Correlation matrix of all the parameters including nuisance parameters used in the profile likelihood unfolding fit on $A_{C}$.

Left panel.The vertical bars (boxes) represent the statistical (bin-to-bin systematic) uncertainties, while the horizontal bars give the bin widths. The global uncertainty (of 5.7%) is not graphically represented. The blue line represents the average of all the points. $ 12 < \mathrm{B} \, p_T < 70$ GeV and $ 0 < |y| < 2.4 $. Global uncertanties are not included in the table (5.7%)

Right panel.The vertical bars (boxes) represent the statistical (bin-to-bin systematic) uncertainties, while the horizontal bars give the bin widths. The global uncertainty (of 5.7%) is not graphically represented. The blue line represents the average of all the points. $ 12 < \mathrm{B} \, p_T < 70$ GeV and $ 0 < |y| < 2.4 $. Global uncertanties are not included in the table (5.7%)

Differential fiducial cross section (without the acceptance correction) for the DY process measured in the muon channel, as a function of $p_{\textrm{T}}$ for $15<m_{\mu\mu}<60$ GeV. The quoted error is the quadratic sum of the statistical and systematic uncertainties. The global normalisation uncertainty of 3.5% is listed separately.

Differential fiducial cross section (without the acceptance correction) for the DY process measured in the muon channel, as a function of $p_{\textrm{T}}$ for $60<m_{\mu\mu}<120$ GeV. The quoted error is the quadratic sum of the statistical and systematic uncertainties. The global normalisation uncertainty of 3.5% is listed separately.

Differential fiducial cross section (without the acceptance correction) for the DY process measured in the muon channel, as a function of $\phi^*$ for $15<m_{\mu\mu}<60$ GeV. The quoted error is the quadratic sum of the statistical and systematic uncertainties. The global normalisation uncertainty of 3.5% is listed separately.

Differential fiducial cross section (without the acceptance correction) for the DY process measured in the muon channel, as a function of $\phi^*$ for $60<m_{\mu\mu}<120$ GeV. The quoted error is the quadratic sum of the statistical and systematic uncertainties. The global normalisation uncertainty of 3.5% is listed separately.

Integrated fiducial cross section for the DY process measured in the muon channel. The quoted error is the quadratic sum of the statistical and systematic uncertainties. The global normalisation uncertainty of 3.5% is listed separately.

Differential cross section for the DY process measured in the muon channel, as a function of dimuon invariant mass. The quoted error is the quadratic sum of the statistical and systematic uncertainties. The global normalisation uncertainty of 3.5% is listed separately.

Differential cross section for the DY process measured in the muon channel, as a function of rapidity in the centre-of-mass frame for $15<m_{\mu\mu}<60$ GeV. The quoted error is the quadratic sum of the statistical and systematic uncertainties. The global normalisation uncertainty of 3.5% is listed separately.

Differential cross section for the DY process measured in the muon channel, as a function of rapidity in the centre-of-mass frame for $60<m_{\mu\mu}<120$ GeV. The quoted error is the quadratic sum of the statistical and systematic uncertainties. The global normalisation uncertainty of 3.5% is listed separately.

Differential cross section for the DY process measured in the muon channel, as a function of $p_{\textrm{T}}$ for $15<m_{\mu\mu}<60$ GeV. The quoted error is the quadratic sum of the statistical and systematic uncertainties. The global normalisation uncertainty of 3.5% is listed separately.

Differential cross section for the DY process measured in the muon channel, as a function of $p_{\textrm{T}}$ for $60<m_{\mu\mu}<120$ GeV. The quoted error is the quadratic sum of the statistical and systematic uncertainties. The global normalisation uncertainty of 3.5% is listed separately.

Differential cross section for the DY process measured in the muon channel, as a function of $\phi^*$ for $15<m_{\mu\mu}<60$ GeV. The quoted error is the quadratic sum of the statistical and systematic uncertainties. The global normalisation uncertainty of 3.5% is listed separately.

Differential cross section for the DY process measured in the muon channel, as a function of $\phi^*$ for $60<m_{\mu\mu}<120$ GeV. The quoted error is the quadratic sum of the statistical and systematic uncertainties. The global normalisation uncertainty of 3.5% is listed separately.

Integrated cross section for the DY process measured in the muon channel. The quoted error is the quadratic sum of the statistical and systematic uncertainties. The global normalisation uncertainty of 3.5% is listed separately.

Forward-backward ratios for $15<m_{\mu\mu}<60$ GeV. Quoted uncertainties are the quadratic sum of the statistical and systematic uncertainties.

Forward-backward ratios for $60<m_{\mu\mu}<120$ GeV. Quoted uncertainties are the quadratic sum of the statistical and systematic uncertainties.

Correlation matrix for the systematic uncertainties, excluding integrated luminosity, as a function of dimuon invariant mass.

Correlation matrix for the systematic uncertainties, excluding integrated luminosity, as a function of rapidity in the centre-of-mass frame for $15<m_{\mu\mu}<60$ GeV.

Correlation matrix for the systematic uncertainties, excluding integrated luminosity, as a function of rapidity in the centre-of-mass frame for $60<m_{\mu\mu}<120$ GeV.

Correlation matrix for the systematic uncertainties, excluding integrated luminosity, as a function of $p_{\textrm{T}}$ for $15<m_{\mu\mu}<60$ GeV.

Correlation matrix for the systematic uncertainties, excluding integrated luminosity, as a function of $p_{\textrm{T}}$ for $60<m_{\mu\mu}<120$ GeV.

Correlation matrix for the systematic uncertainties, excluding integrated luminosity, as a function of $\phi^*$ for $15<m_{\mu\mu}<60$ GeV.

Correlation matrix for the systematic uncertainties, excluding integrated luminosity, as a function of $\phi^*$ for $60<m_{\mu\mu}<120$ GeV.

Correlation matrix for the systematic uncertainties, excluding integrated luminosity, as a function of rapidity in the centre-of-mass frame, putting together low and high masses. Each bin is labeled lm_i or hm_i, where lm stands for $15<m_{\mu\mu}<60$ GeV, hm stands for $60<m_{\mu\mu}<120$ GeV, and i is the corresponding bin number in rapidity in the centre-of-mass frame. The global normalisation uncertainty of 3.5% is not included. Data from Figure [3, 4, 4].

Correlation matrix for the systematic uncertainties, excluding integrated luminosity, as a function of $p_{\textrm{T}}$, putting together low and high masses. Each bin is labeled lm_i or hm_i, where lm stands for $15<m_{\mu\mu}<60$ GeV, hm stands for $60<m_{\mu\mu}<120$ GeV, and i is the corresponding bin number in $p_{\textrm{T}}$. The global normalisation uncertainty of 3.5% is not included. Data from Figure [3, 4, 4].

Correlation matrix for the systematic uncertainties, excluding integrated luminosity, as a function of $\phi^*$, putting together low and high masses. Each bin is labeled lm_i or hm_i, where lm stands for $15<m_{\mu\mu}<60$ GeV, hm stands for $60<m_{\mu\mu}<120$ GeV, and i is the corresponding bin number in $\phi^*$. The global normalisation uncertainty of 3.5% is not included. Data from Figure [3, 4, 4].

$\Upsilon(1S)$ production cross-section in $p$Pb and Pb$p$, as a function of $y^*$. The uncertainty is the sum in quadrature of the statistical and systematic components.

$\Upsilon(2S)$ production cross-section in $p$Pb and Pb$p$, as a function of $p_{T}$. The uncertainty is the sum in quadrature of the statistical and systematic components.

$\Upsilon(2S)$ production cross-section in $p$Pb and Pb$p$, as a function of $y^*$. The uncertainty is the sum in quadrature of the statistical and systematic components.

Scaled $pp$ differential cross-section in $p_{T}$ at $\sqrt{s_{NN}}=8.16$ TeV. The first uncertainty is statistical, the second is systematic, which includes the systematic uncertainty from the $pp$ measurement and that estimated by changing the interpolation function.

Scaled $pp$ differential cross-section in $y$ at $\sqrt{s_{NN}}=8.16$ TeV. The first uncertainty is statistical, the second is systematic, which includes the systematic uncertainty from the $pp$ measurement and that estimated by changing the interpolation function.

$\Upsilon(1S)$ nuclear modification factor, $R_{p{\rm Pb}}^{\Upsilon(1S)}$, in $p$Pb and Pb$p$ as a function of $p_{T}$ integrated over $y^*$ in the range $1.5 < y^* < 4.0$ for $p$Pb and $-5.0 < y^* < -2.5$ for Pb$p$. The quoted uncertainties are the sum in quadrature of the statistical and systematic components.

$\Upsilon(1S)$ nuclear modification factor, $R_{p{\rm Pb}}^{\Upsilon(1S)}$, in $p$Pb and Pb$p$ as a function of $y^*$ integrated over $p_{T}$ in the range $0 < p_{T} < 25$ GeV$/c$. The quoted uncertainties are the sum in quadrature of the statistical and systematic components.

$\Upsilon(2S)$ nuclear modification factor, $R_{p{\rm Pb}}^{\Upsilon(2S)}$, in $p$Pb and Pb$p$ as a function of $p_{T}$ integrated over $y^*$ in the range $1.5 < y^* < 4.0$ for $p$Pb and $-5.0 < y^* < -2.5$ for Pb$p$. The quoted uncertainties are the sum in quadrature of the statistical and systematic components.

$\Upsilon(2S)$ nuclear modification factor, $R_{p{\rm Pb}}^{\Upsilon(2S)}$, in $p$Pb and Pb$p$ as a function of $y^*$ integrated over $p_{T}$ in the range $0 < p_{T} < 25$ GeV$/c$. The quoted uncertainties are the sum in quadrature of the statistical and systematic components.

$\Upsilon(1S)$ forward-to-backward ratio, $R_{{\rm FB}}^{\Upsilon(1S)}$, as a function of $p_{T}$ integrated over $\vert y^* \vert$ in the range $2.5 < \vert y^* \vert < 4.0$. The quoted uncertainties are the sum in quadrature of the statistical and systematic components.

$\Upsilon(1S)$ forward-to-backward ratio, $R_{{\rm FB}}^{\Upsilon(1S)}$, as a function of $\vert y^* \vert$ integrated over $p_{T}$ in the range $0 < p_{T} < 25$ GeV/c. The quoted uncertainties are the sum in quadrature of the statistical and systematic components.

$\Upsilon(2S)$ to $\Upsilon(1S)$ ratio, in $p$Pb and Pb$p$ as a function of $p_{T}$ integrated over $y^*$ in the range $1.5 < y^* < 4.0$ for $p$Pb and $-5.0 < y^* < -2.5$ for Pb$p$. The quoted uncertainties are the sum in quadrature of the statistical and systematic components.

$\Upsilon(2S)$ to $\Upsilon(1S)$ ratio, in $p$Pb and Pb$p$ as a function of $y^*$ integrated over $p_{T}$ in the range $0 < p_{T} < 25$ GeV/c. The quoted uncertainties are the sum in quadrature of the statistical and systematic components.

$\Upsilon(1S)$ to non-prompt $J/\psi$, in $p$Pb and Pb$p$ as a function of $y^*$ integrated over $p_{T}$ in the range $0 < p_{T} < 25$ GeV/c. The quoted uncertainties are the sum in quadrature of the statistical and systematic components.

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: $i_{\rm bin} = 4 \times i_y + i_{p_T}$.

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Differential cross-sections multiplied by dimuon branching fractions for $\Upsilon$(1S), $\Upsilon$(2S) and $\Upsilon$(3S) states versus $p_T$ integrated over $y$ between 2.0 and 4.5.

Differential cross-sections multiplied by dimuon branching fractions for $\Upsilon$(1S), $\Upsilon$(2S) and $\Upsilon$(3S) states versus $y$ integrated over $p_T$ from 0 to 15 GeV/c.

Ratios of double-differential cross-sections times dimuon branching fractions for $\Upsilon$(2S) to $\Upsilon$(1S).

Ratios of double-differential cross-sections times dimuon branching fractions for $\Upsilon$(3S) to $\Upsilon$(1S).

Ratios of differential cross-sections times dimuon branching fractions versus $p_T$ over $y$ for $\Upsilon$(2S) to $\Upsilon$(1S) and $\Upsilon$(3S) to $\Upsilon$(1S).

Ratios of differential cross-sections times dimuon branching fractions versus $y$ over $p_T$ for $\Upsilon$(2S) to $\Upsilon$(1S) and $\Upsilon$(3S) to $\Upsilon$(1S).

The cross-section ratios between 13 TeV and 8 TeV in different bins of $p_T$ and $y$ for $\Upsilon$(1S).

The cross-section ratios between 13 TeV and 8 TeV in different bins of $p_T$ and $y$ for $\Upsilon$(2S).

The cross-section ratios between 13 TeV and 8 TeV in different bins of $p_T$ and $y$ for $\Upsilon$(3S).

Ratios of differential cross-sections between 13 TeV and 8 TeV measurements versus $p_T$ over $y$ for $\Upsilon$(1S), $\Upsilon$(2S) and $\Upsilon$(3S).

Ratios of differential cross-sections between 13 TeV and 8 TeV measurements versus $y$ over $p_T$ for $\Upsilon$(1S), $\Upsilon$(2S) and $\Upsilon$(3S).

Double-differential cross section times the dimuon branching fraction of the Y(2S) meson for different ranges of pT in bins of |y| and for the full |y| < 1.2 range, for the unpolarized decay hypothesis. The global uncertainty in the integrated luminosity of 2.3% is not included in the systematic uncertainties.

Double-differential cross section times the dimuon branching fraction of the Y(3S) meson for different ranges of pT in bins of |y| and for the full |y| < 1.2 range, for the unpolarized decay hypothesis. The global uncertainty in the integrated luminosity of 2.3% is not included in the systematic uncertainties.

Multiplicative scaling factors to obtain the J/psi differential cross sections for different polarization scenarios (Lambda_{Theta} = +1, +0.10, -1) from the unpolarized cross section measurements given in Table 1.

Multiplicative scaling factors to obtain the psi(2S) differential cross sections for different polarization scenarios (Lambda_{Theta} = +1, +0.03, -1) from the unpolarized cross section measurements given in Table 2.

Multiplicative scaling factors to obtain the Y(1S) differential cross sections for different polarization scenarios (Lambda_{Theta} = +1, k, -1) from the unpolarized cross section measurements given in Table 3. The parameter k corresponds to a linear interpolation of the CMS measured value as a function of pT for pT < 50 GeV. For pT > 50 GeV, where no measurements exist, k is taken as the average of all the measured values for pT < 50 GeV.

Multiplicative scaling factors to obtain the Y(2S) differential cross sections for different polarization scenarios (Lambda_{Theta} = +1, k, -1) from the unpolarized cross section measurements given in Table 3. The parameter k corresponds to a linear interpolation of the CMS measured value as a function of pT for pT < 50 GeV. For pT > 50 GeV, where no measurements exist, k is taken as the average of all the measured values for pT < 50 GeV.

Multiplicative scaling factors to obtain the Y(3S) differential cross sections for different polarization scenarios (Lambda_{Theta} = +1, k, -1) from the unpolarized cross section measurements given in Table 3. The parameter k corresponds to a linear interpolation of the CMS measured value as a function of pT for pT < 50 GeV. For pT > 50 GeV, where no measurements exist, k is taken as the average of all the measured values for pT < 50 GeV.

Ratio of differential cross section times branching fractions of the prompt psi(2S) to J/psi mesons assuming unpolarized productions as a function of pT for |y| < 1.2.

Ratios of differential cross section times branching fractions of the prompt Y(2S) to Y(1S) and Y(3S) to Y(1S) mesons assuming unpolarized productions as a function of pT for |y| < 1.2.

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.

The differential cross section measurement as a function of the transverse momentum of the second leading jet.

The differential cross section measurement as a function of the transverse momentum of the third leading jet.

The differential cross section measurement as a function of the transverse momentum of the fourth leading jet.

The differential cross section measurement as a function of the scalar sum of the transverse momenta of jets (HT) for events with one or more jets.

The differential cross section measurement as a function of the scalar sum of the transverse momenta of jets (HT) for events with two or more jets.

The differential cross section measurement as a function of the scalar sum of the transverse momenta of jets (HT) for events with three or more jets.

The differential cross section measurement as a function of the scalar sum of the transverse momenta of jets (HT) for events with four or more jets.

The differential cross section measurement as a function of the transverse momentum of the dijet system of the two highest pT jets for events with two or more jets.

The differential cross section measurement as a function of the transverse momentum of the dijet system of the two highest pT jets for events with three or more jets.

The differential cross section measurement as a function of the transverse momentum of the dijet system of the two highest pT jets for events with four or more jets.

The differential cross section measurement as a function of the dijet invariant mass of the two highest pT jets for events with two or more jets.

The differential cross section measurement as a function of the dijet invariant mass of the two highest pT jets for events with three or more jets.

The differential cross section measurement as a function of the dijet invariant mass of the two highest pT jets for events with four or more jets.

The differential cross section measurement as a function of the absolute value of the pseudorapidity of the first leading jet.

The differential cross section measurement as a function of the absolute value of the pseudorapidity of the second leading jet.

The differential cross section measurement as a function of the absolute value of the pseudorapidity of the third leading jet.

The differential cross section measurement as a function of the absolute value of the pseudorapidity of the fourth leading jet.

The differential cross section measurement as a function of the rapidity difference between the two highest pT jets for events with two or more jets.

The differential cross section measurement as a function of the rapidity difference between the two highest pT jets for events with three or more jets.

The differential cross section measurement as a function of the rapidity difference between the two highest pT jets for events with four or more jets.

The differential cross section measurement as a function of the rapidity difference between the first and the third highest pT jets for events with three or more jets.

The differential cross section measurement as a function of the rapidity difference between the second and the third highest pT jets for events with three or more jets.

The differential cross section measurement as a function of the rapidity difference between the most forward and the most backward jets for events with two or more jets.

The differential cross section measurement as a function of the rapidity difference between the most forward and the most backward jets for events with three or more jets.

The differential cross section measurement as a function of the rapidity difference between the most forward and the most backward jets for events with four or more jets.

The differential cross section measurement as a function of the azimuthal angle separation between the two highest pT jets for events with two or more jets.

The differential cross section measurement as a function of the azimuthal angle separation between the most forward and the most backward jets for events with two or more jets.

The differential cross section measurement as a function of DeltaR separation between the two highest pT jets for events with two or more jets.

The differential cross section measurement as a function of the azimuthal angle separation between the first leading jet and the muon.

The differential cross section measurement as a function of the azimuthal angle separation between the second leading jet and the muon.

The differential cross section measurement as a function of the azimuthal angle separation between the third leading jet and the muon.

The differential cross section measurement as a function of the azimuthal angle separation between the fourth leading jet and the muon.

Average number of jets as a function of HT for events with one or more jets.

Average number of jets as a function of HT for events with two or more jets.

Average number of jets as a function of the rapidity difference between the two highest pT jets for events with two or more jets.

Average number of jets as a function of the rapidity difference between the most forward and the most backward jets for events with two or more jets.