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Sketch of the Collins-Soper reference frame, in which the angles ~$\theta_{\text{CS}}$ and~$\phics$ are defined with respect to the negatively charged lepton~$\ell$~(see text). The notations $\hat x, \hat y$ and $\hat z$ denote the unit vectors along the corresponding axes in this reference frame.

The angular coefficients $A_{0-4}$ and the difference $A_0-A_2$, shown as a function of~\ptz, as predicted from \DYNNLO calculations at~NLO and~NNLO in~QCD. The NLO~predictions for $A_0-A_2$ are compatible with zero, as expected from the Lam--Tung relation~\cite{Lam:1978pu,Lam:1978zr,Lam:1980uc}. The error bars show the total uncertainty of the predictions, including contributions from statistical uncertainties, QCD~scale variations and~PDFs. The statistical uncertainties of the NNLO~predictions are dominant and an order of magnitude larger than those of the NLO~predictions.

The angular coefficients $A_{0-4}$ and the difference $A_0-A_2$, shown as a function of~\ptz, as predicted from \DYNNLO calculations at~NLO and~NNLO in~QCD. The NLO~predictions for $A_0-A_2$ are compatible with zero, as expected from the Lam--Tung relation~\cite{Lam:1978pu,Lam:1978zr,Lam:1980uc}. The error bars show the total uncertainty of the predictions, including contributions from statistical uncertainties, QCD~scale variations and~PDFs. The statistical uncertainties of the NNLO~predictions are dominant and an order of magnitude larger than those of the NLO~predictions.

The angular coefficients $A_{0-4}$ and the difference $A_0-A_2$, shown as a function of~\ptz, as predicted from \DYNNLO calculations at~NLO and~NNLO in~QCD. The NLO~predictions for $A_0-A_2$ are compatible with zero, as expected from the Lam--Tung relation~\cite{Lam:1978pu,Lam:1978zr,Lam:1980uc}. The error bars show the total uncertainty of the predictions, including contributions from statistical uncertainties, QCD~scale variations and~PDFs. The statistical uncertainties of the NNLO~predictions are dominant and an order of magnitude larger than those of the NLO~predictions.

The angular coefficients $A_{0-4}$ and the difference $A_0-A_2$, shown as a function of~\ptz, as predicted from \DYNNLO calculations at~NLO and~NNLO in~QCD. The NLO~predictions for $A_0-A_2$ are compatible with zero, as expected from the Lam--Tung relation~\cite{Lam:1978pu,Lam:1978zr,Lam:1980uc}. The error bars show the total uncertainty of the predictions, including contributions from statistical uncertainties, QCD~scale variations and~PDFs. The statistical uncertainties of the NNLO~predictions are dominant and an order of magnitude larger than those of the NLO~predictions.

The angular coefficients $A_{0-4}$ and the difference $A_0-A_2$, shown as a function of~\ptz, as predicted from \DYNNLO calculations at~NLO and~NNLO in~QCD. The NLO~predictions for $A_0-A_2$ are compatible with zero, as expected from the Lam--Tung relation~\cite{Lam:1978pu,Lam:1978zr,Lam:1980uc}. The error bars show the total uncertainty of the predictions, including contributions from statistical uncertainties, QCD~scale variations and~PDFs. The statistical uncertainties of the NNLO~predictions are dominant and an order of magnitude larger than those of the NLO~predictions.

The angular coefficients $A_{0-4}$ and the difference $A_0-A_2$, shown as a function of~\ptz, as predicted from \DYNNLO calculations at~NLO and~NNLO in~QCD. The NLO~predictions for $A_0-A_2$ are compatible with zero, as expected from the Lam--Tung relation~\cite{Lam:1978pu,Lam:1978zr,Lam:1980uc}. The error bars show the total uncertainty of the predictions, including contributions from statistical uncertainties, QCD~scale variations and~PDFs. The statistical uncertainties of the NNLO~predictions are dominant and an order of magnitude larger than those of the NLO~predictions.

Comparison of the expected yields (left) and acceptance times efficiency of selected events (right) as a function of $\yz$ (top) and $\ptz$ (bottom), for the $ee_{\text{CC}}$, $\mu\mu_{\text{CC}}$, and $ee_{\text{CF}}$ events. Also shown are the expected yields at the event generator level over the full phase space considered for the measurement, which corresponds to all events with a dilepton mass in the chosen window, $80 < \mz < 100$~GeV.

Comparison of the expected yields (left) and acceptance times efficiency of selected events (right) as a function of $\yz$ (top) and $\ptz$ (bottom), for the $ee_{\text{CC}}$, $\mu\mu_{\text{CC}}$, and $ee_{\text{CF}}$ events. Also shown are the expected yields at the event generator level over the full phase space considered for the measurement, which corresponds to all events with a dilepton mass in the chosen window, $80 < \mz < 100$~GeV.

Comparison of the expected yields (left) and acceptance times efficiency of selected events (right) as a function of $\yz$ (top) and $\ptz$ (bottom), for the $ee_{\text{CC}}$, $\mu\mu_{\text{CC}}$, and $ee_{\text{CF}}$ events. Also shown are the expected yields at the event generator level over the full phase space considered for the measurement, which corresponds to all events with a dilepton mass in the chosen window, $80 < \mz < 100$~GeV.

Comparison of the expected yields (left) and acceptance times efficiency of selected events (right) as a function of $\yz$ (top) and $\ptz$ (bottom), for the $ee_{\text{CC}}$, $\mu\mu_{\text{CC}}$, and $ee_{\text{CF}}$ events. Also shown are the expected yields at the event generator level over the full phase space considered for the measurement, which corresponds to all events with a dilepton mass in the chosen window, $80 < \mz < 100$~GeV.

The $\costhetacs$ (left) and $\phics$ (right) angular distributions, averaged over all $Z$-boson \pt, for the $ee_{\text{CC}}$ (top), $\mu\mu_{\text{CC}}$ (middle) and $ee_{\text{CF}}$ (bottom) channels. The distributions are shown separately for the different background sources contributing to each channel. The multijet background is determined from data, as explained in the text.

The $\costhetacs$ (left) and $\phics$ (right) angular distributions, averaged over all $Z$-boson \pt, for the $ee_{\text{CC}}$ (top), $\mu\mu_{\text{CC}}$ (middle) and $ee_{\text{CF}}$ (bottom) channels. The distributions are shown separately for the different background sources contributing to each channel. The multijet background is determined from data, as explained in the text.

The $\costhetacs$ (left) and $\phics$ (right) angular distributions, averaged over all $Z$-boson \pt, for the $ee_{\text{CC}}$ (top), $\mu\mu_{\text{CC}}$ (middle) and $ee_{\text{CF}}$ (bottom) channels. The distributions are shown separately for the different background sources contributing to each channel. The multijet background is determined from data, as explained in the text.

The $\costhetacs$ (left) and $\phics$ (right) angular distributions, averaged over all $Z$-boson \pt, for the $ee_{\text{CC}}$ (top), $\mu\mu_{\text{CC}}$ (middle) and $ee_{\text{CF}}$ (bottom) channels. The distributions are shown separately for the different background sources contributing to each channel. The multijet background is determined from data, as explained in the text.

The $\costhetacs$ (left) and $\phics$ (right) angular distributions, averaged over all $Z$-boson \pt, for the $ee_{\text{CC}}$ (top), $\mu\mu_{\text{CC}}$ (middle) and $ee_{\text{CF}}$ (bottom) channels. The distributions are shown separately for the different background sources contributing to each channel. The multijet background is determined from data, as explained in the text.

The $\costhetacs$ (left) and $\phics$ (right) angular distributions, averaged over all $Z$-boson \pt, for the $ee_{\text{CC}}$ (top), $\mu\mu_{\text{CC}}$ (middle) and $ee_{\text{CF}}$ (bottom) channels. The distributions are shown separately for the different background sources contributing to each channel. The multijet background is determined from data, as explained in the text.

Fractional background contributions as a function of $\ptll$, for the $ee_{\text{CC}}$ (top), $\mu\mu_{\text{CC}}$ (middle) and $ee_{\text{CF}}$ (bottom) channels. The distributions are shown separately for the relevant background contributions to each channel together with the summed total background fraction. The label ``Non-fiducial~$Z$'' refers to signal events which are generated outside the phase space used to extract the angular coefficients (see text).

Fractional background contributions as a function of $\ptll$, for the $ee_{\text{CC}}$ (top), $\mu\mu_{\text{CC}}$ (middle) and $ee_{\text{CF}}$ (bottom) channels. The distributions are shown separately for the relevant background contributions to each channel together with the summed total background fraction. The label ``Non-fiducial~$Z$'' refers to signal events which are generated outside the phase space used to extract the angular coefficients (see text).

Fractional background contributions as a function of $\ptll$, for the $ee_{\text{CC}}$ (top), $\mu\mu_{\text{CC}}$ (middle) and $ee_{\text{CF}}$ (bottom) channels. The distributions are shown separately for the relevant background contributions to each channel together with the summed total background fraction. The label ``Non-fiducial~$Z$'' refers to signal events which are generated outside the phase space used to extract the angular coefficients (see text).

The $\costhetacs$ (left) and $\phics$ (right) angular distributions, averaged over all $\ptll$, for the $ee_{\text{CC}}$ (top), $\mu\mu_{\text{CC}}$ (middle) and $ee_{\text{CF}}$ (bottom) channels. In the panels showing the ratios of the data to the summed signal+background predictions, the uncertainty bars on the points are only statistical.

The $\costhetacs$ (left) and $\phics$ (right) angular distributions, averaged over all $\ptll$, for the $ee_{\text{CC}}$ (top), $\mu\mu_{\text{CC}}$ (middle) and $ee_{\text{CF}}$ (bottom) channels. In the panels showing the ratios of the data to the summed signal+background predictions, the uncertainty bars on the points are only statistical.

The $\costhetacs$ (left) and $\phics$ (right) angular distributions, averaged over all $\ptll$, for the $ee_{\text{CC}}$ (top), $\mu\mu_{\text{CC}}$ (middle) and $ee_{\text{CF}}$ (bottom) channels. In the panels showing the ratios of the data to the summed signal+background predictions, the uncertainty bars on the points are only statistical.

The $\costhetacs$ (left) and $\phics$ (right) angular distributions, averaged over all $\ptll$, for the $ee_{\text{CC}}$ (top), $\mu\mu_{\text{CC}}$ (middle) and $ee_{\text{CF}}$ (bottom) channels. In the panels showing the ratios of the data to the summed signal+background predictions, the uncertainty bars on the points are only statistical.

The $\costhetacs$ (left) and $\phics$ (right) angular distributions, averaged over all $\ptll$, for the $ee_{\text{CC}}$ (top), $\mu\mu_{\text{CC}}$ (middle) and $ee_{\text{CF}}$ (bottom) channels. In the panels showing the ratios of the data to the summed signal+background predictions, the uncertainty bars on the points are only statistical.

The $\costhetacs$ (left) and $\phics$ (right) angular distributions, averaged over all $\ptll$, for the $ee_{\text{CC}}$ (top), $\mu\mu_{\text{CC}}$ (middle) and $ee_{\text{CF}}$ (bottom) channels. In the panels showing the ratios of the data to the summed signal+background predictions, the uncertainty bars on the points are only statistical.

Shapes of polynomials $P_{0,4,8}$ as a function of $\costhetacs$ (top left) and $P_{2,3,5,7,8}$ as a function of~$\phics$ (top right). Shown below are the templated polynomials for the $\yz$-integrated $ee_{\text{CC}}$~events at low~(5--8~GeV), medium~(22--25.5~GeV), and high~(132--173~GeV) values of~$\ptz$ projected onto each of the dimensions~$\costhetacs$ and~$\phics$. The $\ptll$~dimension that normally enters through migrations is also integrated over. The differences between the polynomials and the templates reflect the acceptance shape after event selection.

Shapes of polynomials $P_{0,4,8}$ as a function of $\costhetacs$ (top left) and $P_{2,3,5,7,8}$ as a function of~$\phics$ (top right). Shown below are the templated polynomials for the $\yz$-integrated $ee_{\text{CC}}$~events at low~(5--8~GeV), medium~(22--25.5~GeV), and high~(132--173~GeV) values of~$\ptz$ projected onto each of the dimensions~$\costhetacs$ and~$\phics$. The $\ptll$~dimension that normally enters through migrations is also integrated over. The differences between the polynomials and the templates reflect the acceptance shape after event selection.

Shapes of polynomials $P_{0,4,8}$ as a function of $\costhetacs$ (top left) and $P_{2,3,5,7,8}$ as a function of~$\phics$ (top right). Shown below are the templated polynomials for the $\yz$-integrated $ee_{\text{CC}}$~events at low~(5--8~GeV), medium~(22--25.5~GeV), and high~(132--173~GeV) values of~$\ptz$ projected onto each of the dimensions~$\costhetacs$ and~$\phics$. The $\ptll$~dimension that normally enters through migrations is also integrated over. The differences between the polynomials and the templates reflect the acceptance shape after event selection.

Shapes of polynomials $P_{0,4,8}$ as a function of $\costhetacs$ (top left) and $P_{2,3,5,7,8}$ as a function of~$\phics$ (top right). Shown below are the templated polynomials for the $\yz$-integrated $ee_{\text{CC}}$~events at low~(5--8~GeV), medium~(22--25.5~GeV), and high~(132--173~GeV) values of~$\ptz$ projected onto each of the dimensions~$\costhetacs$ and~$\phics$. The $\ptll$~dimension that normally enters through migrations is also integrated over. The differences between the polynomials and the templates reflect the acceptance shape after event selection.

Shapes of polynomials $P_{0,4,8}$ as a function of $\costhetacs$ (top left) and $P_{2,3,5,7,8}$ as a function of~$\phics$ (top right). Shown below are the templated polynomials for the $\yz$-integrated $ee_{\text{CC}}$~events at low~(5--8~GeV), medium~(22--25.5~GeV), and high~(132--173~GeV) values of~$\ptz$ projected onto each of the dimensions~$\costhetacs$ and~$\phics$. The $\ptll$~dimension that normally enters through migrations is also integrated over. The differences between the polynomials and the templates reflect the acceptance shape after event selection.

Shapes of polynomials $P_{0,4,8}$ as a function of $\costhetacs$ (top left) and $P_{2,3,5,7,8}$ as a function of~$\phics$ (top right). Shown below are the templated polynomials for the $\yz$-integrated $ee_{\text{CC}}$~events at low~(5--8~GeV), medium~(22--25.5~GeV), and high~(132--173~GeV) values of~$\ptz$ projected onto each of the dimensions~$\costhetacs$ and~$\phics$. The $\ptll$~dimension that normally enters through migrations is also integrated over. The differences between the polynomials and the templates reflect the acceptance shape after event selection.

Shapes of polynomials $P_{0,4,8}$ as a function of $\costhetacs$ (top left) and $P_{2,3,5,7,8}$ as a function of~$\phics$ (top right). Shown below are the templated polynomials for the $\yz$-integrated $ee_{\text{CC}}$~events at low~(5--8~GeV), medium~(22--25.5~GeV), and high~(132--173~GeV) values of~$\ptz$ projected onto each of the dimensions~$\costhetacs$ and~$\phics$. The $\ptll$~dimension that normally enters through migrations is also integrated over. The differences between the polynomials and the templates reflect the acceptance shape after event selection.

Shapes of polynomials $P_{0,4,8}$ as a function of $\costhetacs$ (top left) and $P_{2,3,5,7,8}$ as a function of~$\phics$ (top right). Shown below are the templated polynomials for the $\yz$-integrated $ee_{\text{CC}}$~events at low~(5--8~GeV), medium~(22--25.5~GeV), and high~(132--173~GeV) values of~$\ptz$ projected onto each of the dimensions~$\costhetacs$ and~$\phics$. The $\ptll$~dimension that normally enters through migrations is also integrated over. The differences between the polynomials and the templates reflect the acceptance shape after event selection.

Uncertainty breakdown for $A_{0}-A_{2}$ as a function of $\ptz$ in the $\yz$-integrated $ee_{\text{CC}}+\mu\mu_{\text{CC}}$ measurement: the systematic uncertainty (top) and the total uncertainty (bottom). The left column shows the unregularised version, while the right column shows the regularised one.

Uncertainty breakdown for $A_{0}-A_{2}$ as a function of $\ptz$ in the $\yz$-integrated $ee_{\text{CC}}+\mu\mu_{\text{CC}}$ measurement: the systematic uncertainty (top) and the total uncertainty (bottom). The left column shows the unregularised version, while the right column shows the regularised one.

Uncertainty breakdown for $A_{0}-A_{2}$ as a function of $\ptz$ in the $\yz$-integrated $ee_{\text{CC}}+\mu\mu_{\text{CC}}$ measurement: the systematic uncertainty (top) and the total uncertainty (bottom). The left column shows the unregularised version, while the right column shows the regularised one.

Uncertainty breakdown for $A_{0}-A_{2}$ as a function of $\ptz$ in the $\yz$-integrated $ee_{\text{CC}}+\mu\mu_{\text{CC}}$ measurement: the systematic uncertainty (top) and the total uncertainty (bottom). The left column shows the unregularised version, while the right column shows the regularised one.

The total uncertainty as a function of $\ptz$ along with a breakdown into statistical and systematic components for all coefficients in the regularised $\yz$-integrated $ee_{\text{CC}}+\mu\mu_{\text{CC}}$ measurement.

The total uncertainty as a function of $\ptz$ along with a breakdown into statistical and systematic components for all coefficients in the regularised $\yz$-integrated $ee_{\text{CC}}+\mu\mu_{\text{CC}}$ measurement.

The total uncertainty as a function of $\ptz$ along with a breakdown into statistical and systematic components for all coefficients in the regularised $\yz$-integrated $ee_{\text{CC}}+\mu\mu_{\text{CC}}$ measurement.

The total uncertainty as a function of $\ptz$ along with a breakdown into statistical and systematic components for all coefficients in the regularised $\yz$-integrated $ee_{\text{CC}}+\mu\mu_{\text{CC}}$ measurement.

The total uncertainty as a function of $\ptz$ along with a breakdown into statistical and systematic components for all coefficients in the regularised $\yz$-integrated $ee_{\text{CC}}+\mu\mu_{\text{CC}}$ measurement.

The total uncertainty as a function of $\ptz$ along with a breakdown into statistical and systematic components for all coefficients in the regularised $\yz$-integrated $ee_{\text{CC}}+\mu\mu_{\text{CC}}$ measurement.

The total uncertainty as a function of $\ptz$ along with a breakdown into statistical and systematic components for all coefficients in the regularised $\yz$-integrated $ee_{\text{CC}}+\mu\mu_{\text{CC}}$ measurement.

The total uncertainty as a function of $\ptz$ along with a breakdown into statistical and systematic components for all coefficients in the regularised $\yz$-integrated $ee_{\text{CC}}+\mu\mu_{\text{CC}}$ measurement.

Differences between the measured angular coefficients in the $\mu\mu_{\text{CC}}$ and $ee_{\text{CC}}$ channels, shown as a function of~\ptz\ from top left to bottom right, for all measured coefficients in the $\yz$-integrated configuration. The full (open) circles represent the measured differences before (after) regularisation. The error bars represent the total uncertainty in the measurements.

Differences between the measured angular coefficients in the $\mu\mu_{\text{CC}}$ and $ee_{\text{CC}}$ channels, shown as a function of~\ptz\ from top left to bottom right, for all measured coefficients in the $\yz$-integrated configuration. The full (open) circles represent the measured differences before (after) regularisation. The error bars represent the total uncertainty in the measurements.

Differences between the measured angular coefficients in the $\mu\mu_{\text{CC}}$ and $ee_{\text{CC}}$ channels, shown as a function of~\ptz\ from top left to bottom right, for all measured coefficients in the $\yz$-integrated configuration. The full (open) circles represent the measured differences before (after) regularisation. The error bars represent the total uncertainty in the measurements.

Differences between the measured angular coefficients in the $\mu\mu_{\text{CC}}$ and $ee_{\text{CC}}$ channels, shown as a function of~\ptz\ from top left to bottom right, for all measured coefficients in the $\yz$-integrated configuration. The full (open) circles represent the measured differences before (after) regularisation. The error bars represent the total uncertainty in the measurements.

Differences between the measured angular coefficients in the $\mu\mu_{\text{CC}}$ and $ee_{\text{CC}}$ channels, shown as a function of~\ptz\ from top left to bottom right, for all measured coefficients in the $\yz$-integrated configuration. The full (open) circles represent the measured differences before (after) regularisation. The error bars represent the total uncertainty in the measurements.

Differences between the measured angular coefficients in the $\mu\mu_{\text{CC}}$ and $ee_{\text{CC}}$ channels, shown as a function of~\ptz\ from top left to bottom right, for all measured coefficients in the $\yz$-integrated configuration. The full (open) circles represent the measured differences before (after) regularisation. The error bars represent the total uncertainty in the measurements.

Differences between the measured angular coefficients in the $\mu\mu_{\text{CC}}$ and $ee_{\text{CC}}$ channels, shown as a function of~\ptz\ from top left to bottom right, for all measured coefficients in the $\yz$-integrated configuration. The full (open) circles represent the measured differences before (after) regularisation. The error bars represent the total uncertainty in the measurements.

Differences between the measured angular coefficients in the $\mu\mu_{\text{CC}}$ and $ee_{\text{CC}}$ channels, shown as a function of~\ptz\ from top left to bottom right, for all measured coefficients in the $\yz$-integrated configuration. The full (open) circles represent the measured differences before (after) regularisation. The error bars represent the total uncertainty in the measurements.

Measurements of the angular coefficients in the $\yz$-integrated and $\yz$-binned configurations versus $\ptz$. Among the $\yz$-integrated configurations, are shown $A_{0,2}$ and $A_{0}-A_{2}$ (top left), $A_{1,3,4}$ (middle left), and $A_{5,6,7}$ (bottom left). The $\yz$-binned $\Ai$ are overlayed in each accessible $\yz$ bin for $A_{1}$ (top right), $A_{3}$ (middle right), and $A_{4}$ (bottom right). The error bars represent the total uncertainty in the measurements.

Measurements of the angular coefficients in the $\yz$-integrated and $\yz$-binned configurations versus $\ptz$. Among the $\yz$-integrated configurations, are shown $A_{0,2}$ and $A_{0}-A_{2}$ (top left), $A_{1,3,4}$ (middle left), and $A_{5,6,7}$ (bottom left). The $\yz$-binned $\Ai$ are overlayed in each accessible $\yz$ bin for $A_{1}$ (top right), $A_{3}$ (middle right), and $A_{4}$ (bottom right). The error bars represent the total uncertainty in the measurements.

Measurements of the angular coefficients in the $\yz$-integrated and $\yz$-binned configurations versus $\ptz$. Among the $\yz$-integrated configurations, are shown $A_{0,2}$ and $A_{0}-A_{2}$ (top left), $A_{1,3,4}$ (middle left), and $A_{5,6,7}$ (bottom left). The $\yz$-binned $\Ai$ are overlayed in each accessible $\yz$ bin for $A_{1}$ (top right), $A_{3}$ (middle right), and $A_{4}$ (bottom right). The error bars represent the total uncertainty in the measurements.

Measurements of the angular coefficients in the $\yz$-integrated and $\yz$-binned configurations versus $\ptz$. Among the $\yz$-integrated configurations, are shown $A_{0,2}$ and $A_{0}-A_{2}$ (top left), $A_{1,3,4}$ (middle left), and $A_{5,6,7}$ (bottom left). The $\yz$-binned $\Ai$ are overlayed in each accessible $\yz$ bin for $A_{1}$ (top right), $A_{3}$ (middle right), and $A_{4}$ (bottom right). The error bars represent the total uncertainty in the measurements.

Measurements of the angular coefficients in the $\yz$-integrated and $\yz$-binned configurations versus $\ptz$. Among the $\yz$-integrated configurations, are shown $A_{0,2}$ and $A_{0}-A_{2}$ (top left), $A_{1,3,4}$ (middle left), and $A_{5,6,7}$ (bottom left). The $\yz$-binned $\Ai$ are overlayed in each accessible $\yz$ bin for $A_{1}$ (top right), $A_{3}$ (middle right), and $A_{4}$ (bottom right). The error bars represent the total uncertainty in the measurements.

Measurements of the angular coefficients in the $\yz$-integrated and $\yz$-binned configurations versus $\ptz$. Among the $\yz$-integrated configurations, are shown $A_{0,2}$ and $A_{0}-A_{2}$ (top left), $A_{1,3,4}$ (middle left), and $A_{5,6,7}$ (bottom left). The $\yz$-binned $\Ai$ are overlayed in each accessible $\yz$ bin for $A_{1}$ (top right), $A_{3}$ (middle right), and $A_{4}$ (bottom right). The error bars represent the total uncertainty in the measurements.

Reweighted $\costhetacs$ (left) and $\phics$ (right) distribution integrated over $\yz$ in the $ee_{\text{CC}}$ (top), $\mu\mu_{\text{CC}}$ (middle), and $ee_{\text{CF}}$ (bottom) channels and the corresponding pulls of the distributions after reweighting them predictions to data. The pulls are computed using the full statistical and systematic uncertainties. Two points in the bottom-left pull plot near $\costhetacs=0$ fall below the range shown, but the number of events in these two bins is very small.

Reweighted $\costhetacs$ (left) and $\phics$ (right) distribution integrated over $\yz$ in the $ee_{\text{CC}}$ (top), $\mu\mu_{\text{CC}}$ (middle), and $ee_{\text{CF}}$ (bottom) channels and the corresponding pulls of the distributions after reweighting them predictions to data. The pulls are computed using the full statistical and systematic uncertainties. Two points in the bottom-left pull plot near $\costhetacs=0$ fall below the range shown, but the number of events in these two bins is very small.

Reweighted $\costhetacs$ (left) and $\phics$ (right) distribution integrated over $\yz$ in the $ee_{\text{CC}}$ (top), $\mu\mu_{\text{CC}}$ (middle), and $ee_{\text{CF}}$ (bottom) channels and the corresponding pulls of the distributions after reweighting them predictions to data. The pulls are computed using the full statistical and systematic uncertainties. Two points in the bottom-left pull plot near $\costhetacs=0$ fall below the range shown, but the number of events in these two bins is very small.

Reweighted $\costhetacs$ (left) and $\phics$ (right) distribution integrated over $\yz$ in the $ee_{\text{CC}}$ (top), $\mu\mu_{\text{CC}}$ (middle), and $ee_{\text{CF}}$ (bottom) channels and the corresponding pulls of the distributions after reweighting them predictions to data. The pulls are computed using the full statistical and systematic uncertainties. Two points in the bottom-left pull plot near $\costhetacs=0$ fall below the range shown, but the number of events in these two bins is very small.

Reweighted $\costhetacs$ (left) and $\phics$ (right) distribution integrated over $\yz$ in the $ee_{\text{CC}}$ (top), $\mu\mu_{\text{CC}}$ (middle), and $ee_{\text{CF}}$ (bottom) channels and the corresponding pulls of the distributions after reweighting them predictions to data. The pulls are computed using the full statistical and systematic uncertainties. Two points in the bottom-left pull plot near $\costhetacs=0$ fall below the range shown, but the number of events in these two bins is very small.

Reweighted $\costhetacs$ (left) and $\phics$ (right) distribution integrated over $\yz$ in the $ee_{\text{CC}}$ (top), $\mu\mu_{\text{CC}}$ (middle), and $ee_{\text{CF}}$ (bottom) channels and the corresponding pulls of the distributions after reweighting them predictions to data. The pulls are computed using the full statistical and systematic uncertainties. Two points in the bottom-left pull plot near $\costhetacs=0$ fall below the range shown, but the number of events in these two bins is very small.

Distributions of the angular coefficients $A_0$ (top), $A_2$ (middle) and $A_0-A_2$ (bottom) as a function of~$\ptz$. The results from the $\yz$-integrated measurements are compared to the \DYNNLO\ and \POWHEG \MINLO predictions (left). The differences between the two calculations and the data are also shown (right), with the shaded band around zero representing the total uncertainty in the measurements. The error bars for the calculations show the total uncertainty for \DYNNLO, but only the statistical uncertainties for \POWHEG \MINLO (see text).

Distributions of the angular coefficients $A_0$ (top), $A_2$ (middle) and $A_0-A_2$ (bottom) as a function of~$\ptz$. The results from the $\yz$-integrated measurements are compared to the \DYNNLO\ and \POWHEG \MINLO predictions (left). The differences between the two calculations and the data are also shown (right), with the shaded band around zero representing the total uncertainty in the measurements. The error bars for the calculations show the total uncertainty for \DYNNLO, but only the statistical uncertainties for \POWHEG \MINLO (see text).

Distributions of the angular coefficients $A_0$ (top), $A_2$ (middle) and $A_0-A_2$ (bottom) as a function of~$\ptz$. The results from the $\yz$-integrated measurements are compared to the \DYNNLO\ and \POWHEG \MINLO predictions (left). The differences between the two calculations and the data are also shown (right), with the shaded band around zero representing the total uncertainty in the measurements. The error bars for the calculations show the total uncertainty for \DYNNLO, but only the statistical uncertainties for \POWHEG \MINLO (see text).

Distributions of the angular coefficients $A_0$ (top), $A_2$ (middle) and $A_0-A_2$ (bottom) as a function of~$\ptz$. The results from the $\yz$-integrated measurements are compared to the \DYNNLO\ and \POWHEG \MINLO predictions (left). The differences between the two calculations and the data are also shown (right), with the shaded band around zero representing the total uncertainty in the measurements. The error bars for the calculations show the total uncertainty for \DYNNLO, but only the statistical uncertainties for \POWHEG \MINLO (see text).

Distributions of the angular coefficients $A_0$ (top), $A_2$ (middle) and $A_0-A_2$ (bottom) as a function of~$\ptz$. The results from the $\yz$-integrated measurements are compared to the \DYNNLO\ and \POWHEG \MINLO predictions (left). The differences between the two calculations and the data are also shown (right), with the shaded band around zero representing the total uncertainty in the measurements. The error bars for the calculations show the total uncertainty for \DYNNLO, but only the statistical uncertainties for \POWHEG \MINLO (see text).

Distributions of the angular coefficients $A_0$ (top), $A_2$ (middle) and $A_0-A_2$ (bottom) as a function of~$\ptz$. The results from the $\yz$-integrated measurements are compared to the \DYNNLO\ and \POWHEG \MINLO predictions (left). The differences between the two calculations and the data are also shown (right), with the shaded band around zero representing the total uncertainty in the measurements. The error bars for the calculations show the total uncertainty for \DYNNLO, but only the statistical uncertainties for \POWHEG \MINLO (see text).

Distributions of the angular coefficients $A_1$ (top), $A_3$ (middle) and $A_4$ (bottom) as a function of~$\ptz$. The results from the $\yz$-integrated measurements are compared to the \DYNNLO\ and \POWHEG \MINLO predictions (left). The differences between the two calculations and the data are also shown (right), with the shaded band around zero representing the total uncertainty in the measurements. The error bars for the calculations show the total uncertainty for \DYNNLO, but only the statistical uncertainties for \POWHEG \MINLO (see text).

Distributions of the angular coefficients $A_1$ (top), $A_3$ (middle) and $A_4$ (bottom) as a function of~$\ptz$. The results from the $\yz$-integrated measurements are compared to the \DYNNLO\ and \POWHEG \MINLO predictions (left). The differences between the two calculations and the data are also shown (right), with the shaded band around zero representing the total uncertainty in the measurements. The error bars for the calculations show the total uncertainty for \DYNNLO, but only the statistical uncertainties for \POWHEG \MINLO (see text).

Distributions of the angular coefficients $A_1$ (top), $A_3$ (middle) and $A_4$ (bottom) as a function of~$\ptz$. The results from the $\yz$-integrated measurements are compared to the \DYNNLO\ and \POWHEG \MINLO predictions (left). The differences between the two calculations and the data are also shown (right), with the shaded band around zero representing the total uncertainty in the measurements. The error bars for the calculations show the total uncertainty for \DYNNLO, but only the statistical uncertainties for \POWHEG \MINLO (see text).

Distributions of the angular coefficients $A_1$ (top), $A_3$ (middle) and $A_4$ (bottom) as a function of~$\ptz$. The results from the $\yz$-integrated measurements are compared to the \DYNNLO\ and \POWHEG \MINLO predictions (left). The differences between the two calculations and the data are also shown (right), with the shaded band around zero representing the total uncertainty in the measurements. The error bars for the calculations show the total uncertainty for \DYNNLO, but only the statistical uncertainties for \POWHEG \MINLO (see text).

Distributions of the angular coefficients $A_1$ (top), $A_3$ (middle) and $A_4$ (bottom) as a function of~$\ptz$. The results from the $\yz$-integrated measurements are compared to the \DYNNLO\ and \POWHEG \MINLO predictions (left). The differences between the two calculations and the data are also shown (right), with the shaded band around zero representing the total uncertainty in the measurements. The error bars for the calculations show the total uncertainty for \DYNNLO, but only the statistical uncertainties for \POWHEG \MINLO (see text).

Distributions of the angular coefficients $A_1$ (top), $A_3$ (middle) and $A_4$ (bottom) as a function of~$\ptz$. The results from the $\yz$-integrated measurements are compared to the \DYNNLO\ and \POWHEG \MINLO predictions (left). The differences between the two calculations and the data are also shown (right), with the shaded band around zero representing the total uncertainty in the measurements. The error bars for the calculations show the total uncertainty for \DYNNLO, but only the statistical uncertainties for \POWHEG \MINLO (see text).

Distributions of the angular coefficients $A_5$ (top), $A_6$ (middle) and $A_7$ (bottom) as a function of~$\ptz$. The results from the $\yz$-integrated measurements are compared to the \DYNNLO\ and \POWHEG \MINLO predictions (left). The differences between the two calculations and the data are also shown (right), with the shaded band around zero representing the total uncertainty in the measurements. The error bars for the calculations show the total uncertainty for \DYNNLO, but only the statistical uncertainties for \POWHEG \MINLO (see text).

Distributions of the angular coefficients $A_5$ (top), $A_6$ (middle) and $A_7$ (bottom) as a function of~$\ptz$. The results from the $\yz$-integrated measurements are compared to the \DYNNLO\ and \POWHEG \MINLO predictions (left). The differences between the two calculations and the data are also shown (right), with the shaded band around zero representing the total uncertainty in the measurements. The error bars for the calculations show the total uncertainty for \DYNNLO, but only the statistical uncertainties for \POWHEG \MINLO (see text).

Distributions of the angular coefficients $A_5$ (top), $A_6$ (middle) and $A_7$ (bottom) as a function of~$\ptz$. The results from the $\yz$-integrated measurements are compared to the \DYNNLO\ and \POWHEG \MINLO predictions (left). The differences between the two calculations and the data are also shown (right), with the shaded band around zero representing the total uncertainty in the measurements. The error bars for the calculations show the total uncertainty for \DYNNLO, but only the statistical uncertainties for \POWHEG \MINLO (see text).

Distributions of the angular coefficients $A_5$ (top), $A_6$ (middle) and $A_7$ (bottom) as a function of~$\ptz$. The results from the $\yz$-integrated measurements are compared to the \DYNNLO\ and \POWHEG \MINLO predictions (left). The differences between the two calculations and the data are also shown (right), with the shaded band around zero representing the total uncertainty in the measurements. The error bars for the calculations show the total uncertainty for \DYNNLO, but only the statistical uncertainties for \POWHEG \MINLO (see text).

Distributions of the angular coefficients $A_5$ (top), $A_6$ (middle) and $A_7$ (bottom) as a function of~$\ptz$. The results from the $\yz$-integrated measurements are compared to the \DYNNLO\ and \POWHEG \MINLO predictions (left). The differences between the two calculations and the data are also shown (right), with the shaded band around zero representing the total uncertainty in the measurements. The error bars for the calculations show the total uncertainty for \DYNNLO, but only the statistical uncertainties for \POWHEG \MINLO (see text).

Distributions of the angular coefficients $A_5$ (top), $A_6$ (middle) and $A_7$ (bottom) as a function of~$\ptz$. The results from the $\yz$-integrated measurements are compared to the \DYNNLO\ and \POWHEG \MINLO predictions (left). The differences between the two calculations and the data are also shown (right), with the shaded band around zero representing the total uncertainty in the measurements. The error bars for the calculations show the total uncertainty for \DYNNLO, but only the statistical uncertainties for \POWHEG \MINLO (see text).

Distributions of the angular coefficients $A_1$ (top), $A_3$ (middle) and $A_4$ (bottom) as a function of~$\ptz$ for~$0 < |\yz| < 1$. The results from the measurements are compared to the \DYNNLO\ and \POWHEG \MINLO predictions (left). The differences between the two calculations and the data are also shown (right), with the shaded band around zero representing the total uncertainty in the measurements. The error bars for the calculations show the total uncertainty for \DYNNLO, but only the statistical uncertainties for \POWHEG \MINLO (see text).

Distributions of the angular coefficients $A_1$ (top), $A_3$ (middle) and $A_4$ (bottom) as a function of~$\ptz$ for~$0 < |\yz| < 1$. The results from the measurements are compared to the \DYNNLO\ and \POWHEG \MINLO predictions (left). The differences between the two calculations and the data are also shown (right), with the shaded band around zero representing the total uncertainty in the measurements. The error bars for the calculations show the total uncertainty for \DYNNLO, but only the statistical uncertainties for \POWHEG \MINLO (see text).

Distributions of the angular coefficients $A_1$ (top), $A_3$ (middle) and $A_4$ (bottom) as a function of~$\ptz$ for~$0 < |\yz| < 1$. The results from the measurements are compared to the \DYNNLO\ and \POWHEG \MINLO predictions (left). The differences between the two calculations and the data are also shown (right), with the shaded band around zero representing the total uncertainty in the measurements. The error bars for the calculations show the total uncertainty for \DYNNLO, but only the statistical uncertainties for \POWHEG \MINLO (see text).

Distributions of the angular coefficients $A_1$ (top), $A_3$ (middle) and $A_4$ (bottom) as a function of~$\ptz$ for~$0 < |\yz| < 1$. The results from the measurements are compared to the \DYNNLO\ and \POWHEG \MINLO predictions (left). The differences between the two calculations and the data are also shown (right), with the shaded band around zero representing the total uncertainty in the measurements. The error bars for the calculations show the total uncertainty for \DYNNLO, but only the statistical uncertainties for \POWHEG \MINLO (see text).

Distributions of the angular coefficients $A_1$ (top), $A_3$ (middle) and $A_4$ (bottom) as a function of~$\ptz$ for~$0 < |\yz| < 1$. The results from the measurements are compared to the \DYNNLO\ and \POWHEG \MINLO predictions (left). The differences between the two calculations and the data are also shown (right), with the shaded band around zero representing the total uncertainty in the measurements. The error bars for the calculations show the total uncertainty for \DYNNLO, but only the statistical uncertainties for \POWHEG \MINLO (see text).

Distributions of the angular coefficients $A_1$ (top), $A_3$ (middle) and $A_4$ (bottom) as a function of~$\ptz$ for~$0 < |\yz| < 1$. The results from the measurements are compared to the \DYNNLO\ and \POWHEG \MINLO predictions (left). The differences between the two calculations and the data are also shown (right), with the shaded band around zero representing the total uncertainty in the measurements. The error bars for the calculations show the total uncertainty for \DYNNLO, but only the statistical uncertainties for \POWHEG \MINLO (see text).

Distributions of the angular coefficients $A_1$ (top), $A_3$ (middle) and $A_4$ (bottom) as a function of~$\ptz$ for~$1 < |\yz| < 2$. The results from the measurements are compared to the \DYNNLO\ and \POWHEG \MINLO predictions (left). The differences between the two calculations and the data are also shown (right), with the shaded band around zero representing the total uncertainty in the measurements. The error bars for the calculations show the total uncertainty for \DYNNLO, but only the statistical uncertainties for \POWHEG \MINLO (see text).

Distributions of the angular coefficients $A_1$ (top), $A_3$ (middle) and $A_4$ (bottom) as a function of~$\ptz$ for~$1 < |\yz| < 2$. The results from the measurements are compared to the \DYNNLO\ and \POWHEG \MINLO predictions (left). The differences between the two calculations and the data are also shown (right), with the shaded band around zero representing the total uncertainty in the measurements. The error bars for the calculations show the total uncertainty for \DYNNLO, but only the statistical uncertainties for \POWHEG \MINLO (see text).

Distributions of the angular coefficients $A_1$ (top), $A_3$ (middle) and $A_4$ (bottom) as a function of~$\ptz$ for~$1 < |\yz| < 2$. The results from the measurements are compared to the \DYNNLO\ and \POWHEG \MINLO predictions (left). The differences between the two calculations and the data are also shown (right), with the shaded band around zero representing the total uncertainty in the measurements. The error bars for the calculations show the total uncertainty for \DYNNLO, but only the statistical uncertainties for \POWHEG \MINLO (see text).

Distributions of the angular coefficients $A_1$ (top), $A_3$ (middle) and $A_4$ (bottom) as a function of~$\ptz$ for~$1 < |\yz| < 2$. The results from the measurements are compared to the \DYNNLO\ and \POWHEG \MINLO predictions (left). The differences between the two calculations and the data are also shown (right), with the shaded band around zero representing the total uncertainty in the measurements. The error bars for the calculations show the total uncertainty for \DYNNLO, but only the statistical uncertainties for \POWHEG \MINLO (see text).

Distributions of the angular coefficients $A_1$ (top), $A_3$ (middle) and $A_4$ (bottom) as a function of~$\ptz$ for~$1 < |\yz| < 2$. The results from the measurements are compared to the \DYNNLO\ and \POWHEG \MINLO predictions (left). The differences between the two calculations and the data are also shown (right), with the shaded band around zero representing the total uncertainty in the measurements. The error bars for the calculations show the total uncertainty for \DYNNLO, but only the statistical uncertainties for \POWHEG \MINLO (see text).

Distributions of the angular coefficients $A_1$ (top), $A_3$ (middle) and $A_4$ (bottom) as a function of~$\ptz$ for~$1 < |\yz| < 2$. The results from the measurements are compared to the \DYNNLO\ and \POWHEG \MINLO predictions (left). The differences between the two calculations and the data are also shown (right), with the shaded band around zero representing the total uncertainty in the measurements. The error bars for the calculations show the total uncertainty for \DYNNLO, but only the statistical uncertainties for \POWHEG \MINLO (see text).

Distributions of the angular coefficients $A_3$ (top) and $A_4$ (bottom) as a function of~$\ptz$ for~$2 < |\yz| < 3.5$. The results from the measurements are compared to the \DYNNLO\ and \POWHEG \MINLO predictions (left). The differences between the two calculations and the data are also shown (right), with the shaded band around zero representing the total uncertainty in the measurements. The error bars for the calculations show the total uncertainty for \DYNNLO, but only the statistical uncertainties for \POWHEG \MINLO (see text).

Distributions of the angular coefficients $A_3$ (top) and $A_4$ (bottom) as a function of~$\ptz$ for~$2 < |\yz| < 3.5$. The results from the measurements are compared to the \DYNNLO\ and \POWHEG \MINLO predictions (left). The differences between the two calculations and the data are also shown (right), with the shaded band around zero representing the total uncertainty in the measurements. The error bars for the calculations show the total uncertainty for \DYNNLO, but only the statistical uncertainties for \POWHEG \MINLO (see text).

Distributions of the angular coefficients $A_3$ (top) and $A_4$ (bottom) as a function of~$\ptz$ for~$2 < |\yz| < 3.5$. The results from the measurements are compared to the \DYNNLO\ and \POWHEG \MINLO predictions (left). The differences between the two calculations and the data are also shown (right), with the shaded band around zero representing the total uncertainty in the measurements. The error bars for the calculations show the total uncertainty for \DYNNLO, but only the statistical uncertainties for \POWHEG \MINLO (see text).

Distributions of the angular coefficients $A_3$ (top) and $A_4$ (bottom) as a function of~$\ptz$ for~$2 < |\yz| < 3.5$. The results from the measurements are compared to the \DYNNLO\ and \POWHEG \MINLO predictions (left). The differences between the two calculations and the data are also shown (right), with the shaded band around zero representing the total uncertainty in the measurements. The error bars for the calculations show the total uncertainty for \DYNNLO, but only the statistical uncertainties for \POWHEG \MINLO (see text).

Distributions of the angular coefficients $A_0$, $A_2$, $A_0-A_2$ and $A_1$ (from top to bottom) as a function of~$\ptz$. The results from the $\yz$-integrated measurements are compared to the \DYNNLO\ predictions at~NLO and at~NNLO, as well as to those from $\POWHEGBOX +~\PYTHIA$8 and $\POWHEGBOX +~\HERWIG$~(left). The differences between the calculations and the data are also shown (right), with the shaded band around zero representing the total uncertainty in the measurements. The error bars for the calculations show the total uncertainty for \DYNNLO, but only the statistical uncertainties for \POWHEGBOX.

Distributions of the angular coefficients $A_0$, $A_2$, $A_0-A_2$ and $A_1$ (from top to bottom) as a function of~$\ptz$. The results from the $\yz$-integrated measurements are compared to the \DYNNLO\ predictions at~NLO and at~NNLO, as well as to those from $\POWHEGBOX +~\PYTHIA$8 and $\POWHEGBOX +~\HERWIG$~(left). The differences between the calculations and the data are also shown (right), with the shaded band around zero representing the total uncertainty in the measurements. The error bars for the calculations show the total uncertainty for \DYNNLO, but only the statistical uncertainties for \POWHEGBOX.

Distributions of the angular coefficients $A_0$, $A_2$, $A_0-A_2$ and $A_1$ (from top to bottom) as a function of~$\ptz$. The results from the $\yz$-integrated measurements are compared to the \DYNNLO\ predictions at~NLO and at~NNLO, as well as to those from $\POWHEGBOX +~\PYTHIA$8 and $\POWHEGBOX +~\HERWIG$~(left). The differences between the calculations and the data are also shown (right), with the shaded band around zero representing the total uncertainty in the measurements. The error bars for the calculations show the total uncertainty for \DYNNLO, but only the statistical uncertainties for \POWHEGBOX.

Distributions of the angular coefficients $A_0$, $A_2$, $A_0-A_2$ and $A_1$ (from top to bottom) as a function of~$\ptz$. The results from the $\yz$-integrated measurements are compared to the \DYNNLO\ predictions at~NLO and at~NNLO, as well as to those from $\POWHEGBOX +~\PYTHIA$8 and $\POWHEGBOX +~\HERWIG$~(left). The differences between the calculations and the data are also shown (right), with the shaded band around zero representing the total uncertainty in the measurements. The error bars for the calculations show the total uncertainty for \DYNNLO, but only the statistical uncertainties for \POWHEGBOX.

Distributions of the angular coefficients $A_0$, $A_2$, $A_0-A_2$ and $A_1$ (from top to bottom) as a function of~$\ptz$. The results from the $\yz$-integrated measurements are compared to the \DYNNLO\ predictions at~NLO and at~NNLO, as well as to those from $\POWHEGBOX +~\PYTHIA$8 and $\POWHEGBOX +~\HERWIG$~(left). The differences between the calculations and the data are also shown (right), with the shaded band around zero representing the total uncertainty in the measurements. The error bars for the calculations show the total uncertainty for \DYNNLO, but only the statistical uncertainties for \POWHEGBOX.

Distributions of the angular coefficients $A_0$, $A_2$, $A_0-A_2$ and $A_1$ (from top to bottom) as a function of~$\ptz$. The results from the $\yz$-integrated measurements are compared to the \DYNNLO\ predictions at~NLO and at~NNLO, as well as to those from $\POWHEGBOX +~\PYTHIA$8 and $\POWHEGBOX +~\HERWIG$~(left). The differences between the calculations and the data are also shown (right), with the shaded band around zero representing the total uncertainty in the measurements. The error bars for the calculations show the total uncertainty for \DYNNLO, but only the statistical uncertainties for \POWHEGBOX.

Distributions of the angular coefficients $A_0$, $A_2$, $A_0-A_2$ and $A_1$ (from top to bottom) as a function of~$\ptz$. The results from the $\yz$-integrated measurements are compared to the \DYNNLO\ predictions at~NLO and at~NNLO, as well as to those from $\POWHEGBOX +~\PYTHIA$8 and $\POWHEGBOX +~\HERWIG$~(left). The differences between the calculations and the data are also shown (right), with the shaded band around zero representing the total uncertainty in the measurements. The error bars for the calculations show the total uncertainty for \DYNNLO, but only the statistical uncertainties for \POWHEGBOX.

Distributions of the angular coefficients $A_0$, $A_2$, $A_0-A_2$ and $A_1$ (from top to bottom) as a function of~$\ptz$. The results from the $\yz$-integrated measurements are compared to the \DYNNLO\ predictions at~NLO and at~NNLO, as well as to those from $\POWHEGBOX +~\PYTHIA$8 and $\POWHEGBOX +~\HERWIG$~(left). The differences between the calculations and the data are also shown (right), with the shaded band around zero representing the total uncertainty in the measurements. The error bars for the calculations show the total uncertainty for \DYNNLO, but only the statistical uncertainties for \POWHEGBOX.

Distributions of the angular coefficients $A_0$ (top), $A_2$ (middle) and $A_0-A_2$ (bottom) as a function of~$\ptz$. The results from the $\yz$-integrated measurements are compared to various predictions from the \SHERPA~event generator~(left). The differences between the calculations and the data are also shown (right), with the shaded band around zero representing the total uncertainty in the measurements. The error bars for the \SHERPA~predictions represent only the statistical uncertainties.

Distributions of the angular coefficients $A_0$ (top), $A_2$ (middle) and $A_0-A_2$ (bottom) as a function of~$\ptz$. The results from the $\yz$-integrated measurements are compared to various predictions from the \SHERPA~event generator~(left). The differences between the calculations and the data are also shown (right), with the shaded band around zero representing the total uncertainty in the measurements. The error bars for the \SHERPA~predictions represent only the statistical uncertainties.

Distributions of the angular coefficients $A_0$ (top), $A_2$ (middle) and $A_0-A_2$ (bottom) as a function of~$\ptz$. The results from the $\yz$-integrated measurements are compared to various predictions from the \SHERPA~event generator~(left). The differences between the calculations and the data are also shown (right), with the shaded band around zero representing the total uncertainty in the measurements. The error bars for the \SHERPA~predictions represent only the statistical uncertainties.

Distributions of the angular coefficients $A_0$ (top), $A_2$ (middle) and $A_0-A_2$ (bottom) as a function of~$\ptz$. The results from the $\yz$-integrated measurements are compared to various predictions from the \SHERPA~event generator~(left). The differences between the calculations and the data are also shown (right), with the shaded band around zero representing the total uncertainty in the measurements. The error bars for the \SHERPA~predictions represent only the statistical uncertainties.

Distributions of the angular coefficients $A_0$ (top), $A_2$ (middle) and $A_0-A_2$ (bottom) as a function of~$\ptz$. The results from the $\yz$-integrated measurements are compared to various predictions from the \SHERPA~event generator~(left). The differences between the calculations and the data are also shown (right), with the shaded band around zero representing the total uncertainty in the measurements. The error bars for the \SHERPA~predictions represent only the statistical uncertainties.

Distributions of the angular coefficients $A_0$ (top), $A_2$ (middle) and $A_0-A_2$ (bottom) as a function of~$\ptz$. The results from the $\yz$-integrated measurements are compared to various predictions from the \SHERPA~event generator~(left). The differences between the calculations and the data are also shown (right), with the shaded band around zero representing the total uncertainty in the measurements. The error bars for the \SHERPA~predictions represent only the statistical uncertainties.

Shapes of the polynomials $P_{0,4,8}$ as a function of~$\costhetacs$ and $\phics$ (top). Below these are the templated polynomials for the $\yz$-integrated $ee_{CC}$~events at low~($5-8$~GeV), medium~($22-25.5$~GeV), and high~($132-173$~GeV) values of~$\ptz$.

Shapes of the polynomials $P_{0,4,8}$ as a function of~$\costhetacs$ and $\phics$ (top). Below these are the templated polynomials for the $\yz$-integrated $ee_{CC}$~events at low~($5-8$~GeV), medium~($22-25.5$~GeV), and high~($132-173$~GeV) values of~$\ptz$.

Shapes of the polynomials $P_{0,4,8}$ as a function of~$\costhetacs$ and $\phics$ (top). Below these are the templated polynomials for the $\yz$-integrated $ee_{CC}$~events at low~($5-8$~GeV), medium~($22-25.5$~GeV), and high~($132-173$~GeV) values of~$\ptz$.

Shapes of the polynomials $P_{0,4,8}$ as a function of~$\costhetacs$ and $\phics$ (top). Below these are the templated polynomials for the $\yz$-integrated $ee_{CC}$~events at low~($5-8$~GeV), medium~($22-25.5$~GeV), and high~($132-173$~GeV) values of~$\ptz$.

Shapes of the polynomials $P_{0,4,8}$ as a function of~$\costhetacs$ and $\phics$ (top). Below these are the templated polynomials for the $\yz$-integrated $ee_{CC}$~events at low~($5-8$~GeV), medium~($22-25.5$~GeV), and high~($132-173$~GeV) values of~$\ptz$.

Shapes of the polynomials $P_{0,4,8}$ as a function of~$\costhetacs$ and $\phics$ (top). Below these are the templated polynomials for the $\yz$-integrated $ee_{CC}$~events at low~($5-8$~GeV), medium~($22-25.5$~GeV), and high~($132-173$~GeV) values of~$\ptz$.

Shapes of the polynomials $P_{0,4,8}$ as a function of~$\costhetacs$ and $\phics$ (top). Below these are the templated polynomials for the $\yz$-integrated $ee_{CC}$~events at low~($5-8$~GeV), medium~($22-25.5$~GeV), and high~($132-173$~GeV) values of~$\ptz$.

Shapes of the polynomials $P_{0,4,8}$ as a function of~$\costhetacs$ and $\phics$ (top). Below these are the templated polynomials for the $\yz$-integrated $ee_{CC}$~events at low~($5-8$~GeV), medium~($22-25.5$~GeV), and high~($132-173$~GeV) values of~$\ptz$.

Shapes of the polynomials $P_{0,4,8}$ as a function of~$\costhetacs$ and $\phics$ (top). Below these are the templated polynomials for the $\yz$-integrated $ee_{CC}$~events at low~($5-8$~GeV), medium~($22-25.5$~GeV), and high~($132-173$~GeV) values of~$\ptz$.

Shapes of the polynomials $P_{0,4,8}$ as a function of~$\costhetacs$ and $\phics$ (top). Below these are the templated polynomials for the $\yz$-integrated $ee_{CC}$~events at low~($5-8$~GeV), medium~($22-25.5$~GeV), and high~($132-173$~GeV) values of~$\ptz$.

Shapes of the polynomials $P_{0,4,8}$ as a function of~$\costhetacs$ and $\phics$ (top). Below these are the templated polynomials for the $\yz$-integrated $ee_{CC}$~events at low~($5-8$~GeV), medium~($22-25.5$~GeV), and high~($132-173$~GeV) values of~$\ptz$.

Shapes of the polynomials $P_{0,4,8}$ as a function of~$\costhetacs$ and $\phics$ (top). Below these are the templated polynomials for the $\yz$-integrated $ee_{CC}$~events at low~($5-8$~GeV), medium~($22-25.5$~GeV), and high~($132-173$~GeV) values of~$\ptz$.

Shapes of the polynomials $P_{1,2,3}$ as a function of~$\costhetacs$ and $\phics$ (top). Below these are the templated polynomials for the $\yz$-integrated $ee_{CC}$~events at low~($5-8$~GeV), medium~($22-25.5$~GeV), and high~($132-173$~GeV) values of~$\ptz$.

Shapes of the polynomials $P_{1,2,3}$ as a function of~$\costhetacs$ and $\phics$ (top). Below these are the templated polynomials for the $\yz$-integrated $ee_{CC}$~events at low~($5-8$~GeV), medium~($22-25.5$~GeV), and high~($132-173$~GeV) values of~$\ptz$.

Shapes of the polynomials $P_{1,2,3}$ as a function of~$\costhetacs$ and $\phics$ (top). Below these are the templated polynomials for the $\yz$-integrated $ee_{CC}$~events at low~($5-8$~GeV), medium~($22-25.5$~GeV), and high~($132-173$~GeV) values of~$\ptz$.

Shapes of the polynomials $P_{1,2,3}$ as a function of~$\costhetacs$ and $\phics$ (top). Below these are the templated polynomials for the $\yz$-integrated $ee_{CC}$~events at low~($5-8$~GeV), medium~($22-25.5$~GeV), and high~($132-173$~GeV) values of~$\ptz$.

Shapes of the polynomials $P_{1,2,3}$ as a function of~$\costhetacs$ and $\phics$ (top). Below these are the templated polynomials for the $\yz$-integrated $ee_{CC}$~events at low~($5-8$~GeV), medium~($22-25.5$~GeV), and high~($132-173$~GeV) values of~$\ptz$.

Shapes of the polynomials $P_{1,2,3}$ as a function of~$\costhetacs$ and $\phics$ (top). Below these are the templated polynomials for the $\yz$-integrated $ee_{CC}$~events at low~($5-8$~GeV), medium~($22-25.5$~GeV), and high~($132-173$~GeV) values of~$\ptz$.

Shapes of the polynomials $P_{1,2,3}$ as a function of~$\costhetacs$ and $\phics$ (top). Below these are the templated polynomials for the $\yz$-integrated $ee_{CC}$~events at low~($5-8$~GeV), medium~($22-25.5$~GeV), and high~($132-173$~GeV) values of~$\ptz$.

Shapes of the polynomials $P_{1,2,3}$ as a function of~$\costhetacs$ and $\phics$ (top). Below these are the templated polynomials for the $\yz$-integrated $ee_{CC}$~events at low~($5-8$~GeV), medium~($22-25.5$~GeV), and high~($132-173$~GeV) values of~$\ptz$.

Shapes of the polynomials $P_{1,2,3}$ as a function of~$\costhetacs$ and $\phics$ (top). Below these are the templated polynomials for the $\yz$-integrated $ee_{CC}$~events at low~($5-8$~GeV), medium~($22-25.5$~GeV), and high~($132-173$~GeV) values of~$\ptz$.

Shapes of the polynomials $P_{1,2,3}$ as a function of~$\costhetacs$ and $\phics$ (top). Below these are the templated polynomials for the $\yz$-integrated $ee_{CC}$~events at low~($5-8$~GeV), medium~($22-25.5$~GeV), and high~($132-173$~GeV) values of~$\ptz$.

Shapes of the polynomials $P_{1,2,3}$ as a function of~$\costhetacs$ and $\phics$ (top). Below these are the templated polynomials for the $\yz$-integrated $ee_{CC}$~events at low~($5-8$~GeV), medium~($22-25.5$~GeV), and high~($132-173$~GeV) values of~$\ptz$.

Shapes of the polynomials $P_{1,2,3}$ as a function of~$\costhetacs$ and $\phics$ (top). Below these are the templated polynomials for the $\yz$-integrated $ee_{CC}$~events at low~($5-8$~GeV), medium~($22-25.5$~GeV), and high~($132-173$~GeV) values of~$\ptz$.

Shapes of the polynomials $P_{5,6,7}$ as a function of~$\costhetacs$ and $\phics$ (top). Below these are the templated polynomials for the $\yz$-integrated $ee_{CC}$~events at low~($5-8$~GeV), medium~($22-25.5$~GeV), and high~($132-173$~GeV) values of~$\ptz$.

Shapes of the polynomials $P_{5,6,7}$ as a function of~$\costhetacs$ and $\phics$ (top). Below these are the templated polynomials for the $\yz$-integrated $ee_{CC}$~events at low~($5-8$~GeV), medium~($22-25.5$~GeV), and high~($132-173$~GeV) values of~$\ptz$.

Shapes of the polynomials $P_{5,6,7}$ as a function of~$\costhetacs$ and $\phics$ (top). Below these are the templated polynomials for the $\yz$-integrated $ee_{CC}$~events at low~($5-8$~GeV), medium~($22-25.5$~GeV), and high~($132-173$~GeV) values of~$\ptz$.

Shapes of the polynomials $P_{5,6,7}$ as a function of~$\costhetacs$ and $\phics$ (top). Below these are the templated polynomials for the $\yz$-integrated $ee_{CC}$~events at low~($5-8$~GeV), medium~($22-25.5$~GeV), and high~($132-173$~GeV) values of~$\ptz$.

Shapes of the polynomials $P_{5,6,7}$ as a function of~$\costhetacs$ and $\phics$ (top). Below these are the templated polynomials for the $\yz$-integrated $ee_{CC}$~events at low~($5-8$~GeV), medium~($22-25.5$~GeV), and high~($132-173$~GeV) values of~$\ptz$.

Shapes of the polynomials $P_{5,6,7}$ as a function of~$\costhetacs$ and $\phics$ (top). Below these are the templated polynomials for the $\yz$-integrated $ee_{CC}$~events at low~($5-8$~GeV), medium~($22-25.5$~GeV), and high~($132-173$~GeV) values of~$\ptz$.

Shapes of the polynomials $P_{5,6,7}$ as a function of~$\costhetacs$ and $\phics$ (top). Below these are the templated polynomials for the $\yz$-integrated $ee_{CC}$~events at low~($5-8$~GeV), medium~($22-25.5$~GeV), and high~($132-173$~GeV) values of~$\ptz$.

Shapes of the polynomials $P_{5,6,7}$ as a function of~$\costhetacs$ and $\phics$ (top). Below these are the templated polynomials for the $\yz$-integrated $ee_{CC}$~events at low~($5-8$~GeV), medium~($22-25.5$~GeV), and high~($132-173$~GeV) values of~$\ptz$.

Shapes of the polynomials $P_{5,6,7}$ as a function of~$\costhetacs$ and $\phics$ (top). Below these are the templated polynomials for the $\yz$-integrated $ee_{CC}$~events at low~($5-8$~GeV), medium~($22-25.5$~GeV), and high~($132-173$~GeV) values of~$\ptz$.

Shapes of the polynomials $P_{5,6,7}$ as a function of~$\costhetacs$ and $\phics$ (top). Below these are the templated polynomials for the $\yz$-integrated $ee_{CC}$~events at low~($5-8$~GeV), medium~($22-25.5$~GeV), and high~($132-173$~GeV) values of~$\ptz$.

Shapes of the polynomials $P_{5,6,7}$ as a function of~$\costhetacs$ and $\phics$ (top). Below these are the templated polynomials for the $\yz$-integrated $ee_{CC}$~events at low~($5-8$~GeV), medium~($22-25.5$~GeV), and high~($132-173$~GeV) values of~$\ptz$.

Shapes of the polynomials $P_{5,6,7}$ as a function of~$\costhetacs$ and $\phics$ (top). Below these are the templated polynomials for the $\yz$-integrated $ee_{CC}$~events at low~($5-8$~GeV), medium~($22-25.5$~GeV), and high~($132-173$~GeV) values of~$\ptz$.

Correlation matrix between the $\ptz$ bins of $A_{0}$ before (left) and after (right) regularisation.

Correlation matrix between the $\ptz$ bins of $A_{0}$ before (left) and after (right) regularisation.

Residuals of a fifth-order (left) and fourth-order (right) polynomial fit to the measured $A_{0}$ spectrum in the $ee_{\text{CC}}$ $\yz$-integrated channel, regularised with sixth-order derivatives.

Residuals of a fifth-order (left) and fourth-order (right) polynomial fit to the measured $A_{0}$ spectrum in the $ee_{\text{CC}}$ $\yz$-integrated channel, regularised with sixth-order derivatives.

For the $ee_{\text{CC}}+\mu\mu_{\text{CC}}$ channel, the derived regularisation bias uncertainty in the $\yz$-integrated $A_0$ coefficient for various regularisation strengths (left) along with the corresponding statistical uncertainty of the coefficient (right) versus $\ptz$. The unregularised statistical uncertainty is shown for comparison.

For the $ee_{\text{CC}}+\mu\mu_{\text{CC}}$ channel, the derived regularisation bias uncertainty in the $\yz$-integrated $A_0$ coefficient for various regularisation strengths (left) along with the corresponding statistical uncertainty of the coefficient (right) versus $\ptz$. The unregularised statistical uncertainty is shown for comparison.

For the $ee_{\text{CC}}+\mu\mu_{\text{CC}}$ channel in the $\yz$-integrated configuration, overlays of regularised with unregularised results are shown for $A_{0-7}$.

For the $ee_{\text{CC}}+\mu\mu_{\text{CC}}$ channel in the $\yz$-integrated configuration, overlays of regularised with unregularised results are shown for $A_{0-7}$.

For the $ee_{\text{CC}}+\mu\mu_{\text{CC}}$ channel in the $\yz$-integrated configuration, overlays of regularised with unregularised results are shown for $A_{0-7}$.

For the $ee_{\text{CC}}+\mu\mu_{\text{CC}}$ channel in the $\yz$-integrated configuration, overlays of regularised with unregularised results are shown for $A_{0-7}$.

For the $ee_{\text{CC}}+\mu\mu_{\text{CC}}$ channel in the $\yz$-integrated configuration, overlays of regularised with unregularised results are shown for $A_{0-7}$.

For the $ee_{\text{CC}}+\mu\mu_{\text{CC}}$ channel in the $\yz$-integrated configuration, overlays of regularised with unregularised results are shown for $A_{0-7}$.

For the $ee_{\text{CC}}+\mu\mu_{\text{CC}}$ channel in the $\yz$-integrated configuration, overlays of regularised with unregularised results are shown for $A_{0-7}$.

For the $ee_{\text{CC}}+\mu\mu_{\text{CC}}$ channel in the $\yz$-integrated configuration, overlays of regularised with unregularised results are shown for $A_{0-7}$.

For the $ee_{\text{CC}}+\mu\mu_{\text{CC}}$ channel in the $\yz$-integrated configuration, overlays of regularised with unregularised results are shown for $A_{0}-A_{2}$.

Categorisation of parameters leading to the data statistical uncertainty in the measured coefficients illustrated by the uncertainty categorisation for $A_{0}$ in $\ptz$ bin 0.

Statistical uncertainty decomposition for the unregularised (left) and regularised (right) measurement of the $A_{0}$ coefficient in the $ee_{\text{CC}}+\mu\mu_{\text{CC}}$ channel for the integrated $\yz$ configuration.

Statistical uncertainty decomposition for the unregularised (left) and regularised (right) measurement of the $A_{0}$ coefficient in the $ee_{\text{CC}}+\mu\mu_{\text{CC}}$ channel for the integrated $\yz$ configuration.

Left: Example of the distribution of the fitted value of $A_5$ in one $\ptz$ bin from pseudo-data along with the observed value represented by a dashed line. The $p$-value computed as the right-sided tail probability is used to calculate the individual values of $Z_i$. Right: Two-dimensional distribution of the fitted $A_5$ from pseudo-data for two neighbouring $\ptz$ bins. The upper left corner of the shaded area represents the value measured in the observed data, while the shaded area represents the $p$-value used to calculate $Z_{ij}$.

Left: Example of the distribution of the fitted value of $A_5$ in one $\ptz$ bin from pseudo-data along with the observed value represented by a dashed line. The $p$-value computed as the right-sided tail probability is used to calculate the individual values of $Z_i$. Right: Two-dimensional distribution of the fitted $A_5$ from pseudo-data for two neighbouring $\ptz$ bins. The upper left corner of the shaded area represents the value measured in the observed data, while the shaded area represents the $p$-value used to calculate $Z_{ij}$.

Distribution of the test statistic $Q_{\rm{signed}}^{\rm{cov}}$ from pseudo-experiments, along with the observed value represented by the vertical dashed line. The area to the right of the dashed line is used to compute the significance of non-zero positive values of the observed $A_{5,6,7}$.

The measured angular coefficients $A_0$, $A_2$, $A_0-A_2$, $A_{5}$, $A_{6}$, and $A_{7}$ in bins of $\yz$.

The measured angular coefficients $A_0$, $A_2$, $A_0-A_2$, $A_{5}$, $A_{6}$, and $A_{7}$ in bins of $\yz$.

The measured angular coefficients $A_0$, $A_2$, $A_0-A_2$, $A_{5}$, $A_{6}$, and $A_{7}$ in bins of $\yz$.

The measured angular coefficients $A_0$, $A_2$, $A_0-A_2$, $A_{5}$, $A_{6}$, and $A_{7}$ in bins of $\yz$.

The measured angular coefficients $A_0$, $A_2$, $A_0-A_2$, $A_{5}$, $A_{6}$, and $A_{7}$ in bins of $\yz$.

The measured angular coefficients $A_0$, $A_2$, $A_0-A_2$, $A_{5}$, $A_{6}$, and $A_{7}$ in bins of $\yz$.