The unfolded differential charge asymmetry as a function of the longitudinal boost of the top pair system. The measured values are given with statistical and systematic uncertainties. The SM theory predictions calculated at NNLO in QCD and NLO in EW theory are listed. The scale uncertainty is obtained by varying renormalisation and factorisation scales independently by a factor of 2 or 0.5 around $\mu_0$ to calculate the maximum and minimum value of the asymmetry, respectively. The nominal value $\mu_0$ is chosen as $H_T/4$. The variations in which one scale is multiplied by 2 while the other scale is divided by 2 are excluded. Finally, the scale and MC integration uncertainties are added in quadrature.

The unfolded inclusive leptonic asymmetry. The unfolded $A_C^{\ell\bar{\ell}}$ is obtained in the reduced phase-space defined by the requirement $|\Delta |\eta_{\ell\bar{\ell}}||<2.5$. The measured values are given with statistical and systematic uncertainties. The SM theory predictions calculated at NLO in QCD and NLO in EW theory are listed. The theory uncertainty is obtained by varying both scales by a factor of 0.5 or 2.0 to calculate the minimum and maximum value of the asymmetry, respectively.

The unfolded differential leptonic asymmetry as a function of the invariant mass of the di-lepton pair. The unfolded $A_C^{\ell\bar{\ell}}$ is obtained in the reduced phase-space defined by the requirement $|\Delta |\eta_{\ell\bar{\ell}}||<2.5$. The measured values are given with statistical and systematic uncertainties. The SM theory predictions calculated at NLO in QCD and NLO in EW theory are listed. The theory uncertainty is obtained by varying both scales by a factor of 0.5 or 2.0 to calculate the minimum and maximum value of the asymmetry, respectively.

The unfolded differential leptonic asymmetry as a function of the transverse momentum of the di-lepton pair. The unfolded $A_C^{\ell\bar{\ell}}$ is obtained in the reduced phase-space defined by the requirement $|\Delta |\eta_{\ell\bar{\ell}}||<2.5$. The measured values are given with statistical and systematic uncertainties. The SM theory predictions calculated at NLO in QCD and NLO in EW theory are listed. The theory uncertainty is obtained by varying both scales by a factor of 0.5 or 2.0 to calculate the minimum and maximum value of the asymmetry, respectively.

The unfolded differential leptonic asymmetry as a function of the longitudinal boost of the di-lepton pair. The unfolded $A_C^{\ell\bar{\ell}}$ is obtained in the reduced phase-space defined by the requirement $|\Delta |\eta_{\ell\bar{\ell}}||<2.5$. The measured values are given with statistical and systematic uncertainties. The SM theory predictions calculated at NLO in QCD and NLO in EW theory are listed. The theory uncertainty is obtained by varying both scales by a factor of 0.5 or 2.0 to calculate the minimum and maximum value of the asymmetry, respectively.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{t\bar{t}}$ inclusive measurement. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{t\bar{t}}$ vs $\beta_{z,t\bar{t}}$ measurement for $\beta_{z,t\bar{t}}$ $\in$ [0,0.3]. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{t\bar{t}}$ vs $\beta_{z,t\bar{t}}$ measurement for $\beta_{z,t\bar{t}}$ $\in$ [0.3,0.6]. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{t\bar{t}}$ vs $\beta_{z,t\bar{t}}$ measurement for $\beta_{z,t\bar{t}}$ $\in$ [0.6,0.8]. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{t\bar{t}}$ vs $\beta_{z,t\bar{t}}$ measurement for $\beta_{z,t\bar{t}}$ $\in$ [0.8,1]. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{t\bar{t}}$ vs $m_{t\bar{t}}$ measurement for $m_{t\bar{t}}$ < 500 GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{t\bar{t}}$ vs $m_{t\bar{t}}$ measurement for $m_{t\bar{t}}$ $\in$ [500,750] GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{t\bar{t}}$ vs $m_{t\bar{t}}$ measurement for $m_{t\bar{t}}$ $\in$ [750,1000] GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{t\bar{t}}$ vs $m_{t\bar{t}}$ measurement for $m_{t\bar{t}}$ $\in$ [1000,1500] GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{t\bar{t}}$ vs $m_{t\bar{t}}$ measurement for $m_{t\bar{t}}$ > 1500 GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{t\bar{t}}$ vs $p_{T,t\bar{t}}$ measurement for $p_{T,t\bar{t}}$ < 30 GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{t\bar{t}}$ vs $p_{T,t\bar{t}}$ measurement for $p_{T,t\bar{t}}$ $\in$ [30,120] GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{t\bar{t}}$ vs $p_{T,t\bar{t}}$ measurement for $p_{T,t\bar{t}}$ > 120 GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{\ell\ell}$ inclusive measurement. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{\ell\ell}$ vs $\beta_{z,\ell\bar{\ell}}$ measurement for $\beta_{z,\ell\bar{\ell}}$ $\in$[0,0.3]. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{\ell\ell}$ vs $\beta_{z,\ell\bar{\ell}}$ measurement for $\beta_{z,\ell\bar{\ell}}$ $\in$[0.3,0.6]. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{\ell\ell}$ vs $\beta_{z,\ell\bar{\ell}}$ measurement for $\beta_{z,\ell\bar{\ell}}$ $\in$[0.6,0.8]. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{\ell\ell}$ vs $\beta_{z,\ell\bar{\ell}}$ measurement for $\beta_{z,\ell\bar{\ell}}$ $\in$[0.8,1]. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{\ell\ell}$ vs $m_{\ell\bar{\ell}}$ measurement for $m_{\ell\bar{\ell}}$ < 200 GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{\ell\ell}$ vs $m_{\ell\bar{\ell}}$ measurement for $m_{\ell\bar{\ell}}$ $\in$ [200,300] GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{\ell\ell}$ vs $m_{\ell\bar{\ell}}$ measurement for $m_{\ell\bar{\ell}}$ $\in$ [300,400] GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{\ell\ell}$ vs $m_{\ell\bar{\ell}}$ measurement for $m_{\ell\bar{\ell}}$ > 400 GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{\ell\ell}$ vs $p_{T,\ell\bar{\ell}}$ measurement for $p_{T,\ell\bar{\ell}}$ < 20 GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{\ell\ell}$ vs $p_{T,\ell\bar{\ell}}$ measurement for $p_{T,\ell\bar{\ell}}$ $\in$ [20, 70] GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{\ell\ell}$ vs $p_{T,\ell\bar{\ell}}$ measurement for $p_{T,\ell\bar{\ell}}$ > 70 GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Post-marginalisation correlation coefficients $\rho_{ij}$ of nuisance parameters for the $A_C^{t\bar{t}}$ inclusive measurement. Only $|\rho_{ij}| > 0.05$ values are included.

Post-marginalisation correlation coefficients $\rho_{ij}$ of nuisance parameters for the $A_C^{t\bar{t}}$ vs $m_{t\bar{t}}$ measurement. Only $|\rho_{ij}| > 0.05$ values are included.

Post-marginalisation correlation coefficients $\rho_{ij}$ of nuisance parameters for the $A_C^{t\bar{t}}$ vs $p_{T,t\bar{t}}$ measurement. Only $|\rho_{ij}| > 0.05$ values are included.

Post-marginalisation correlation coefficients $\rho_{ij}$ of nuisance parameters for the $A_C^{t\bar{t}}$ vs $\beta_{z,t\bar{t}}$ measurement. Only $|\rho_{ij}| > 0.05$ values are included.

Post-marginalisation correlation coefficients $\rho_{ij}$ of nuisance parameters for the $A_C^{\ell\ell}$ inclusive measurement. Only $|\rho_{ij}| > 0.05$ values are included.

Post-marginalisation correlation coefficients $\rho_{ij}$ of nuisance parameters for the $A_C^{\ell\ell}$ vs $m_{\ell\bar{\ell}}$ measurement. Only $|\rho_{ij}| > 0.05$ values are included.

Post-marginalisation correlation coefficients $\rho_{ij}$ of nuisance parameters for the $A_C^{\ell\ell}$ vs $p_{T,\ell\bar{\ell}}$ measurement. Only $|\rho_{ij}| > 0.05$ values are included.

Post-marginalisation correlation coefficients $\rho_{ij}$ of nuisance parameters for the $A_C^{\ell\ell}$ vs $\beta_{z,\ell\bar{\ell}}$ measurement. Only $|\rho_{ij}| > 0.05$ values are included.

Covariance matrix for the $A_C^{t\bar{t}}$ vs $m_{t\bar{t}}$ measurement.

Covariance matrix for the $A_C^{t\bar{t}}$ vs $p_{T,t\bar{t}}$ measurement.

Covariance matrix for the $A_C^{t\bar{t}}$ vs $\beta_{z,t\bar{t}}$ measurement.

Covariance matrix for the $A_C^{\ell\ell}$ vs $m_{\ell\bar{\ell}}$ measurement.

Covariance matrix for the $A_C^{\ell\ell}$ vs $p_{T,\ell\bar{\ell}}$ measurement.

Covariance matrix for the $A_C^{\ell\ell}$ vs $\beta_{z,\ell\bar{\ell}}$ measurement.

Correlation coefficients $\rho_{i,j}$ for the statistical and systematic uncertainties between the $i$-th and $j$-th bin of the differential $A_E$ measurement as a function of the jet scattering angle $\theta_j$

The effects on the energy asymmetry of $1\sigma$ variations in its influencing nuisance parameters for the three $\theta_j$ bins. These are extracted from the samples of the posterior distribution with $\sigma_i^{(j)} = c_{ij}/\sqrt{c_{jj}}$ being the estimated shift of bin $i$ in conjunction with a shift $\Delta\theta_j$ of nuisance parameter $j$. The data statistical (Data stat.) uncertainty is obtained from running the unfolding with all nuisance parameters being fixed to their post-marginalised values, the MC statistical uncertainty on the response matrix ($t\bar{t}$ response MC stat.) is evaluated using a bootstrapping method from the covariance matrix of the ensemble of repeated unfolding results with varied response matrices. The $\gamma$ variations denote the statistical uncertainties of the background predictions in the corresponding bin of the $\Delta E$ vs $\theta_{j}$ distribution. The numbers appended to the $W$+jets PDF variations denote the corresponding NNPDF3.0 PDF sets.

The effects on the energy asymmetry of $1\sigma$ variations in its influencing nuisance parameters for the three $\theta_j$ bins. These are extracted from the samples of the posterior distribution with $\sigma_i^{(j)} = c_{ij}/\sqrt{c_{jj}}$ being the estimated shift of bin $i$ in conjunction with a shift $\Delta\theta_j$ of nuisance parameter $j$. The data statistical (Data stat.) uncertainty is obtained from running the unfolding with all nuisance parameters being fixed to their post-marginalised values, the MC statistical uncertainty on the response matrix ($t\bar{t}$ response MC stat.) is evaluated using a bootstrapping method from the covariance matrix of the ensemble of repeated unfolding results with varied response matrices. The $\gamma$ variations denote the statistical uncertainties of the background predictions in the corresponding bin of the $\Delta E$ vs $\theta_{j}$ distribution. The numbers appended to the $W$+jets PDF variations denote the corresponding NNPDF3.0 PDF sets.

Covariances $c_{ij}$ for the highest ranked systematic uncertainties in the energy asymmetry measurement differential in $\theta_j$.

Covariances $c_{ij}$ for the highest ranked systematic uncertainties in the energy asymmetry measurement differential in $\theta_j$.

Definition of the fiducial phase space with lepton candidate ($\ell$), hadronic top candidate ($j_h$), leptonic top candidate ($j_l$) and associated jet candidate ($j_a$).

Definition of the fiducial phase space with lepton candidate ($\ell$), hadronic top candidate ($j_h$), leptonic top candidate ($j_l$) and associated jet candidate ($j_a$).