Summary of results for cross-section of non-prompt $\psi(2S)$ decaying to a muon pair for 13 TeV data in fb/GeV. Uncertainties are statistical and systematic, respectively.

Summary of results for non-prompt fraction of $J/\psi$ decaying to a muon pair as a percentage for 13 TeV data. Uncertainties are statistical and systematic, respectively.

Summary of results for non-prompt fraction of $\psi(2S)$ decaying to a muon pair as a percentage for 13 TeV data. Uncertainties are statistical and systematic, respectively.

Summary of results for prompt $\psi(2S)$ over $J/\psi$ ratio as a percentage for 13 TeV data. Uncertainties are statistical and systematic, respectively.

Summary of results for non-prompt $\psi(2S)$ over $J/\psi$ ratio as a percentage for 13 TeV data. Uncertainties are statistical and systematic, respectively.

Correction factors for an assumed angular dependence $\propto 1+\lambda_{\theta} \cos^2\theta $ in the helicity frame, for several values of the parameter $\lambda_{\theta}$. The correction factors were found to be the same (within 1% - 2%) for $J/\psi$ and $\psi(2S)$ mesons, for prompt and non-prompt production mechanisms, and for the three rapidity intervals considered in this paper.

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

Charged-hadron spectrum in the centrality interval 5-10% for p+Pb, divided by 〈TPPB〉. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Charged-hadron spectrum in the centrality interval 10-20% for p+Pb, divided by 〈TPPB〉. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Charged-hadron spectrum in the centrality interval 20-30% for p+Pb, divided by 〈TPPB〉. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Charged-hadron spectrum in the centrality interval 30-40% for p+Pb, divided by 〈TPPB〉. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Charged-hadron spectrum in the centrality interval 40-60% for p+Pb, divided by 〈TPPB〉. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Charged-hadron spectrum in the centrality interval 60-90% for p+Pb, divided by 〈TPPB〉. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Charged-hadron spectrum in the centrality interval 0-90% for p+Pb, divided by 〈TPPB〉. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Charged-hadron cross-section in pp collisions. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Charged-hadron spectrum in the centrality interval 0-5% for Pb+Pb, divided by 〈TAA〉. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature. The systematic uncertainty on momentum bias is negligible at low pT; in such cases, it is omitted in the table below.

Charged-hadron spectrum in the centrality interval 5-10% for Pb+Pb, divided by 〈TAA〉. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature. The systematic uncertainty on momentum bias is negligible at low pT; in such cases, it is omitted in the table below.

Charged-hadron spectrum in the centrality interval 10-20% for Pb+Pb, divided by 〈TAA〉. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature. The systematic uncertainty on momentum bias is negligible at low pT; in such cases, it is omitted in the table below.

Charged-hadron spectrum in the centrality interval 20-30% for Pb+Pb, divided by 〈TAA〉. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature. The systematic uncertainty on momentum bias is negligible at low pT; in such cases, it is omitted in the table below.

Charged-hadron spectrum in the centrality interval 30-40% for Pb+Pb, divided by 〈TAA〉. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature. The systematic uncertainty on momentum bias is negligible at low pT; in such cases, it is omitted in the table below.

Charged-hadron spectrum in the centrality interval 40-50% for Pb+Pb, divided by 〈TAA〉. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature. The systematic uncertainty on momentum bias is negligible at low pT; in such cases, it is omitted in the table below.

Charged-hadron spectrum in the centrality interval 50-60% for Pb+Pb, divided by 〈TAA〉. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature. The systematic uncertainty on momentum bias is negligible at low pT; in such cases, it is omitted in the table below.

Charged-hadron spectrum in the centrality interval 60-80% for Pb+Pb, divided by 〈TAA〉. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature. The systematic uncertainty on momentum bias is negligible at low pT; in such cases, it is omitted in the table below.

Charged-hadron cross-section in pp collisions. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Charged-hadron spectrum in the centrality interval 0-5% for Xe+Xe, divided by 〈TAA〉. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Charged-hadron spectrum in the centrality interval 5-10% for Xe+Xe, divided by 〈TAA〉. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Charged-hadron spectrum in the centrality interval 10-20% for Xe+Xe, divided by 〈TAA〉. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Charged-hadron spectrum in the centrality interval 20-30% for Xe+Xe, divided by 〈TAA〉. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Charged-hadron spectrum in the centrality interval 30-40% for Xe+Xe, divided by 〈TAA〉. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Charged-hadron spectrum in the centrality interval 40-50% for Xe+Xe, divided by 〈TAA〉. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Charged-hadron spectrum in the centrality interval 50-60% for Xe+Xe, divided by 〈TAA〉. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Charged-hadron spectrum in the centrality interval 60-80% for Xe+Xe, divided by 〈TAA〉. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 0-5% for p+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 5-10% for p+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 10-20% for p+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 20-30% for p+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 30-40% for p+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 40-60% for p+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 60-90% for p+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 0-90% for p+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 0-5% for Pb+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature. The systematic uncertainty on momentum bias is negligible at low pT; in such cases, it is omitted in the table below.

Nuclear modification factor in centrality interval 5-10% for Pb+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature. The systematic uncertainty on momentum bias is negligible at low pT; in such cases, it is omitted in the table below.

Nuclear modification factor in centrality interval 10-20% for Pb+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature. The systematic uncertainty on momentum bias is negligible at low pT; in such cases, it is omitted in the table below.

Nuclear modification factor in centrality interval 20-30% for Pb+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature. The systematic uncertainty on momentum bias is negligible at low pT; in such cases, it is omitted in the table below.

Nuclear modification factor in centrality interval 30-40% for Pb+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature. The systematic uncertainty on momentum bias is negligible at low pT; in such cases, it is omitted in the table below.

Nuclear modification factor in centrality interval 40-50% for Pb+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature. The systematic uncertainty on momentum bias is negligible at low pT; in such cases, it is omitted in the table below.

Nuclear modification factor in centrality interval 50-60% for Pb+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature. The systematic uncertainty on momentum bias is negligible at low pT; in such cases, it is omitted in the table below.

Nuclear modification factor in centrality interval 60-80% for Pb+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature. The systematic uncertainty on momentum bias is negligible at low pT; in such cases, it is omitted in the table below.

Nuclear modification factor in centrality interval 0-5% for Xe+Xe. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 5-10% for Xe+Xe. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 10-20% for Xe+Xe. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 20-30% for Xe+Xe. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 30-40% for Xe+Xe. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 40-50% for Xe+Xe. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 50-60% for Xe+Xe. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 60-80% for Xe+Xe. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 0-5% for p+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 0-5% for p+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 0-5% for p+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 0-5% for p+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 5-10% for p+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 5-10% for p+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 5-10% for p+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 5-10% for p+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 10-20% for p+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 10-20% for p+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 10-20% for p+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 10-20% for p+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 20-30% for p+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 20-30% for p+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 20-30% for p+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 20-30% for p+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 30-40% for p+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 30-40% for p+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 30-40% for p+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 30-40% for p+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 40-60% for p+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 40-60% for p+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 40-60% for p+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 40-60% for p+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 60-90% for p+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 60-90% for p+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 60-90% for p+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 60-90% for p+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 0-90% for p+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 0-90% for p+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 0-90% for p+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 0-90% for p+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 0-5% for Pb+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 0-5% for Pb+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 0-5% for Pb+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 0-5% for Pb+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 5-10% for Pb+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 5-10% for Pb+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 5-10% for Pb+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 5-10% for Pb+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 10-20% for Pb+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 10-20% for Pb+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 10-20% for Pb+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 10-20% for Pb+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 20-30% for Pb+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 20-30% for Pb+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 20-30% for Pb+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 20-30% for Pb+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 30-40% for Pb+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 30-40% for Pb+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 30-40% for Pb+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 30-40% for Pb+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 40-50% for Pb+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 40-50% for Pb+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 40-50% for Pb+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 40-50% for Pb+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 50-60% for Pb+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 50-60% for Pb+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 50-60% for Pb+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 50-60% for Pb+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 60-80% for Pb+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 60-80% for Pb+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 60-80% for Pb+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 60-80% for Pb+Pb. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 0-5% for Xe+Xe. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 0-5% for Xe+Xe. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 0-5% for Xe+Xe. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 5-10% for Xe+Xe. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 5-10% for Xe+Xe. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 5-10% for Xe+Xe. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 10-20% for Xe+Xe. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 10-20% for Xe+Xe. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 10-20% for Xe+Xe. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 20-30% for Xe+Xe. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 20-30% for Xe+Xe. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 20-30% for Xe+Xe. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 30-40% for Xe+Xe. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 30-40% for Xe+Xe. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 30-40% for Xe+Xe. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 40-50% for Xe+Xe. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 40-50% for Xe+Xe. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 40-50% for Xe+Xe. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 50-60% for Xe+Xe. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 50-60% for Xe+Xe. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 50-60% for Xe+Xe. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 60-80% for Xe+Xe. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 60-80% for Xe+Xe. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

Nuclear modification factor in centrality interval 60-80% for Xe+Xe. The systematic uncertainties are described in the section 7 of the paper. The total systematic uncertainties are determined by adding the contributions from all relevant sources in quadrature.

$K^-$ (a), invariant yields as a function of $m_T-m_0$ for various rapidity regions in 10--40\% central Au+Au collisions at ${\sqrt{s_{\mathrm{NN}}} = \mathrm{3\,GeV}}$. Statistics and systematic uncertainties are added quadratic here for plotting. Solid and dashed black lines depict $m_T$ exponential function fits to the measured data points with arbitrate scaling factors in each rapidity windows.

$\phi$ meson (b) invariant yields as a function of $m_T-m_0$ for various rapidity regions in 10--40\% central Au+Au collisions at ${\sqrt{s_{\mathrm{NN}}} = \mathrm{3\,GeV}}$. Statistics and systematic uncertainties are added quadratic here for plotting. Solid and dashed black lines depict $m_T$ exponential function fits to the measured data points with arbitrate scaling factors in each rapidity windows.

$\Xi^-$ (c) invariant yields as a function of $m_T-m_0$ for various rapidity regions in 10--40\% central Au+Au collisions at ${\sqrt{s_{\mathrm{NN}}} = \mathrm{3\,GeV}}$. Statistics and systematic uncertainties are added quadratic here for plotting. Solid and dashed black lines depict $m_T$ exponential function fits to the measured data points with arbitrate scaling factors in each rapidity windows.

$K^-$ (a), invariant yields as a function of $m_T-m_0$ for various rapidity regions in 40--60\% central Au+Au collisions at ${\sqrt{s_{\mathrm{NN}}} = \mathrm{3\,GeV}}$. Statistics and systematic uncertainties are added quadratic here for plotting. Solid and dashed black lines depict $m_T$ exponential function fits to the measured data points with arbitrate scaling factors in each rapidity windows.

$\phi$ meson (b) invariant yields as a function of $m_T-m_0$ for various rapidity regions in 40--60\% central Au+Au collisions at ${\sqrt{s_{\mathrm{NN}}} = \mathrm{3\,GeV}}$. Statistics and systematic uncertainties are added quadratic here for plotting. Solid and dashed black lines depict $m_T$ exponential function fits to the measured data points with arbitrate scaling factors in each rapidity windows.

Rapidity density distributions of $K^-$ (squares), $p_T$-integrated yields $dN/dy$ in 0--10\% (a), 10--40\% (b) and 40--60\% central (c) Au+Au collisions at ${\sqrt{s_{\mathrm{NN}}} = \mathrm{3\,GeV}}$. %The full symbols show the measured data, while the open ones are data reflected with respect to $y=0$ in the center-of-mass frame. Solid lines depict Gaussian function fits to the data points.

Rapidity density distributions of $\phi$ meson (circles) $p_T$-integrated yields $dN/dy$ in 0--10\% (a), 10--40\% (b) and 40--60\% central (c) Au+Au collisions at ${\sqrt{s_{\mathrm{NN}}} = \mathrm{3\,GeV}}$. %The full symbols show the measured data, while the open ones are data reflected with respect to $y=0$ in the center-of-mass frame. Solid lines depict Gaussian function fits to the data points.

Rapidity density distributions of $\Xi^-$ (diamonds) $p_T$-integrated yields $dN/dy$ in 0--10\% (a), 10--40\% (b) and 40--60\% central (c) Au+Au collisions at ${\sqrt{s_{\mathrm{NN}}} = \mathrm{3\,GeV}}$. %The full symbols show the measured data, while the open ones are data reflected with respect to $y=0$ in the center-of-mass frame. Solid lines depict Gaussian function fits to the data points.

$\phi/K^-$ (a) and $\phi/\Xi^-$ (b) ratio as a function of collision energy, $\sqrt{s_{\mathrm{NN}}}$. The solid black circles show the measurements presented here in 0-10\% centrality bin, while empty markers in black or grey are used for data from various other energies and/or collision systems. The grey solid line represents a THERMUS calculation based on the Grand Canonical Ensemble (GCE) while the dotted lines depict calculations based on the Canonical Ensemble (CE) with different parameters of strangeness correlation radius ($r_c$). The green dashed line, green shaded band and the solid red line show transport model calculations from the public versions $\mathrm{UrQMD}^{1}$, modified $\mathrm{UrQMD}^{2}$ and SMASH, respectively.

$\Upsilon(1S)$ 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).

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.

Normalized distribution of the variable $\Delta^{p_{\mathrm{T}}}_{13}$, defined in Eq (16) of the paper, in data after unfolding to particle level.

Normalized distribution of the variable $\Delta^{p_{\mathrm{T}}}_{23}$, defined in Eq (16) of the paper, in data after unfolding to particle level.

Normalized distribution of the variable $\Delta^{p_{\mathrm{T}}}_{14}$, defined in Eq (16) of the paper, in data after unfolding to particle level.

Normalized distribution of the variable $\Delta^{p_{\mathrm{T}}}_{24}$, defined in Eq (16) of the paper, in data after unfolding to particle level.

Normalized distribution of the variable $\Delta\phi_{12}$, defined in Eq (16) of the paper, in data after unfolding to particle level.

Normalized distribution of the variable $\Delta\phi_{13}$, defined in Eq (16) of the paper, in data after unfolding to particle level.

Normalized distribution of the variable $\Delta\phi_{23}$, defined in Eq (16) of the paper, in data after unfolding to particle level.

Normalized distribution of the variable $\Delta\phi_{14}$, defined in Eq (16) of the paper, in data after unfolding to particle level.

Normalized distribution of the variable $\Delta\phi_{24}$, defined in Eq (16) of the paper, in data after unfolding to particle level.

Normalized distribution of the variable $\Delta y_{12}$, defined in Eq (16) of the paper, in data after unfolding to particle level.

Normalized distribution of the variable $\Delta y_{34}$, defined in Eq (16) of the paper, in data after unfolding to particle level.

Normalized distribution of the variable $\Delta y_{13}$, defined in Eq (16) of the paper, in data after unfolding to particle level.

Normalized distribution of the variable $\Delta y_{23}$, defined in Eq (16) of the paper, in data after unfolding to particle level.

Normalized distribution of the variable $\Delta y_{14}$, defined in Eq (16) of the paper, in data after unfolding to particle level.

Normalized distribution of the variable $\Delta y_{24}$, defined in Eq (16) of the paper, in data after unfolding to particle level.

Normalized distribution of the variable $\phi_{1+2} - \phi_{3+4}$, defined in Eq (16) of the paper, in data after unfolding to particle level.

Normalized distribution of the variable $\phi_{1+3} - \phi_{2+4}$, defined in Eq (16) of the paper, in data after unfolding to particle level.

Normalized distribution of the variable $\phi_{1+4} - \phi_{2+3}$, defined in Eq (16) of the paper, in data after unfolding to particle level.