Spline interpolation of the weight function (depending of $\cos \theta_{P_c}$) applied to $\Lambda_{b}^{0}$ candidates. The weight function is determined as the inverse of the density of $\Lambda_{b}^{0}$ candidates in the narrow pentaquark peak region while the interpolation is done between the bin centers.

The covariance matrix for the kinematic bins matrix of the $D_s^+$ production asymmetry measured using the combined $\sqrt{s} =7$ and 8 TeV data sets (corresponding to Table 1). The statistical and systematic uncertainties are combined. The kinematic bins are indexed as follows: the three rapidity bins, y, in the range from 2.0 to 4.5 are indexed with $i_y$ ranging from 0 to 2 with the following bin edges: 2.0, 3.0, 3.5, 4.5. The four $p_{\rm T}$ bins in the range from 2.5 to 25.0 GeV/c are indexed with $i_{p_T}$ from 0 to 3 with the following bin edges: 2.5, 4.7, 6.5, 8.5, 25.0 GeV/c. The index of a kinematic bins is then given by: $i_{\rm bin} = 4 \times i_y + i_{p_T}$.

The covariance matrix for the kinematic bins matrix of the $D_s^+$ production asymmetry measured using the $\sqrt{s} =7$ TeV data set (corresponding to Table 2). The statistical and systematic uncertainties are combined. The kinematic bins are indexed as follows: the three rapidity bins, y, in the range from 2.0 to 4.5 are indexed with $i_y$ ranging from 0 to 2 with the following bin edges: 2.0, 3.0, 3.5, 4.5. The four $p_{\rm T}$ bins in the range from 2.5 to 25.0 GeV/c are indexed with $i_{p_T}$ from 0 to 3 with the following bin edges: 2.5, 4.7, 6.5, 8.5, 25.0 GeV/c. The index of a kinematic bins is then given by: $i_{\rm bin} = 4 \times i_y + i_{p_T}$.

The covariance matrix for the kinematic bins matrix of the $D_s^+$ production asymmetry measured using the $\sqrt{s} =8$ TeV data set (corresponding to Table 3). The statistical and systematic uncertainties are combined. The kinematic bins are indexed as follows: the three rapidity bins, y, in the range from 2.0 to 4.5 are indexed with $i_y$ ranging from 0 to 2 with the following bin edges: 2.0, 3.0, 3.5, 4.5. The four $p_{\rm T}$ bins in the range from 2.5 to 25.0 GeV/c are indexed with $i_{p_T}$ from 0 to 3 with the following bin edges: 2.5, 4.7, 6.5, 8.5, 25.0 GeV/c. The index of a kinematic bins is then given by: $i_{\rm bin} = 4 \times i_y + i_{p_T}$.

The ratios of the $Wj$, $W^+j$ and $W^-j$ cross-sections to the $Z^0 j$ cross-section, and the ratio of the $W^+j$ to $W^-j$ cross-sections.

The asymmetry of $W^+j$ and $W^-j$ production, given by $A(Wj)\equiv (\sigma_{W^+j}-\sigma_{W^-j})/(\sigma_{W^+j}+\sigma_{W^-j})$.

The asymmetry of $W^+j$ and $W^-j$ production, given by $A(Wj)\equiv (\sigma_{W^+j}-\sigma_{W^-j})/(\sigma_{W^+j}+\sigma_{W^-j})$.

The measured cross-sections for $Wj$ production in four bins of $\eta^{\mu}$. The uncertainties shown are statistical, systematic and due to the luminosity determination.

The measured cross-sections for $Wj$ production in four bins of $\eta^{\mu}$. The uncertainties shown are statistical, systematic and due to the luminosity determination.

The measured cross-sections for $Wj$ production in four bins of $\eta^{\rm jet}$. The uncertainties shown are statistical, systematic and due to the luminosity determination.

The measured cross-sections for $Wj$ production in four bins of $\eta^{\rm jet}$. The uncertainties shown are statistical, systematic and due to the luminosity determination.

The measured cross-sections for $Wj$ production in five bins of $p^{\rm jet}_T$. The uncertainties shown are statistical, systematic and due to the luminosity determination.

The measured cross-sections for $Wj$ production in five bins of $p^{\rm jet}_T$. The uncertainties shown are statistical, systematic and due to the luminosity determination.

The measured cross-sections for $Zj$ production in four bins of $y^Z$. The uncertainties shown are statistical, systematic and due to the luminosity determination.

The measured cross-sections for $Z^0 j$ production in four bins of $y^Z$. The uncertainties shown are statistical, systematic and due to the luminosity determination.

The measured cross-sections for $Zj$ production in four bins of $\eta^{\rm jet}$. The uncertainties shown are statistical, systematic and due to the luminosity determination.

The measured cross-sections for $Z^0 j$ production in four bins of $\eta^{\rm jet}$. The uncertainties shown are statistical, systematic and due to the luminosity determination.

The measured cross-sections for $Zj$ production in bins of $p^{\rm jet}_T$. The uncertainties shown are statistical, systematic and due to the luminosity determination.

The measured cross-sections for $Z^0 j$ production in bins of $p^{\rm jet}_T$. The uncertainties shown are statistical, systematic and due to the luminosity determination.

The measured cross-sections for $Zj$ production in bins of $|\Delta\phi|$. The uncertainties shown are statistical, systematic and due to the luminosity determination.

The measured cross-sections for $Z^0 j$ production in bins of $|\Delta\phi|$. The uncertainties shown are statistical, systematic and due to the luminosity determination.

The correlation matrix for the systematic uncertainties on the $W^+j$ production cross-section measurements presented in Table 1 in bins of $\eta^{\mu}$, where the rows and columns correspond to the individual bins.

The correlation matrix for the systematic uncertainties on the $W^+j$ production cross-section measurements presented in Table 1 in bins of $\eta^{\mu}$, where the rows and columns correspond to the individual bins.

The correlation matrix for the systematic uncertainties on the $W^-j$ production cross-section measurements presented in Table 1 in bins of $\eta^{\mu}$, where the rows and columns correspond to the individual bins.

The correlation matrix for the systematic uncertainties on the $W^-j$ production cross-section measurements presented in Table 1 in bins of $\eta^{\mu}$, where the rows and columns correspond to the individual bins.

The correlation matrix for the systematic uncertainties on the $W^+j$ production cross-section measurements presented in Table 5 in bins of $\eta^{\rm jet}$, where the rows and columns correspond to the individual bins.

The correlation matrix for the systematic uncertainties on the $W^+j$ production cross-section measurements presented in Table 5 in bins of $\eta^{\rm jet}$, where the rows and columns correspond to the individual bins.

The correlation matrix for the systematic uncertainties on the $W^-j$ production cross-section measurements presented in Table 5 in bins of $\eta^{\rm jet}$, where the rows and columns correspond to the individual bins.

The correlation matrix for the systematic uncertainties on the $W^-j$ production cross-section measurements presented in Table 5 in bins of $\eta^{\rm jet}$, where the rows and columns correspond to the individual bins.

The correlation matrix for the systematic uncertainties on the $W^+j$ production cross-section measurements presented in Table 3 in bins of $p_T^{\rm jet}$, where the rows and columns correspond to the individual bins.

The correlation matrix for the systematic uncertainties on the $W^+j$ production cross-section measurements presented in Table 3 in bins of $p_T^{\rm jet}$, where the rows and columns correspond to the individual bins.

The correlation matrix for the systematic uncertainties on the $W^-j$ production cross-section measurements presented in Table 3 in bins of $p_T^{\rm jet}$, where the rows and columns correspond to the individual bins.

The correlation matrix for the systematic uncertainties on the $W^-j$ production cross-section measurements presented in Table 3 in bins of $p_T^{\rm jet}$, where the rows and columns correspond to the individual bins.

The correlation matrix for the systematic uncertainties on the $Zj$ production cross-section measurements presented in Table 4 as a function of $y^Z$, where the rows and columns correspond to the individual bins.

The correlation matrix for the systematic uncertainties on the $Z^0 j$ production cross-section measurements presented in Table 4 as a function of $y^Z$, where the rows and columns correspond to the individual bins.

The correlation matrix for the systematic uncertainties on the $Zj$ production cross-section measurements presented in Table 5 as a function of $\eta^{\rm jet}$, where the rows and columns correspond to the individual bins.

The correlation matrix for the systematic uncertainties on the $Z^0 j$ production cross-section measurements presented in Table 5 as a function of $\eta^{\rm jet}$, where the rows and columns correspond to the individual bins.

The correlation matrix for the systematic uncertainties on the $Zj$ production cross-section measurements presented in Table 6 as a function of $p_T^{\rm jet}$, where the rows and columns correspond to the individual bins.

The correlation matrix for the systematic uncertainties on the $Z^0 j$ production cross-section measurements presented in Table 6 as a function of $p_T^{\rm jet}$, where the rows and columns correspond to the individual bins.

The correlation matrix for the systematic uncertainties on the $Zj$ production cross-section measurements presented in Table 7 as a function of $|\Delta\phi|$, where the rows and columns correspond to the individual bins.

The correlation matrix for the systematic uncertainties on the $Z^0 j$ production cross-section measurements presented in Table 7 as a function of $|\Delta\phi|$, where the rows and columns correspond to the individual bins.

The correlation matrix for the systematic uncertainties on the $W^+j$ and $W^-j$ production cross-section measurements presented in Table 1 in bins of $\eta\mu$. The first four rows/columns correspond to the $W^+j$ cross-section in bins of $\eta\mu$ and the second four rows/columns correspond to the $W^-j$ cross-section in bins of $\eta\mu$. The matrix is used to calculate the ratio and asymmetry of $W^+j$ and $W^-j$ production as a function of $\eta\mu$.

The correlation matrix for the systematic uncertainties on the $W^+j$ and $W^-j$ production cross-section measurements presented in Table 1 in bins of $\eta^\mu$. The matrix is used to calculate the ratio and asymmetry of $W^+j$ and $W^-j$ production as a function of $\eta^\mu$.

The correlation matrix for the systematic uncertainties on the $W^+j$, $W^-j$ and $Zj$ production cross-section measurements presented in Tables 2 and 5 in bins of $\eta^{\rm jet}$. The first four rows/columns correspond to the $W^+j$ cross-section in bins of $\eta^{\rm jet}$, the middle four correspond to the $W^-j$ cross-section in bins of $\eta^{\rm jet}$ and the final four correspond to the $Zj$ cross-section in bins of $\eta^{\rm jet}$. The matrix is used to calculate the ratios of $Wj$ to $Zj$ production and the charge ratio and asymmetry of $Wj$ production in the total fiducial region.

The correlation matrix for the systematic uncertainties on the $W^+j$, $W^-j$ and $Z^0 j$ production cross-section measurements presented in Tables 2 and 5 in bins of $\eta^{\rm jet}$. The matrix is used to calculate the ratios of $Wj$ to $Z^0 j$ production and the charge ratio and asymmetry of $Wj$ production in the total fiducial region.

The frame-invariant polarization parameter $\tilde{\lambda}$ measured in the helicity frame for the $\Upsilon(1S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=7\,\mathrm{TeV}$. The first uncertainty is statistical and the second represents the systematic uncertainty.

The polarization parameter $\lambda_{\theta}$ measured in the helicity frame for the $\Upsilon(1S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=8\,\mathrm{TeV}$. The first quoted uncertainty is statistical and the second is systematic.

The polarization parameter $\lambda_{\theta\phi}$ measured in the helicity frame for the $\Upsilon(1S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=8\,\mathrm{TeV}$. The first quoted uncertainty is statistical and the second is systematic.

The polarization parameter $\lambda_{\phi}$ measured in the helicity frame for the $\Upsilon(1S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=8\,\mathrm{TeV}$. The first quoted uncertainty is statistical and the second is systematic.

The frame-invariant polarization parameter $\tilde{\lambda}$ measured in the helicity frame for the $\Upsilon(1S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=8\,\mathrm{TeV}$. The first quoted uncertainty is statistical and the second is systematic.

The polarization parameter $\lambda_\theta$ measured in the Collins-Soper frame for the $\Upsilon(1S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=7\,\mathrm{TeV}$. The first quoted uncertainty is statistical and the second is systematic.

The polarization parameter $\lambda_{\theta\phi}$ measured in the Collins-Soper frame for the $\Upsilon(1S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=7\,\mathrm{TeV}$. The first quoted uncertainty is statistical and the second is systematic.

The polarization parameter $\lambda_\phi$ measured in the Collins-Soper frame for the $\Upsilon(1S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=7\,\mathrm{TeV}$. The first quoted uncertainty is statistical and the second is systematic.

The frame-invariant polarization parameter $\tilde{\lambda}$ measured in the Collins-Soper frame for the $\Upsilon(1S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=7\,\mathrm{TeV}$. The first quoted uncertainty is statistical and the second is systematic.

The polarization parameter $\lambda_\theta$ measured in the Collins-Soper frame for the $\Upsilon(1S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=8\,\mathrm{TeV}$. The first quoted uncertainty is statistical and the second is systematic.

The polarization parameter $\lambda_{\theta\phi}$ measured in the Collins-Soper frame for the $\Upsilon(1S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=8\,\mathrm{TeV}$. The first quoted uncertainty is statistical and the second is systematic.

The polarization parameter $\lambda_\phi$ measured in the Collins-Soper frame for the $\Upsilon(1S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=8\,\mathrm{TeV}$. The first quoted uncertainty is statistical and the second is systematic.

The frame-invariant polarization parameter $\tilde{\lambda}$ measured in the Collins-Soper frame for the $\Upsilon(1S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=8\,\mathrm{TeV}$. The first quoted uncertainty is statistical and the second is systematic.

The polarization parameter $\lambda_\theta$ measured in the Gottfried-Jackson frame for the $\Upsilon(1S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=7\,\mathrm{TeV}$. The first quoted uncertainty is statistical and the second is systematic.

The polarization parameter $\lambda_{\theta\phi}$ measured in the Gottfried-Jackson frame for the $\Upsilon(1S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=7\,\mathrm{TeV}$. The first quoted uncertainty is statistical and the second is systematic.

The polarization parameter $\lambda_\phi$ measured in the Gottfried-Jackson frame for the $\Upsilon(1S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=7\,\mathrm{TeV}$. The first quoted uncertainty is statistical and the second is systematic.

The frame-invariant polarization parameter $\tilde{\lambda}$ measured in the Gottfried-Jackson frame for the $\Upsilon(1S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=7\,\mathrm{TeV}$. The first quoted uncertainty is statistical and the second is systematic.

The polarization parameter $\lambda_\theta$ measured in the Gottfried-Jackson frame for the $\Upsilon(1S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=8\,\mathrm{TeV}$. The first quoted uncertainty is statistical and the second is systematic.

The polarization parameter $\lambda_{\theta\phi}$ measured in the Gottfried-Jackson frame for the $\Upsilon(1S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=8\,\mathrm{TeV}$. The first quoted uncertainty is statistical and the second is systematic.

The polarization parameter $\lambda_\phi$ measured in the Gottfried-Jackson frame for the $\Upsilon(1S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=8\,\mathrm{TeV}$. The first quoted uncertainty is statistical and the second is systematic.

The frame-invariant polarization parameter $\tilde{\lambda}$ measured in the Gottfried-Jackson frame for the $\Upsilon(1S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=8\,\mathrm{TeV}$. The first quoted uncertainty is statistical and the second is systematic.

Values of the polarization parameter $\lambda_\theta$ measured in the helicity(SH), Collins-Soper(CS) and Gottfried-Jackson(TH) frames for the $\Upsilon(1S)$ produced at $\sqrt{s}=7$ TeV in the rapidity range $2.2 < y^\Upsilon < 4.5$ and different bins of $p_{T}^{\Upsilon}$. The first quoted uncertainty is statistical and the second is systematic.

Values of the polarization parameter $\lambda_{\theta\phi}$ measured in the helicity(SH), Collins-Soper(CS) and Gottfried-Jackson(TH) frames for the $\Upsilon(1S)$ produced at $\sqrt{s}=7$ TeV in the rapidity range $2.2 < y^\Upsilon < 4.5$ and different bins of $p_{T}^{\Upsilon}$. The first quoted uncertainty is statistical and the second is systematic.

Values of the polarization parameter $\lambda_{\phi}$ measured in the helicity(SH), Collins-Soper(CS) and Gottfried-Jackson(TH) frames for the $\Upsilon(1S)$ produced at $\sqrt{s}=7$ TeV in the rapidity range $2.2 < y^\Upsilon < 4.5$ and different bins of $p_{T}^{\Upsilon}$. The first quoted uncertainty is statistical and the second is systematic.

Values of the frame-invariant polarization parameter $\tilde{\lambda}$ measured in the helicity(SH), Collins-Soper(CS) and Gottfried-Jackson(TH) frames for the $\Upsilon(1S)$ produced at $\sqrt{s}=7$ TeV in the rapidity range $2.2 < y^\Upsilon < 4.5$ and different bins of $p_{T}^{\Upsilon}$. The first quoted uncertainty is statistical and the second is systematic.

Values of the polarization parameter $\lambda_{\theta}$ measured in the helicity(SH), Collins-Soper(CS) and Gottfried-Jackson(TH) frames for the $\Upsilon(1S)$ produced at $\sqrt{s}=8$ TeV in the rapidity range $2.2 < y^\Upsilon < 4.5$ and different bins of $p_{T}^{\Upsilon}$. The first quoted uncertainty is statistical and the second is systematic.

Values of the polarization parameter $\lambda_{\theta\phi}$ measured in the helicity(SH), Collins-Soper(CS) and Gottfried-Jackson(TH) frames for the $\Upsilon(1S)$ produced at $\sqrt{s}=8$ TeV in the rapidity range $2.2 < y^\Upsilon < 4.5$ and different bins of $p_{T}^{\Upsilon}$. The first quoted uncertainty is statistical and the second is systematic.

Values of the polarization parameter $\lambda_{\phi}$ measured in the helicity(SH), Collins-Soper(CS) and Gottfried-Jackson(TH) frames for the $\Upsilon(1S)$ produced at $\sqrt{s}=8$ TeV in the rapidity range $2.2 < y^\Upsilon < 4.5$ and different bins of $p_{T}^{\Upsilon}$. The first quoted uncertainty is statistical and the second is systematic.

Values of the frame-invariant polarization parameter $\tilde{\lambda}$ measured in the helicity(SH), Collins-Soper(CS) and Gottfried-Jackson(TH) frames for the $\Upsilon(1S)$ produced at $\sqrt{s}=8$ TeV in the rapidity range $2.2 < y^\Upsilon < 4.5$ and different bins of $p_{T}^{\Upsilon}$. The first quoted uncertainty is statistical and the second is systematic.

The polarization parameter $\lambda_{\theta}$ measured in the helicity frame for the $\Upsilon(2S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=7\,\mathrm{TeV}$. The first uncertainty is statistical and the second is systematic.

The polarization parameter $\lambda_{\theta\phi}$ measured in the helicity frame for the $\Upsilon(2S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=7\,\mathrm{TeV}$. The first uncertainty is statistical and the second represents the systematic uncertainty.

The polarization parameter $\lambda_{\phi}$ measured in the helicity frame for the $\Upsilon(2S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=7\,\mathrm{TeV}$. The first uncertainty is statistical and the second is systematic.

The frame-invariant polarization parameter $\tilde{\lambda}$ measured in the helicity frame for the $\Upsilon(2S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=7\,\mathrm{TeV}$. The first uncertainty is statistical and the second represents the systematic uncertainty.

The polarization parameter $\lambda_{\theta}$ measured in the helicity frame for the $\Upsilon(2S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=8\,\mathrm{TeV}$. The first uncertainty is statistical and the second is systematic.

The polarization parameter $\lambda_{\theta\phi}$ measured in the helicity frame for the $\Upsilon(2S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=8\,\mathrm{TeV}$. The first uncertainty is statistical and the second represents the systematic uncertainty.

The polarization parameter $\lambda_{\phi}$ measured in the helicity frame for the $\Upsilon(2S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=8\,\mathrm{TeV}$. The first uncertainty is statistical and the second is systematic.

The frame-invariant polarization parameter $\tilde{\lambda}$ measured in the helicity frame for the $\Upsilon(2S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=8\,\mathrm{TeV}$. The first uncertainty is statistical and the second represents the systematic uncertainty.

The polarization parameter $\lambda_{\theta}$ measured in the Collins-Soper frame for the $\Upsilon(2S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=7\,\mathrm{TeV}$. The first uncertainty is statistical and the second is systematic.

The polarization parameter $\lambda_{\theta\phi}$ measured in the Collins-Soper frame for the $\Upsilon(2S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=7\,\mathrm{TeV}$. The first uncertainty is statistical and the second represents the systematic uncertainty.

The polarization parameter $\lambda_{\phi}$ measured in the Collins-Soper frame for the $\Upsilon(2S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=7\,\mathrm{TeV}$. The first uncertainty is statistical and the second is systematic.

The frame-invariant polarization parameter $\tilde{\lambda}$ measured in the Collins-Soper frame for the $\Upsilon(2S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=7\,\mathrm{TeV}$. The first uncertainty is statistical and the second represents the systematic uncertainty.

The polarization parameter $\lambda_{\theta}$ measured in the Collins-Soper frame for the $\Upsilon(2S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=8\,\mathrm{TeV}$. The first uncertainty is statistical and the second is systematic.

The polarization parameter $\lambda_{\theta\phi}$ measured in the Collins-Soper frame for the $\Upsilon(2S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=8\,\mathrm{TeV}$. The first uncertainty is statistical and the second represents the systematic uncertainty.

The polarization parameter $\lambda_{\phi}$ measured in the Collins-Soper frame for the $\Upsilon(2S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=8\,\mathrm{TeV}$. The first uncertainty is statistical and the second is systematic.

The frame-invariant polarization parameter $\tilde{\lambda}$ measured in the Collins-Soper frame for the $\Upsilon(2S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=8\,\mathrm{TeV}$. The first uncertainty is statistical and the second represents the systematic uncertainty.

The polarization parameter $\lambda_{\theta}$ measured in the Gottfried-Jackson frame for the $\Upsilon(2S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=7\,\mathrm{TeV}$. The first uncertainty is statistical and the second is systematic.

The polarization parameter $\lambda_{\theta\phi}$ measured in the Gottfried-Jackson frame for the $\Upsilon(2S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=7\,\mathrm{TeV}$. The first uncertainty is statistical and the second represents the systematic uncertainty.

The polarization parameter $\lambda_{\phi}$ measured in the Gottfried-Jackson frame for the $\Upsilon(2S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=7\,\mathrm{TeV}$. The first uncertainty is statistical and the second is systematic.

The frame-invariant polarization parameter $\tilde{\lambda}$ measured in the Gottfried-Jackson frame for the $\Upsilon(2S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=7\,\mathrm{TeV}$. The first uncertainty is statistical and the second represents the systematic uncertainty.

The polarization parameter $\lambda_{\theta}$ measured in the Gottfried-Jackson frame for the $\Upsilon(2S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=8\,\mathrm{TeV}$. The first uncertainty is statistical and the second is systematic.

The polarization parameter $\lambda_{\theta\phi}$ measured in the Gottfried-Jackson frame for the $\Upsilon(2S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=8\,\mathrm{TeV}$. The first uncertainty is statistical and the second represents the systematic uncertainty.

The polarization parameter $\lambda_{\phi}$ measured in the Gottfried-Jackson frame for the $\Upsilon(2S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=8\,\mathrm{TeV}$. The first uncertainty is statistical and the second is systematic.

The frame-invariant polarization parameter $\tilde{\lambda}$ measured in the Gottfried-Jackson frame for the $\Upsilon(2S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=8\,\mathrm{TeV}$. The first uncertainty is statistical and the second represents the systematic uncertainty.

Values of the polarization parameter $\lambda_\theta$ measured in the helicity(SH), Collins-Soper(CS) and Gottfried-Jackson(TH) frames for the $\Upsilon(2S)$ produced at $\sqrt{s}=7$ TeV in the rapidity range $2.2 < y^\Upsilon < 4.5$ and different bins of $p_{T}^{\Upsilon}$. The first quoted uncertainty is statistical and the second is systematic.

Values of the polarization parameter $\lambda_{\theta\phi}$ measured in the helicity(SH), Collins-Soper(CS) and Gottfried-Jackson(TH) frames for the $\Upsilon(2S)$ produced at $\sqrt{s}=7$ TeV in the rapidity range $2.2 < y^\Upsilon < 4.5$ and different bins of $p_{T}^{\Upsilon}$. The first quoted uncertainty is statistical and the second is systematic.

Values of the polarization parameter $\lambda_{\phi}$ measured in the helicity(SH), Collins-Soper(CS) and Gottfried-Jackson(TH) frames for the $\Upsilon(2S)$ produced at $\sqrt{s}=7$ TeV in the rapidity range $2.2 < y^\Upsilon < 4.5$ and different bins of $p_{T}^{\Upsilon}$. The first quoted uncertainty is statistical and the second is systematic.

Values of the frame-invariant polarization parameter $\tilde{\lambda}$ measured in the helicity(SH), Collins-Soper(CS) and Gottfried-Jackson(TH) frames for the $\Upsilon(2S)$ produced at $\sqrt{s}=7$ TeV in the rapidity range $2.2 < y^\Upsilon < 4.5$ and different bins of $p_{T}^{\Upsilon}$. The first quoted uncertainty is statistical and the second is systematic.

Values of the polarization parameter $\lambda_{\theta}$ measured in the helicity(SH), Collins-Soper(CS) and Gottfried-Jackson(TH) frames for the $\Upsilon(2S)$ produced at $\sqrt{s}=8$ TeV in the rapidity range $2.2 < y^\Upsilon < 4.5$ and different bins of $p_{T}^{\Upsilon}$. The first quoted uncertainty is statistical and the second is systematic.

Values of the polarization parameter $\lambda_{\theta\phi}$ measured in the helicity(SH), Collins-Soper(CS) and Gottfried-Jackson(TH) frames for the $\Upsilon(2S)$ produced at $\sqrt{s}=8$ TeV in the rapidity range $2.2 < y^\Upsilon < 4.5$ and different bins of $p_{T}^{\Upsilon}$. The first quoted uncertainty is statistical and the second is systematic.

Values of the polarization parameter $\lambda_{\phi}$ measured in the helicity(SH), Collins-Soper(CS) and Gottfried-Jackson(TH) frames for the $\Upsilon(2S)$ produced at $\sqrt{s}=8$ TeV in the rapidity range $2.2 < y^\Upsilon < 4.5$ and different bins of $p_{T}^{\Upsilon}$. The first quoted uncertainty is statistical and the second is systematic.

Values of the frame-invariant polarization parameter $\tilde{\lambda}$ measured in the helicity(SH), Collins-Soper(CS) and Gottfried-Jackson(TH) frames for the $\Upsilon(2S)$ produced at $\sqrt{s}=8$ TeV in the rapidity range $2.2 < y^\Upsilon < 4.5$ and different bins of $p_{T}^{\Upsilon}$. The first quoted uncertainty is statistical and the second is systematic.

The polarization parameter $\lambda_{\theta}$ measured in the helicity frame for the $\Upsilon(3S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=7\,\mathrm{TeV}$. The first uncertainty is statistical and the second is systematic.

The polarization parameter $\lambda_{\theta\phi}$ measured in the helicity frame for the $\Upsilon(3S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=7\,\mathrm{TeV}$. The first uncertainty is statistical and the second represents the systematic uncertainty.

The polarization parameter $\lambda_{\phi}$ measured in the helicity frame for the $\Upsilon(3S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=7\,\mathrm{TeV}$. The first uncertainty is statistical and the second is systematic.

The frame-invariant polarization parameter $\tilde{\lambda}$ measured in the helicity frame for the $\Upsilon(3S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=7\,\mathrm{TeV}$. The first uncertainty is statistical and the second represents the systematic uncertainty.

The polarization parameter $\lambda_{\theta}$ measured in the helicity frame for the $\Upsilon(3S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=8\,\mathrm{TeV}$. The first uncertainty is statistical and the second is systematic.

The polarization parameter $\lambda_{\theta\phi}$ measured in the helicity frame for the $\Upsilon(3S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=8\,\mathrm{TeV}$. The first uncertainty is statistical and the second represents the systematic uncertainty.

The polarization parameter $\lambda_{\phi}$ measured in the helicity frame for the $\Upsilon(3S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=8\,\mathrm{TeV}$. The first uncertainty is statistical and the second is systematic.

The frame-invariant polarization parameter $\tilde{\lambda}$ measured in the helicity frame for the $\Upsilon(3S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=8\,\mathrm{TeV}$. The first uncertainty is statistical and the second represents the systematic uncertainty.

The polarization parameter $\lambda_{\theta}$ measured in the Collins-Soper frame for the $\Upsilon(3S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=7\,\mathrm{TeV}$. The first uncertainty is statistical and the second is systematic.

The polarization parameter $\lambda_{\theta\phi}$ measured in the Collins-Soper frame for the $\Upsilon(3S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=7\,\mathrm{TeV}$. The first uncertainty is statistical and the second represents the systematic uncertainty.

The polarization parameter $\lambda_{\phi}$ measured in the Collins-Soper frame for the $\Upsilon(3S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=7\,\mathrm{TeV}$. The first uncertainty is statistical and the second is systematic.

The frame-invariant polarization parameter $\tilde{\lambda}$ measured in the Collins-Soper frame for the $\Upsilon(3S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=7\,\mathrm{TeV}$. The first uncertainty is statistical and the second represents the systematic uncertainty.

The polarization parameter $\lambda_{\theta}$ measured in the Collins-Soper frame for the $\Upsilon(3S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=8\,\mathrm{TeV}$. The first uncertainty is statistical and the second is systematic.

The polarization parameter $\lambda_{\theta\phi}$ measured in the Collins-Soper frame for the $\Upsilon(3S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=8\,\mathrm{TeV}$. The first uncertainty is statistical and the second represents the systematic uncertainty.

The polarization parameter $\lambda_{\phi}$ measured in the Collins-Soper frame for the $\Upsilon(3S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=8\,\mathrm{TeV}$. The first uncertainty is statistical and the second is systematic.

The frame-invariant polarization parameter $\tilde{\lambda}$ measured in the Collins-Soper frame for the $\Upsilon(3S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=8\,\mathrm{TeV}$. The first uncertainty is statistical and the second represents the systematic uncertainty.

The polarization parameter $\lambda_{\theta}$ measured in the Gottfried-Jackson frame for the $\Upsilon(3S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=7\,\mathrm{TeV}$. The first uncertainty is statistical and the second is systematic.

The polarization parameter $\lambda_{\theta\phi}$ measured in the Gottfried-Jackson frame for the $\Upsilon(3S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=7\,\mathrm{TeV}$. The first uncertainty is statistical and the second represents the systematic uncertainty.

The polarization parameter $\lambda_{\phi}$ measured in the Gottfried-Jackson frame for the $\Upsilon(3S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=7\,\mathrm{TeV}$. The first uncertainty is statistical and the second is systematic.

The frame-invariant polarization parameter $\tilde{\lambda}$ measured in the Gottfried-Jackson frame for the $\Upsilon(3S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=7\,\mathrm{TeV}$. The first uncertainty is statistical and the second represents the systematic uncertainty.

The polarization parameter $\lambda_{\theta}$ measured in the Gottfried-Jackson frame for the $\Upsilon(3S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=8\,\mathrm{TeV}$. The first uncertainty is statistical and the second is systematic.

The polarization parameter $\lambda_{\theta\phi}$ measured in the Gottfried-Jackson frame for the $\Upsilon(3S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=8\,\mathrm{TeV}$. The first uncertainty is statistical and the second represents the systematic uncertainty.

The polarization parameter $\lambda_{\phi}$ measured in the Gottfried-Jackson frame for the $\Upsilon(3S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=8\,\mathrm{TeV}$. The first uncertainty is statistical and the second is systematic.

The frame-invariant polarization parameter $\tilde{\lambda}$ measured in the Gottfried-Jackson frame for the $\Upsilon(3S)$ state in different bins of $p_{T}^{\Upsilon}$ and three rapidity ranges using data collected at $\sqrt{s}=8\,\mathrm{TeV}$. The first uncertainty is statistical and the second represents the systematic uncertainty.

Values of the polarization parameter $\lambda_\theta$ measured in the helicity(SH), Collins-Soper(CS) and Gottfried-Jackson(TH) frames for the $\Upsilon(3S)$ produced at $\sqrt{s}=7$ TeV in the rapidity range $2.2 < y^\Upsilon < 4.5$ and different bins of $p_{T}^{\Upsilon}$. The first quoted uncertainty is statistical and the second is systematic.

Values of the polarization parameter $\lambda_{\theta\phi}$ measured in the helicity(SH), Collins-Soper(CS) and Gottfried-Jackson(TH) frames for the $\Upsilon(3S)$ produced at $\sqrt{s}=7$ TeV in the rapidity range $2.2 < y^\Upsilon < 4.5$ and different bins of $p_{T}^{\Upsilon}$. The first quoted uncertainty is statistical and the second is systematic.

Values of the polarization parameter $\lambda_{\phi}$ measured in the helicity(SH), Collins-Soper(CS) and Gottfried-Jackson(TH) frames for the $\Upsilon(3S)$ produced at $\sqrt{s}=7$ TeV in the rapidity range $2.2 < y^\Upsilon < 4.5$ and different bins of $p_{T}^{\Upsilon}$. The first quoted uncertainty is statistical and the second is systematic.

Values of the frame-invariant polarization parameter $\tilde{\lambda}$ measured in the helicity(SH), Collins-Soper(CS) and Gottfried-Jackson(TH) frames for the $\Upsilon(3S)$ produced at $\sqrt{s}=7$ TeV in the rapidity range $2.2 < y^\Upsilon < 4.5$ and different bins of $p_{T}^{\Upsilon}$. The first quoted uncertainty is statistical and the second is systematic.

Values of the polarization parameter $\lambda_{\theta}$ measured in the helicity(SH), Collins-Soper(CS) and Gottfried-Jackson(TH) frames for the $\Upsilon(3S)$ produced at $\sqrt{s}=8$ TeV in the rapidity range $2.2 < y^\Upsilon < 4.5$ and different bins of $p_{T}^{\Upsilon}$. The first quoted uncertainty is statistical and the second is systematic.

Values of the polarization parameter $\lambda_{\theta\phi}$ measured in the helicity(SH), Collins-Soper(CS) and Gottfried-Jackson(TH) frames for the $\Upsilon(3S)$ produced at $\sqrt{s}=8$ TeV in the rapidity range $2.2 < y^\Upsilon < 4.5$ and different bins of $p_{T}^{\Upsilon}$. The first quoted uncertainty is statistical and the second is systematic.

Values of the polarization parameter $\lambda_{\phi}$ measured in the helicity(SH), Collins-Soper(CS) and Gottfried-Jackson(TH) frames for the $\Upsilon(3S)$ produced at $\sqrt{s}=8$ TeV in the rapidity range $2.2 < y^\Upsilon < 4.5$ and different bins of $p_{T}^{\Upsilon}$. The first quoted uncertainty is statistical and the second is systematic.

Values of the frame-invariant polarization parameter $\tilde{\lambda}$ measured in the helicity(SH), Collins-Soper(CS) and Gottfried-Jackson(TH) frames for the $\Upsilon(3S)$ produced at $\sqrt{s}=8$ TeV in the rapidity range $2.2 < y^\Upsilon < 4.5$ and different bins of $p_{T}^{\Upsilon}$. The first quoted uncertainty is statistical and the second is systematic.

Products of $\overline{B}^0$ production cross-sections and $\mathcal{B}(\overline{B}^0 \rightarrow J\psi \overline{K}^{*0})$ in bins of $p_\rm{T}$ and $y$ in the 2012 data sample.

Asymmetries $a_{\rm p+d}$ $(\%)$ of $\Lambda_b^0$ and $\overline{\Lambda}_b^0$ in bins of $p_\rm{T}$ for the 2011 and 2012 samples.

Asymmetries $a_{\rm p+d}$ $(\%)$ of $\Lambda_b^0$ and $\overline{\Lambda}_b^0$ in bins of $y$ for the 2011 and 2012 samples.