Differential cross sections as function of transverse momentum imbalance between Z boson and dijet for Z+ ≥ 2 jets events.

Differential cross sections as function of transverse momentum imbalance between leading and subleading jet for Z+ ≥ 2 jets events.

Area normalized distribution as function of Delta Phi between Z boson and the leading jet for Z+ ≥ 1 jet events.

Area normalized distribution as function of transverse momentum imbalance between Z boson and the leading jet for Z+ ≥ 1 jet events.

Area normalized distribution as function of Delta Phi between Z boson and dijet for Z+ ≥ 2 jets events.

Area normalized distribution as function of transverse momentum imbalance between Z boson and dijet for Z+ ≥ 2 jets events.

Area normalized distribution as function of transverse momentum imbalance between leading and subleading jet for Z+ ≥ 2 jets events

Response matrix for Delta Phi between Z boson and the leading jet for Z+ ≥ 1 jet events.

Response matrix for transverse momentum imbalance between Z boson and the leading jet for Z+ ≥ 1 jet events.

Response matrix for Delta Phi between Z boson and dijet for Z+ ≥ 2 jets events.

Response matrix for transverse momentum imbalance between Z boson and dijet for Z+ ≥ 2 jets events.

Response matrix for transverse momentum imbalance between the leading jet and subleading jet for Z+ ≥ 2 jets events.

Correlation matrix for Delta Phi between Z boson and the leading jet for Z+ ≥ 1 jet events (for absolute differential cross section measurements).

Correlation matrix for transverse momentum imbalance between Z boson and the leading jet for Z+ ≥ 1 jet events (for absolute differential cross section measurements).

Correlation matrix for Delta Phi between Z boson and dijet for Z+ ≥ 2 jets events (for absolute differential cross section measurements).

Correlation matrix for transverse momentum imbalance between Z boson and dijet for Z+ ≥ 2 jets events (for absolute differential cross section measurements).

Correlation matrix for transverse momentum imbalance between the leading jet and subleading jet for Z+ ≥ 2 jets events (for absolute differential cross section measurements).

Correlation matrix for Delta Phi between Z boson and the leading jet for Z+ ≥ 1 jet events (for normalized differential cross section measurements).

Correlation matrix for transverse momentum imbalance between Z boson and the leading jet for Z+ ≥ 1 jet events (for normalized differential cross section measurements).

Correlation matrix for Delta Phi between Z boson and dijet for Z+ ≥ 2 jets events (for normalized differential cross section measurements).

Correlation matrix for transverse momentum imbalance between Z boson and dijet for Z+ ≥ 2 jets events (for normalized differential cross section measurements).

Correlation matrix for transverse momentum imbalance between the leading jet and subleading jet for Z+ ≥ 2 jets events (for normalized differential cross section measurements).

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].

Mean $p_T$ values of the $\Upsilon(1$S$)$, $\Upsilon(2$S$)$, and $\Upsilon(3$S$)$ states with $p_T\,>\,0\,GeV$ and $|y|\,<\,1.2$ as a function of track multiplicity $N_{track}$

Ratio $\Upsilon(2$S$)\,/\,\Upsilon(1$S$)$ with $|y|\,<\,1.2$ as a function of track multiplicity $N_{track}$ in $0<p_T<5\,$GeV range

Ratio $\Upsilon(2$S$)\,/\,\Upsilon(1$S$)$ with $|y|\,<\,1.2$ as a function of track multiplicity $N_{track}$ in $5<p_T<7\,$GeV range

Ratio $\Upsilon(2$S$)\,/\,\Upsilon(1$S$)$ with $|y|\,<\,1.2$ as a function of track multiplicity $N_{track}$ in $7<p_T<9\,$GeV range

Ratio $\Upsilon(2$S$)\,/\,\Upsilon(1$S$)$ with $|y|\,<\,1.2$ as a function of track multiplicity $N_{track}$ in $9<p_T<11\,$GeV range

Ratio $\Upsilon(2$S$)\,/\,\Upsilon(1$S$)$ with $|y|\,<\,1.2$ as a function of track multiplicity $N_{track}$ in $11<p_T<15\,$GeV range

Ratio $\Upsilon(2$S$)\,/\,\Upsilon(1$S$)$ with $|y|\,<\,1.2$ as a function of track multiplicity $N_{track}$ in $15<p_T<20\,$GeV range

Ratio $\Upsilon(2$S$)\,/\,\Upsilon(1$S$)$ with $|y|\,<\,1.2$ as a function of track multiplicity $N_{track}$ in $20<p_T<50\,$GeV range

Ratio $\Upsilon(3$S$)\,/\,\Upsilon(1$S$)$ with $|y|\,<\,1.2$ as a function of track multiplicity $N_{track}$ in $0<p_T<5\,$GeV range

Ratio $\Upsilon(3$S$)\,/\,\Upsilon(1$S$)$ with $|y|\,<\,1.2$ as a function of track multiplicity $N_{track}$ in $5<p_T<7\,$GeV range

Ratio $\Upsilon(3$S$)\,/\,\Upsilon(1$S$)$ with $|y|\,<\,1.2$ as a function of track multiplicity $N_{track}$ in $7<p_T<9\,$GeV range

Ratio $\Upsilon(3$S$)\,/\,\Upsilon(1$S$)$ with $|y|\,<\,1.2$ as a function of track multiplicity $N_{track}$ in $9<p_T<11\,$GeV range

Ratio $\Upsilon(3$S$)\,/\,\Upsilon(1$S$)$ with $|y|\,<\,1.2$ as a function of track multiplicity $N_{track}$ in $11<p_T<15\,$GeV range

Ratio $\Upsilon(3$S$)\,/\,\Upsilon(1$S$)$ with $|y|\,<\,1.2$ as a function of track multiplicity $N_{track}$ in $15<p_T<20\,$GeV range

Ratio $\Upsilon(3$S$)\,/\,\Upsilon(1$S$)$ with $|y|\,<\,1.2$ as a function of track multiplicity $N_{track}$ in $20<p_T<50\,$GeV range

Ratios $\Upsilon(2$S$)\,/\,\Upsilon(1$S$)$ and $\Upsilon(3$S$)\,/\,\Upsilon(1$S$)$ as functions of "forward" track multiplicity $N_{track}^{\Delta\phi}$ for $\Upsilon(n$S$)$ states with $p_T\,>\,7\,GeV$ and $|y|\,<\,1.2$. Forward tracks are those with momentum direction in $\Delta\phi\,<\,\pi/3$ w.r.t. the $\Upsilon(n$S$)$ momentum direction.

Ratios $\Upsilon(2$S$)\,/\,\Upsilon(1$S$)$ and $\Upsilon(3$S$)\,/\,\Upsilon(1$S$)$ as functions of "transverse" track multiplicity $N_{track}^{\Delta\phi}$ for $\Upsilon(n$S$)$ states with $p_T\,>\,7\,GeV$ and $|y|\,<\,1.2$. Transverse tracks are those with momentum direction in $\pi/3\,<\,\Delta\phi\,<\,2\pi/3$ w.r.t. the $\Upsilon(n$S$)$ momentum direction.

Ratios $\Upsilon(2$S$)\,/\,\Upsilon(1$S$)$ and $\Upsilon(3$S$)\,/\,\Upsilon(1$S$)$ as functions of "backward" track multiplicity $N_{track}^{\Delta\phi}$ for $\Upsilon(n$S$)$ states with $p_T\,>\,7\,GeV$ and $|y|\,<\,1.2$. Backward tracks are those with momentum direction in $\Delta\phi\,>\,2\pi/3$ w.r.t. the $\Upsilon(n$S$)$ momentum direction.

Ratios $\Upsilon(2$S$)\,/\,\Upsilon(1$S$)$ and $\Upsilon(3$S$)\,/\,\Upsilon(1$S$)$ as functions of track multiplicity $N_{track}$ for $\Upsilon(n$S$)$ states with $p_T\,>\,7\,GeV$ and $|y|\,<\,1.2$ and $N^{\Delta R}_{track}\,=\,0$ charged particles produced in $\Delta R\,<\,0.5$ cone around $\Upsilon(n$S$)$ momentum direction.

Ratios $\Upsilon(2$S$)\,/\,\Upsilon(1$S$)$ and $\Upsilon(3$S$)\,/\,\Upsilon(1$S$)$ as functions of track multiplicity $N_{track}$ for $\Upsilon(n$S$)$ states with $p_T\,>\,7\,GeV$ and $|y|\,<\,1.2$ and $N^{\Delta R}_{track}\,=\,1$ charged particles produced in $\Delta R\,<\,0.5$ cone around $\Upsilon(n$S$)$ momentum direction.

Ratios $\Upsilon(2$S$)\,/\,\Upsilon(1$S$)$ and $\Upsilon(3$S$)\,/\,\Upsilon(1$S$)$ as functions of track multiplicity $N_{track}$ for $\Upsilon(n$S$)$ states with $p_T\,>\,7\,GeV$ and $|y|\,<\,1.2$ and $N^{\Delta R}_{track}\,=\,2$ charged particles produced in $\Delta R\,<\,0.5$ cone around $\Upsilon(n$S$)$ momentum direction.

Ratios $\Upsilon(2$S$)\,/\,\Upsilon(1$S$)$ and $\Upsilon(3$S$)\,/\,\Upsilon(1$S$)$ as functions of track multiplicity $N_{track}$ for $\Upsilon(n$S$)$ states with $p_T\,>\,7\,GeV$ and $|y|\,<\,1.2$ and $N^{\Delta R}_{track}\,>\,2$ charged particles produced in $\Delta R\,<\,0.5$ cone around $\Upsilon(n$S$)$ momentum direction.

Ratios $\Upsilon(2$S$)\,/\,\Upsilon(1$S$)$ and $\Upsilon(3$S$)\,/\,\Upsilon(1$S$)$ as functions of track multiplicity $N_{track}$ in transverse sphericity bin $0.00\,<\,S_T\,<\,0.55$ for $\Upsilon(n$S$)$ states with $p_T\,>\,7\,GeV$ and $|y|\,<\,1.2$.

Ratios $\Upsilon(2$S$)\,/\,\Upsilon(1$S$)$ and $\Upsilon(3$S$)\,/\,\Upsilon(1$S$)$ as functions of track multiplicity $N_{track}$ in transverse sphericity bin $0.55\,<\,S_T\,<\,0.70$ for $\Upsilon(n$S$)$ states with $p_T\,>\,7\,GeV$ and $|y|\,<\,1.2$.

Ratios $\Upsilon(2$S$)\,/\,\Upsilon(1$S$)$ and $\Upsilon(3$S$)\,/\,\Upsilon(1$S$)$ as functions of track multiplicity $N_{track}$ in transverse sphericity bin $0.70\,<\,S_T\,<\,0.85$ for $\Upsilon(n$S$)$ states with $p_T\,>\,7\,GeV$ and $|y|\,<\,1.2$.

Ratios $\Upsilon(2$S$)\,/\,\Upsilon(1$S$)$ and $\Upsilon(3$S$)\,/\,\Upsilon(1$S$)$ as functions of track multiplicity $N_{track}$ in transverse sphericity bin $0.85\,<\,S_T\,<\,1.00$ for $\Upsilon(n$S$)$ states with $p_T\,>\,7\,GeV$ and $|y|\,<\,1.2$.

Efficiency-corrected multiplicity bins used in the $\Upsilon(n$S$)$ ratio analysis and the corresponding mean number of charged particle tracks.

Ratio of differential cross section of AK1 jets with respect to AK4 jets a function of jet PT in the rapidity range 1.5<|y|<2.0. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of differential cross section of AK2 jets with respect to AK4 jets a function of jet PT in the rapidity range |y|<0.5. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of differential cross section of AK2 jets with respect to AK4 jets a function of jet PT in the rapidity range 0.5<|y|<1.0. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of differential cross section of AK2 jets with respect to AK4 jets a function of jet PT in the rapidity range 1.0<|y|<1.5. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of differential cross section of AK2 jets with respect to AK4 jets a function of jet PT in the rapidity range 1.5<|y|<2.0. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of differential cross section of AK3 jets with respect to AK4 jets a function of jet PT in the rapidity range |y|<0.5. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of differential cross section of AK3 jets with respect to AK4 jets a function of jet PT in the rapidity range 0.5<|y|<1.0. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of differential cross section of AK3 jets with respect to AK4 jets a function of jet PT in the rapidity range 1.0<|y|<1.5. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of differential cross section of AK3 jets with respect to AK4 jets a function of jet PT in the rapidity range 1.5<|y|<2.0. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of differential cross section of AK4 jets with respect to AK4 jets a function of jet PT in the rapidity range |y|<0.5. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of differential cross section of AK4 jets with respect to AK4 jets a function of jet PT in the rapidity range 0.5<|y|<1.0. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of differential cross section of AK4 jets with respect to AK4 jets a function of jet PT in the rapidity range 1.0<|y|<1.5. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of differential cross section of AK4 jets with respect to AK4 jets a function of jet PT in the rapidity range 1.5<|y|<2.0. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of differential cross section of AK5 jets with respect to AK4 jets a function of jet PT in the rapidity range |y|<0.5. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of differential cross section of AK5 jets with respect to AK4 jets a function of jet PT in the rapidity range 0.5<|y|<1.0. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of differential cross section of AK5 jets with respect to AK4 jets a function of jet PT in the rapidity range 1.0<|y|<1.5. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of differential cross section of AK5 jets with respect to AK4 jets a function of jet PT in the rapidity range 1.5<|y|<2.0. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of differential cross section of AK6 jets with respect to AK4 jets a function of jet PT in the rapidity range |y|<0.5. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of differential cross section of AK6 jets with respect to AK4 jets a function of jet PT in the rapidity range 0.5<|y|<1.0. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of differential cross section of AK6 jets with respect to AK4 jets a function of jet PT in the rapidity range 1.0<|y|<1.5. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of differential cross section of AK6 jets with respect to AK4 jets a function of jet PT in the rapidity range 1.5<|y|<2.0. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of differential cross section of AK7 jets with respect to AK4 jets a function of jet PT in the rapidity range |y|<0.5. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of differential cross section of AK7 jets with respect to AK4 jets a function of jet PT in the rapidity range 0.5<|y|<1.0. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of differential cross section of AK7 jets with respect to AK4 jets a function of jet PT in the rapidity range 1.0<|y|<1.5. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of differential cross section of AK7 jets with respect to AK4 jets a function of jet PT in the rapidity range 1.5<|y|<2.0. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of differential cross section of AK8 jets with respect to AK4 jets a function of jet PT in the rapidity range |y|<0.5. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of differential cross section of AK8 jets with respect to AK4 jets a function of jet PT in the rapidity range 0.5<|y|<1.0. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of differential cross section of AK8 jets with respect to AK4 jets a function of jet PT in the rapidity range 1.0<|y|<1.5. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of differential cross section of AK8 jets with respect to AK4 jets a function of jet PT in the rapidity range 1.5<|y|<2.0. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of differential cross section of AK9 jets with respect to AK4 jets a function of jet PT in the rapidity range |y|<0.5. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of differential cross section of AK9 jets with respect to AK4 jets a function of jet PT in the rapidity range 0.5<|y|<1.0. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of differential cross section of AK9 jets with respect to AK4 jets a function of jet PT in the rapidity range 1.0<|y|<1.5. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of differential cross section of AK9 jets with respect to AK4 jets a function of jet PT in the rapidity range 1.5<|y|<2.0. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of differential cross section of AK10 jets with respect to AK4 jets a function of jet PT in the rapidity range |y|<0.5. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of differential cross section of AK10 jets with respect to AK4 jets a function of jet PT in the rapidity range 0.5<|y|<1.0. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of differential cross section of AK10 jets with respect to AK4 jets a function of jet PT in the rapidity range 1.0<|y|<1.5. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of differential cross section of AK10 jets with respect to AK4 jets a function of jet PT in the rapidity range 1.5<|y|<2.0. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of differential cross section of AK11 jets with respect to AK4 jets a function of jet PT in the rapidity range |y|<0.5. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of differential cross section of AK11 jets with respect to AK4 jets a function of jet PT in the rapidity range 0.5<|y|<1.0. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of differential cross section of AK11 jets with respect to AK4 jets a function of jet PT in the rapidity range 1.0<|y|<1.5. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of differential cross section of AK11 jets with respect to AK4 jets a function of jet PT in the rapidity range 1.5<|y|<2.0. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of differential cross section of AK12 jets with respect to AK4 jets a function of jet PT in the rapidity range |y|<0.5. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of differential cross section of AK12 jets with respect to AK4 jets a function of jet PT in the rapidity range 0.5<|y|<1.0. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of differential cross section of AK12 jets with respect to AK4 jets a function of jet PT in the rapidity range 1.0<|y|<1.5. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of differential cross section of AK12 jets with respect to AK4 jets a function of jet PT in the rapidity range 1.5<|y|<2.0. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of cross section of inclusive anti-KT jets with respect to AK4 jets as a function of jet size in the rapidity range |y|<0.5 and PT 84 < p_{T} < 97 GeV. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of cross section of inclusive anti-KT jets with respect to AK4 jets as a function of jet size in the rapidity range |y|<0.5 and PT 97 < p_{T} < 133 GeV. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of cross section of inclusive anti-KT jets with respect to AK4 jets as a function of jet size in the rapidity range |y|<0.5 and PT 133 < p_{T} < 196 GeV. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of cross section of inclusive anti-KT jets with respect to AK4 jets as a function of jet size in the rapidity range |y|<0.5 and PT 196 < p_{T} < 272 GeV. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of cross section of inclusive anti-KT jets with respect to AK4 jets as a function of jet size in the rapidity range |y|<0.5 and PT 272 < p_{T} < 330 GeV. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of cross section of inclusive anti-KT jets with respect to AK4 jets as a function of jet size in the rapidity range |y|<0.5 and PT 330 < p_{T} < 395 GeV. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of cross section of inclusive anti-KT jets with respect to AK4 jets as a function of jet size in the rapidity range |y|<0.5 and PT 395 < p_{T} < 468 GeV. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of cross section of inclusive anti-KT jets with respect to AK4 jets as a function of jet size in the rapidity range |y|<0.5 and PT 468 < p_{T} < 548 GeV. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of cross section of inclusive anti-KT jets with respect to AK4 jets as a function of jet size in the rapidity range |y|<0.5 and PT 548 < p_{T} < 638 GeV. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of cross section of inclusive anti-KT jets with respect to AK4 jets as a function of jet size in the rapidity range |y|<0.5 and PT 638 < p_{T} < 1588 GeV. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of cross section of inclusive anti-KT jets with respect to AK4 jets as a function of jet size in the rapidity range 0.5<|y|<1.0 and PT 84 < p_{T} < 97 GeV. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of cross section of inclusive anti-KT jets with respect to AK4 jets as a function of jet size in the rapidity range 0.5<|y|<1.0 and PT 97 < p_{T} < 133 GeV. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of cross section of inclusive anti-KT jets with respect to AK4 jets as a function of jet size in the rapidity range 0.5<|y|<1.0 and PT 133 < p_{T} < 196 GeV. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of cross section of inclusive anti-KT jets with respect to AK4 jets as a function of jet size in the rapidity range 0.5<|y|<1.0 and PT 196 < p_{T} < 272 GeV. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of cross section of inclusive anti-KT jets with respect to AK4 jets as a function of jet size in the rapidity range 0.5<|y|<1.0 and PT 272 < p_{T} < 330 GeV. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of cross section of inclusive anti-KT jets with respect to AK4 jets as a function of jet size in the rapidity range 0.5<|y|<1.0 and PT 330 < p_{T} < 395 GeV. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of cross section of inclusive anti-KT jets with respect to AK4 jets as a function of jet size in the rapidity range 0.5<|y|<1.0 and PT 395 < p_{T} < 468 GeV. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of cross section of inclusive anti-KT jets with respect to AK4 jets as a function of jet size in the rapidity range 0.5<|y|<1.0 and PT 468 < p_{T} < 548 GeV. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of cross section of inclusive anti-KT jets with respect to AK4 jets as a function of jet size in the rapidity range 0.5<|y|<1.0 and PT 548 < p_{T} < 638 GeV. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of cross section of inclusive anti-KT jets with respect to AK4 jets as a function of jet size in the rapidity range 0.5<|y|<1.0 and PT 638 < p_{T} < 1588 GeV. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of cross section of inclusive anti-KT jets with respect to AK4 jets as a function of jet size in the rapidity range 1.0<|y|<1.5 and PT 84 < p_{T} < 97 GeV. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of cross section of inclusive anti-KT jets with respect to AK4 jets as a function of jet size in the rapidity range 1.0<|y|<1.5 and PT 97 < p_{T} < 133 GeV. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of cross section of inclusive anti-KT jets with respect to AK4 jets as a function of jet size in the rapidity range 1.0<|y|<1.5 and PT 133 < p_{T} < 196 GeV. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of cross section of inclusive anti-KT jets with respect to AK4 jets as a function of jet size in the rapidity range 1.0<|y|<1.5 and PT 196 < p_{T} < 272 GeV. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of cross section of inclusive anti-KT jets with respect to AK4 jets as a function of jet size in the rapidity range 1.0<|y|<1.5 and PT 272 < p_{T} < 330 GeV. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of cross section of inclusive anti-KT jets with respect to AK4 jets as a function of jet size in the rapidity range 1.0<|y|<1.5 and PT 330 < p_{T} < 395 GeV. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of cross section of inclusive anti-KT jets with respect to AK4 jets as a function of jet size in the rapidity range 1.0<|y|<1.5 and PT 395 < p_{T} < 468 GeV. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of cross section of inclusive anti-KT jets with respect to AK4 jets as a function of jet size in the rapidity range 1.0<|y|<1.5 and PT 468 < p_{T} < 548 GeV. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of cross section of inclusive anti-KT jets with respect to AK4 jets as a function of jet size in the rapidity range 1.0<|y|<1.5 and PT 548 < p_{T} < 638 GeV. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of cross section of inclusive anti-KT jets with respect to AK4 jets as a function of jet size in the rapidity range 1.0<|y|<1.5 and PT 638 < p_{T} < 1588 GeV. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of cross section of inclusive anti-KT jets with respect to AK4 jets as a function of jet size in the rapidity range 1.5<|y|<2.0 and PT 84 < p_{T} < 97 GeV. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of cross section of inclusive anti-KT jets with respect to AK4 jets as a function of jet size in the rapidity range 1.5<|y|<2.0 and PT 97 < p_{T} < 133 GeV. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of cross section of inclusive anti-KT jets with respect to AK4 jets as a function of jet size in the rapidity range 1.5<|y|<2.0 and PT 133 < p_{T} < 196 GeV. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of cross section of inclusive anti-KT jets with respect to AK4 jets as a function of jet size in the rapidity range 1.5<|y|<2.0 and PT 196 < p_{T} < 272 GeV. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of cross section of inclusive anti-KT jets with respect to AK4 jets as a function of jet size in the rapidity range 1.5<|y|<2.0 and PT 272 < p_{T} < 330 GeV. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of cross section of inclusive anti-KT jets with respect to AK4 jets as a function of jet size in the rapidity range 1.5<|y|<2.0 and PT 330 < p_{T} < 395 GeV. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of cross section of inclusive anti-KT jets with respect to AK4 jets as a function of jet size in the rapidity range 1.5<|y|<2.0 and PT 395 < p_{T} < 468 GeV. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of cross section of inclusive anti-KT jets with respect to AK4 jets as a function of jet size in the rapidity range 1.5<|y|<2.0 and PT 468 < p_{T} < 548 GeV. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of cross section of inclusive anti-KT jets with respect to AK4 jets as a function of jet size in the rapidity range 1.5<|y|<2.0 and PT 548 < p_{T} < 638 GeV. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Ratio of cross section of inclusive anti-KT jets with respect to AK4 jets as a function of jet size in the rapidity range 1.5<|y|<2.0 and PT 638 < p_{T} < 1588 GeV. The nonperturbative correction can be used to scale fixed-order theory prediction to compare to data at particle level.

Differential production cross-sections of $\eta_c$ for production in $b$-hadron inclusive decays. The uncertainties are statistical, systematic, and due to the $\eta_c\to p \bar{p}$ and $J/\psi\to p \bar{p}$ branching fractions and $J/\psi$ production cross-section.

$p_{\rm T}$-differential yields of $\Lambda$(1520) (sum of particle and anti-particle states) in p--Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ $\mathrm{=}$ 5.02 TeV in multiplicity interval 20--40\%. The uncertainty 'sys,$p_{\rm T}$-correlated' indicates the systematic uncertainty after removing the contributions of $p_{\rm T}$-uncorrelated uncertainty.

$p_{\rm T}$-differential yields of $\Lambda$(1520) (sum of particle and anti-particle states) in p--Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ $\mathrm{=}$ 5.02 TeV in multiplicity interval 40--60\%. The uncertainty 'sys,$p_{\rm T}$-correlated' indicates the systematic uncertainty after removing the contributions of $p_{\rm T}$-uncorrelated uncertainty.

$p_{\rm T}$-differential yields of $\Lambda$(1520) (sum of particle and anti-particle states) in p--Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ $\mathrm{=}$ 5.02 TeV in multiplicity interval 60--100\%. The uncertainty 'sys,$p_{\rm T}$-correlated' indicates the systematic uncertainty after removing the contributions of $p_{\rm T}$-uncorrelated uncertainty.

Ratio of $p_{\rm T}$-integrated yields of $\Lambda$(1520) (sum of particle and anti-particle states) to charged $\pi$ ($\pi^{+} + \pi^{-}$) at midrapidity as a function of $\langle {\rm d}N_{\rm ch}/{\rm d} \eta_{\rm lab} \rangle$ in inelastic pp collisions at $\sqrt{s}$ $\mathrm{=}$ 7 TeV.

Ratio of $p_{\rm T}$-integrated yields of $\Lambda$(1520) (sum of particle and anti-particle states) to charged $\pi$ ($\pi^{+} + \pi^{-}$) as a function of $\langle {\rm d}N_{\rm ch}/{\rm d} \eta_{\rm lab} \rangle$ in p--Pb collisions at $\sqrt{s}$ $\mathrm{=}$ 5.02 TeV. The uncertainty 'sys,uncorrelated' indicates the multiplicity uncorrelated systematic uncertainty.

Ratio of $p_{\rm T}$-integrated yields of $\Lambda$(1520) (sum of particle and anti-particle states) to K$^{-}$ at midrapidity as a function of $\langle {\rm d}N_{\rm ch}/{\rm d} \eta_{\rm lab} \rangle$ in inelastic pp collisions at $\sqrt{s}$ $\mathrm{=}$ 7 TeV.

Ratio of $p_{\rm T}$-integrated yields of $\Lambda$(1520) (sum of particle and anti-particle states) to K$^{-}$ as a function of $\langle {\rm d}N_{\rm ch}/{\rm d} \eta_{\rm lab} \rangle$ in p--Pb collisions at $\sqrt{s}$ $\mathrm{=}$ 5.02 TeV. The uncertainty 'sys,uncorrelated' indicates the multiplicity uncorrelated systematic uncertainty.

Ratio of $p_{\rm T}$-integrated yields of $\Lambda$(1520) (sum of particle and anti-particle states) to its ground state particle $\Lambda$ ($\Lambda + \bar{\Lambda}$) at midrapidity as a function of $\langle {\rm d}N_{\rm ch}/{\rm d} \eta_{\rm lab} \rangle$ in inelastic pp collisions at $\sqrt{s}$ $\mathrm{=}$ 7 TeV.

Ratio of $p_{\rm T}$-integrated yields of $\Lambda$(1520) (sum of particle and anti-particle states) to its ground state particle $\Lambda$ ($\Lambda + \bar{\Lambda}$) as a function of $\langle {\rm d}N_{\rm ch}/{\rm d} \eta_{\rm lab} \rangle$ in p--Pb collisions at $\sqrt{s}$ $\mathrm{=}$ 5.02 TeV. The uncertainty 'sys,uncorrelated' indicates the multiplicity uncorrelated systematic uncertainty.

$\Upsilon(1S)$ 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: $i_{\rm bin} = 4 \times i_y + i_{p_T}$.

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.