}} $ fractional differential cross sections. |
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Additional Figure 7-c:
The correlation matrice for the $ {m_{\mathrm {T}}^{\text {cluster}}} $ absolute differential cross sections. |
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Additional Figure 7-d:
The correlation matrice for the $ {m_{\mathrm {T}}^{\text {cluster}}} $ fractional differential cross sections. |
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Additional Figure 8:
The response matrix and uncertainty composition for the jet multiplicity cross section measurement. |
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Additional Figure 8-a:
The response matrix for the jet multiplicity cross section measurement. |
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Additional Figure 8-b:
The uncertainty composition for the jet multiplicity cross section measurement. |
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Additional Figure 9:
Expected and observed $\Delta \eta (\ell, \gamma)$ distributions before the maximum likelihood is performed (left). Requirements of $ {m_{\mathrm {T}}^{\text {cluster}}} > $ 150 GeV and a jet veto are applied in addition to the baseline selection to enhance the radiation amplitude zero supression at $\Delta \eta (\ell, \gamma)= $ 0. The shaded uncertainty band incorporates all systematic uncertainties. The corresponding response matrix is also given (right). |
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Additional Figure 9-a:
Expected and observed $\Delta \eta (\ell, \gamma)$ distributions before the maximum likelihood is performed. Requirements of $ {m_{\mathrm {T}}^{\text {cluster}}} > $ 150 GeV and a jet veto are applied in addition to the baseline selection to enhance the radiation amplitude zero supression at $\Delta \eta (\ell, \gamma)= $ 0. The shaded uncertainty band incorporates all systematic uncertainties. |
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Additional Figure 9-b:
The corresponding response matrix. |
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Additional Figure 10:
The uncertainty compositions and correlation matrices for the $\Delta \eta (\ell,\gamma)$ absolute (left) and fractional (right) differential cross sections. Requirements of $ {m_{\mathrm {T}}^{\text {cluster}}} > $ 150 GeV and a jet veto are applied in addition to the baseline selection to enhance the radiation amplitude zero supression at $\Delta \eta (\ell, \gamma)= $ 0. |
png pdf |
Additional Figure 10-a:
The uncertainty composition for the $\Delta \eta (\ell,\gamma)$ absolute differential cross sections. Requirements of $ {m_{\mathrm {T}}^{\text {cluster}}} > $ 150 GeV and a jet veto are applied in addition to the baseline selection to enhance the radiation amplitude zero supression at $\Delta \eta (\ell, \gamma)= $ 0. |
png pdf |
Additional Figure 10-b:
The uncertainty composition for the $\Delta \eta (\ell,\gamma)$ fractional differential cross sections. Requirements of $ {m_{\mathrm {T}}^{\text {cluster}}} > $ 150 GeV and a jet veto are applied in addition to the baseline selection to enhance the radiation amplitude zero supression at $\Delta \eta (\ell, \gamma)= $ 0. |
png pdf |
Additional Figure 10-c:
The correlation matrice for the $\Delta \eta (\ell,\gamma)$ absolute differential cross sections. Requirements of $ {m_{\mathrm {T}}^{\text {cluster}}} > $ 150 GeV and a jet veto are applied in addition to the baseline selection to enhance the radiation amplitude zero supression at $\Delta \eta (\ell, \gamma)= $ 0. |
png pdf |
Additional Figure 10-d:
The correlation matrice for the $\Delta \eta (\ell,\gamma)$ fractional differential cross sections. Requirements of $ {m_{\mathrm {T}}^{\text {cluster}}} > $ 150 GeV and a jet veto are applied in addition to the baseline selection to enhance the radiation amplitude zero supression at $\Delta \eta (\ell, \gamma)= $ 0. |
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