# Measurement of the $\Upsilon$ polarizations in $pp$ collisions at $\sqrt{s}$=7 and 8TeV

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## Abstract

The polarization of the $\Upsilon(1S)$, $\Upsilon(2S)$ and $\Upsilon(3S)$mesons, produced in $pp$ collisions at centre-of-mass energies $\sqrt{s}$=7 and 8TeV, is measured using data samples collected by the LHCb experiment, corresponding to integrated luminosities of 1 and 2fb$^{-1}$, respectively. The measurements are performed in three polarization frames, using $\Upsilon\to\mu^+\mu^-$ decays in the kinematic region of the transverse momentum $p_{T}(\Upsilon)<30GeV/c$, and rapidity $2.2<y(\Upsilon)<4.5$. No large polarization is observed.

## Figures and captions

 (a) Distributions of $\cos\theta_{\mathrm{GJ}}$ for $\Upsilon(1\mathrm{S})$ (red circles), $\Upsilon(2\mathrm{S})$ (blue squares) and $\Upsilon(3\mathrm{S})$ (green diamonds) signal candidates and the background component (histogram) in the region $6< p^{\Upsilon}_{\mathrm{T}} <8 {\mathrm{ Ge V /}c}$, $2.2< y^{\Upsilon} <3.0$ for data accumulated at $\sqrt{s}=7 \mathrm{TeV}$. To improve visibility, the distributions for the $\Upsilon(1\mathrm{S})$ and $\Upsilon(2\mathrm{S})$ signals are scaled by factors of 3 and 2, respectively. (b) Dimuon mass distribution in the region $6< p^{\Upsilon}_{\mathrm{T}} <8 {\mathrm{ Ge V /}c}$, $2.2< y^{\Upsilon} <3.0$ for data accumulated at $\sqrt{s}=7 \mathrm{TeV}$. The thick dark yellow solid curve shows the result of the fit, as described in the text. The three peaks, shown with thin red solid lines, correspond to the $\Upsilon(1\mathrm{S})$ , $\Upsilon(2\mathrm{S})$ and $\Upsilon(3\mathrm{S})$ signals (left to right). The background component is indicated with a dashed blue line. Fig_1.pdf [170 KiB] HiDef png [233 KiB] Thumbnail [199 KiB] *.C file tex code Background-subtracted distributions of (a) $\cos\theta$ and (b) $\phi$ for the $\Upsilon(1\mathrm{S})$ signal candidates in the HX frame, measured in the kinematic region $6< p^{\Upsilon}_{\mathrm{T}} <8 {\mathrm{ Ge V /}c}$ and $2.2< y^{\Upsilon} <3.0$, for data accumulated at $\sqrt{s}=7 \mathrm{TeV}$. Fig_2.pdf [112 KiB] HiDef png [124 KiB] Thumbnail [142 KiB] *.C file tex code The polarization parameters (top) $\uplambda_{\theta}$, (middle) $\uplambda_{\theta\phi}$ and (bottom) $\uplambda_{\phi}$, measured in the HX frame for the $\Upsilon(1\mathrm{S})$ state in different bins of $p^{\Upsilon}_{\mathrm{T}}$ and three rapidity ranges, for data collected at (left) $\sqrt{s} =7 \mathrm{TeV}$ and (right) $\sqrt{s} =8 \mathrm{TeV}$. The results for the rapidity ranges $2.2< y^{\Upsilon} <3.0$, $3.0< y^{\Upsilon} <3.5$ and $3.5< y^{\Upsilon} <4.5$ are shown with red circles, blue squares and green diamonds, respectively. The vertical inner error bars indicate the statistical uncertainty, whilst the outer error bars indicate the sum of the statistical and systematic uncertainties added in quadrature. The horizontal error bars indicate the bin width. Some data points are displaced from the bin centers to improve visibility. Fig_3.pdf [125 KiB] HiDef png [472 KiB] Thumbnail [434 KiB] *.C file tex code The polarization parameters (top) $\uplambda_{\theta}$, (middle) $\uplambda_{\theta\phi}$ and (bottom) $\uplambda_{\phi}$, measured in the CS frame for the $\Upsilon(1\mathrm{S})$ state in different bins of $p^{\Upsilon}_{\mathrm{T}}$ and three rapidity ranges, for data collected at (left) $\sqrt{s} =7 \mathrm{TeV}$ and (right) $\sqrt{s} =8 \mathrm{TeV}$. The results for the rapidity ranges $2.2< y^{\Upsilon} <3.0$, $3.0< y^{\Upsilon} <3.5$ and $3.5< y^{\Upsilon} <4.5$ are shown with red circles, blue squares and green diamonds, respectively. The vertical inner error bars indicate the statistical uncertainty, whilst the outer error bars indicate the sum of the statistical and systematic uncertainties added in quadrature. The horizontal error bars indicate the bin width. Some data points are displaced from the bin centers to improve visibility. Fig_4.pdf [124 KiB] HiDef png [443 KiB] Thumbnail [418 KiB] *.C file tex code The polarization parameters (top) $\uplambda_{\theta}$, (middle) $\uplambda_{\theta\phi}$ and (bottom) $\uplambda_{\phi}$, measured in the GJ frame for the $\Upsilon(1\mathrm{S})$ state in different bins of $p^{\Upsilon}_{\mathrm{T}}$ and three rapidity ranges, for data collected at (left) $\sqrt{s} =7 \mathrm{TeV}$ and (right) $\sqrt{s} =8 \mathrm{TeV}$. The results for the rapidity ranges $2.2< y^{\Upsilon} <3.0$, $3.0< y^{\Upsilon} <3.5$ and $3.5< y^{\Upsilon} <4.5$ are shown with red circles, blue squares and green diamonds, respectively. The vertical inner error bars indicate the statistical uncertainty, whilst the outer error bars indicate the sum of the statistical and systematic uncertainties added in quadrature. The horizontal error bars indicate the bin width. Some data points are displaced from the bin centers to improve visibility. Fig_5.pdf [125 KiB] HiDef png [459 KiB] Thumbnail [429 KiB] *.C file tex code The polarization parameters (top) $\uplambda_{\theta}$, (middle) $\uplambda_{\theta\phi}$ and (bottom) $\uplambda_{\phi}$, measured in the HX frame for the $\Upsilon(2\mathrm{S})$ state in different bins of $p^{\Upsilon}_{\mathrm{T}}$ and three rapidity ranges, for data collected at (left) $\sqrt{s} =7 \mathrm{TeV}$ and (right) $\sqrt{s} =8 \mathrm{TeV}$. The results for the rapidity ranges $2.2< y^{\Upsilon} <3.0$, $3.0< y^{\Upsilon} <3.5$ and $3.5< y^{\Upsilon} <4.5$ are shown with red circles, blue squares and green diamonds, respectively. The vertical inner error bars indicate the statistical uncertainty, whilst the outer error bars indicate the sum of the statistical and systematic uncertainties added in quadrature. The horizontal error bars indicate the bin width. Some data points are displaced from the bin centers to improve visibility. Fig_6.pdf [124 KiB] HiDef png [466 KiB] Thumbnail [416 KiB] *.C file tex code The polarization parameters (top) $\uplambda_{\theta}$, (middle) $\uplambda_{\theta\phi}$ and (bottom) $\uplambda_{\phi}$, measured in the CS frame for the $\Upsilon(2\mathrm{S})$ state in different bins of $p^{\Upsilon}_{\mathrm{T}}$ and three rapidity ranges, for data collected at (left) $\sqrt{s} =7 \mathrm{TeV}$ and (right) $\sqrt{s} =8 \mathrm{TeV}$. The results for the rapidity ranges $2.2< y^{\Upsilon} <3.0$, $3.0< y^{\Upsilon} <3.5$ and $3.5< y^{\Upsilon} <4.5$ are shown with red circles, blue squares and green diamonds, respectively. The vertical inner error bars indicate the statistical uncertainty, whilst the outer error bars indicate the sum of the statistical and systematic uncertainties added in quadrature. The horizontal error bars indicate the bin width. Some data points are displaced from the bin centers to improve visibility. Fig_7.pdf [123 KiB] HiDef png [440 KiB] Thumbnail [396 KiB] *.C file tex code The polarization parameters (top) $\uplambda_{\theta}$, (middle) $\uplambda_{\theta\phi}$ and (bottom) $\uplambda_{\phi}$, measured in the GJ frame for the $\Upsilon(2\mathrm{S})$ state in different bins of $p^{\Upsilon}_{\mathrm{T}}$ and three rapidity ranges, for data collected at (left) $\sqrt{s} =7 \mathrm{TeV}$ and (right) $\sqrt{s} =8 \mathrm{TeV}$. The results for the rapidity ranges $2.2< y^{\Upsilon} <3.0$, $3.0< y^{\Upsilon} <3.5$ and $3.5< y^{\Upsilon} <4.5$ are shown with red circles, blue squares and green diamonds, respectively. The vertical inner error bars indicate the statistical uncertainty, whilst the outer error bars indicate the sum of the statistical and systematic uncertainties added in quadrature. The horizontal error bars indicate the bin width. Some data points are displaced from the bin centers to improve visibility. Fig_8.pdf [124 KiB] HiDef png [453 KiB] Thumbnail [402 KiB] *.C file tex code The polarization parameters (top) $\uplambda_{\theta}$, (middle) $\uplambda_{\theta\phi}$ and (bottom) $\uplambda_{\phi}$, measured in the HX frame for the $\Upsilon(3\mathrm{S})$ state in different bins of $p^{\Upsilon}_{\mathrm{T}}$ and three rapidity ranges, for data collected at (left) $\sqrt{s} =7 \mathrm{TeV}$ and (right) $\sqrt{s} =8 \mathrm{TeV}$. The results for the rapidity ranges $2.2< y^{\Upsilon} <3.0$, $3.0< y^{\Upsilon} <3.5$ and $3.5< y^{\Upsilon} <4.5$ are shown with red circles, blue squares and green diamonds, respectively. The vertical inner error bars indicate the statistical uncertainty, whilst the outer error bars indicate the sum of the statistical and systematic uncertainties added in quadrature. The horizontal error bars indicate the bin width. Some data points are displaced from the bin centers to improve visibility. Fig_9.pdf [125 KiB] HiDef png [491 KiB] Thumbnail [442 KiB] *.C file tex code The polarization parameters $\uplambda_{\theta}$ (top), $\uplambda_{\theta\phi}$ (middle) and $\uplambda_{\phi}$ (bottom), measured in the CS frame for the $\Upsilon(3\mathrm{S})$ state in different bins of $p^{\Upsilon}_{\mathrm{T}}$ and three rapidity ranges, for data collected at $\sqrt{s} =7 \mathrm{TeV}$ (left) and $\sqrt{s} =8 \mathrm{TeV}$ (right). The results for the rapidity ranges $2.2< y^{\Upsilon} <3.0$, $3.0< y^{\Upsilon} <3.5$ and $3.5< y^{\Upsilon} <4.5$ are shown with red circles, blue squares and green diamonds, respectively. The vertical inner error bars indicate the statistical uncertainty, whilst the outer error bars indicate the sum of the statistical and systematic uncertainties added in quadrature. The horizontal error bars indicate the bin width. Some data points are displaced from the bin centers to improve visibility. Fig_10.pdf [124 KiB] HiDef png [456 KiB] Thumbnail [414 KiB] *.C file tex code The polarization parameters $\uplambda_{\theta}$ (top), $\uplambda_{\theta\phi}$ (middle) and $\uplambda_{\phi}$ (bottom), measured in the GJ frame for the $\Upsilon(3\mathrm{S})$ state in different bins of $p^{\Upsilon}_{\mathrm{T}}$ and three rapidity ranges, for data collected at $\sqrt{s} =7 \mathrm{TeV}$ (left) and $\sqrt{s} =8 \mathrm{TeV}$ (right). The results for the rapidity ranges $2.2< y^{\Upsilon} <3.0$, $3.0< y^{\Upsilon} <3.5$ and $3.5< y^{\Upsilon} <4.5$ are shown with red circles, blue squares and green diamonds, respectively. The vertical inner error bars indicate the statistical uncertainty, whilst the outer error bars indicate the sum of the statistical and systematic uncertainties added in quadrature. The horizontal error bars indicate the bin width. Some data points are displaced from the bin centers to improve visibility. Fig_11.pdf [125 KiB] HiDef png [478 KiB] Thumbnail [428 KiB] *.C file tex code The polarization parameters (top) $\uplambda_{\theta}$, (middle) $\uplambda_{\theta\phi}$ and (bottom) $\uplambda_{\phi}$, for $\Upsilon(1\mathrm{S})$ mesons as a function of $p^{\Upsilon}_{\mathrm{T}}$ , for the rapidity range $2.2< y^{\Upsilon} <4.5$, for data collected at (left) $\sqrt{s} =7 \mathrm{TeV}$ and (right) $\sqrt{s} =8 \mathrm{TeV}$. The results for the HX, CS and GJ frames are shown with red circles, blue squares and green diamonds, respectively. The inner error bars indicate the statistical uncertainty, whilst the outer error bars indicate the sum of the statistical and systematic uncertainties added in quadrature. Some data points are displaced from the bin centers to improve visibility. Fig_12.pdf [118 KiB] HiDef png [493 KiB] Thumbnail [440 KiB] *.C file tex code The polarization parameters (top) $\uplambda_{\theta}$, (middle) $\uplambda_{\theta\phi}$ and (bottom) $\uplambda_{\phi}$, for $\Upsilon(2\mathrm{S})$ mesons as a function of $p^{\Upsilon}_{\mathrm{T}}$ , for the rapidity range $2.2< y^{\Upsilon} <4.5$, for data collected at (left) $\sqrt{s} =7 \mathrm{TeV}$ and (right) $\sqrt{s} =8 \mathrm{TeV}$. The results for the HX, CS and GJ frames are shown with red circles, blue squares and green diamonds, respectively. The inner error bars indicate the statistical uncertainty, whilst the outer error bars indicate the sum of the statistical and systematic uncertainties added in quadrature. Some data points are displaced from the bin centers to improve visibility. Fig_13.pdf [116 KiB] HiDef png [451 KiB] Thumbnail [387 KiB] *.C file tex code The polarization parameters (top) $\uplambda_{\theta}$, (middle) $\uplambda_{\theta\phi}$ and (bottom) $\uplambda_{\phi}$, for $\Upsilon(3\mathrm{S})$ mesons as a function of $p^{\Upsilon}_{\mathrm{T}}$ , for the rapidity range $2.2< y^{\Upsilon} <4.5$, for data collected at (left) $\sqrt{s} =7 \mathrm{TeV}$ and (right) $\sqrt{s} =8 \mathrm{TeV}$. The results for the HX, CS and GJ frames are shown with red circles, blue squares and green diamonds, respectively. The inner error bars indicate the statistical uncertainty, whilst the outer error bars indicate the sum of the statistical and systematic uncertainties added in quadrature. Some data points are displaced from the bin centers to improve visibility. Fig_14.pdf [117 KiB] HiDef png [445 KiB] Thumbnail [383 KiB] *.C file tex code The polarization parameter $\tilde\uplambda$ for (top) $\Upsilon(1\mathrm{S})$ mesons, (middle) $\Upsilon(2\mathrm{S})$ mesons and (bottom) $\Upsilon(3\mathrm{S})$ mesons as a function of $p^{\Upsilon}_{\mathrm{T}}$ , for the rapidity range $2.2< y^{\Upsilon} <4.5$, for data collected at (left) $\sqrt{s} =7 \mathrm{TeV}$ and (right) $\sqrt{s} =8 \mathrm{TeV}$. The results for the HX, CS and GJ frames are shown with red circles, blue squares and green diamonds, respectively. The inner error bars indicate the statistical uncertainty, whilst the outer error bars indicate the sum of the statistical and systematic uncertainties added in quadrature. Some data points are displaced from the bin centers to improve visibility. Fig_15.pdf [111 KiB] HiDef png [424 KiB] Thumbnail [345 KiB] *.C file tex code Animated gif made out of all figures. PAPER-2017-028.gif Thumbnail

## Tables and captions

 Ranges of the absolute systematic uncertainties of the parameters $\pmb{\uplambda}$ and $\tilde{\uplambda}$. The ranges indicate variations depending on the $\left( p^{\Upsilon}_{\mathrm{T}} , y^{\Upsilon} \right)$ bin and frame. Table_1.pdf [86 KiB] HiDef png [182 KiB] Thumbnail [86 KiB] tex code Values of $\uplambda_{\theta}$, $\uplambda_{\theta\phi}$, $\uplambda_{\phi}$ and $\tilde \uplambda$ measured in the HX frame for the $\Upsilon(1\mathrm{S})$ produced at $\sqrt{s}=7 {\mathrm{TeV}}$. The first uncertainty is statistical and the second systematic. Table_2.pdf [44 KiB] HiDef png [346 KiB] Thumbnail [171 KiB] tex code Values of $\uplambda_{\theta}$, $\uplambda_{\theta\phi}$, $\uplambda_{\phi}$ and $\tilde \uplambda$ measured in the HX frame for the $\Upsilon(1\mathrm{S})$ produced at $\sqrt{s}=8 {\mathrm{TeV}}$. The first uncertainty is statistical and the second systematic. Table_3.pdf [43 KiB] HiDef png [343 KiB] Thumbnail [170 KiB] tex code Values of $\uplambda_{\theta}$, $\uplambda_{\theta\phi}$, $\uplambda_{\phi}$ and $\tilde \uplambda$ measured in the CS frame for the $\Upsilon(1\mathrm{S})$ produced at $\sqrt{s}=7 {\mathrm{TeV}}$. The first uncertainty is statistical and the second systematic. Table_4.pdf [44 KiB] HiDef png [347 KiB] Thumbnail [171 KiB] tex code Values of $\uplambda_{\theta}$, $\uplambda_{\theta\phi}$, $\uplambda_{\phi}$ and $\tilde \uplambda$ measured in the CS frame for the $\Upsilon(1\mathrm{S})$ produced at $\sqrt{s}=8 {\mathrm{TeV}}$. The first uncertainty is statistical and the second systematic. Table_5.pdf [43 KiB] HiDef png [345 KiB] Thumbnail [170 KiB] tex code Values of $\uplambda_{\theta}$, $\uplambda_{\theta\phi}$, $\uplambda_{\phi}$ and $\tilde \uplambda$ measured in the GJ frame for the $\Upsilon(1\mathrm{S})$ produced at $\sqrt{s}=7 {\mathrm{TeV}}$. The first uncertainty is statistical and the second systematic. Table_6.pdf [44 KiB] HiDef png [344 KiB] Thumbnail [170 KiB] tex code Values of $\uplambda_{\theta}$, $\uplambda_{\theta\phi}$, $\uplambda_{\phi}$ and $\tilde \uplambda$ measured in the GJ frame for the $\Upsilon(1\mathrm{S})$ produced at $\sqrt{s}=8 {\mathrm{TeV}}$. The first uncertainty is statistical and the second systematic. Table_7.pdf [44 KiB] HiDef png [343 KiB] Thumbnail [170 KiB] tex code Values of $\uplambda_{\theta}$, $\uplambda_{\theta\phi}$ and $\uplambda_{\phi}$ measured in the HX, CS and GJ frames for the $\Upsilon(1\mathrm{S})$ produced at $\sqrt{s}=7 {\mathrm{TeV}}$ in the rapidity range $2.2< y^{\Upsilon} <4.5$. The first uncertainty is statistical and the second systematic. Table_8.pdf [44 KiB] HiDef png [287 KiB] Thumbnail [145 KiB] tex code Values of $\uplambda_{\theta}$, $\uplambda_{\theta\phi}$ and $\uplambda_{\phi}$ measured in the HX, CS and GJ frames for the $\Upsilon(1\mathrm{S})$ produced at $\sqrt{s}=8 {\mathrm{TeV}}$ in the rapidity range $2.2< y^{\Upsilon} <4.5$. The first uncertainty is statistical and the second systematic. Table_9.pdf [44 KiB] HiDef png [287 KiB] Thumbnail [145 KiB] tex code Values of $\tilde \uplambda$ measured in the HX, CS and GJ frames for the $\Upsilon(1\mathrm{S})$ produced at $\sqrt{s}=7$ and $8 {\mathrm{TeV}}$ in the rapidity range $2.2< y^{\Upsilon} <4.5$. The first uncertainty is statistical and the second systematic. Table_10.pdf [37 KiB] HiDef png [247 KiB] Thumbnail [121 KiB] tex code Values of $\uplambda_{\theta}$, $\uplambda_{\theta\phi}$, $\uplambda_{\phi}$ and $\tilde \uplambda$ measured in the HX frame for the $\Upsilon(2\mathrm{S})$ produced at $\sqrt{s}=7 {\mathrm{TeV}}$. The first uncertainty is statistical and the second systematic. Table_11.pdf [44 KiB] HiDef png [341 KiB] Thumbnail [171 KiB] tex code Values of $\uplambda_{\theta}$, $\uplambda_{\theta\phi}$, $\uplambda_{\phi}$ and $\tilde \uplambda$ measured in the HX frame for the $\Upsilon(2\mathrm{S})$ produced at $\sqrt{s}=8 {\mathrm{TeV}}$. The first uncertainty is statistical and the second systematic. Table_12.pdf [44 KiB] HiDef png [345 KiB] Thumbnail [171 KiB] tex code Values of $\uplambda_{\theta}$, $\uplambda_{\theta\phi}$, $\uplambda_{\phi}$ and $\tilde \uplambda$ measured in the CS frame for the $\Upsilon(2\mathrm{S})$ produced at $\sqrt{s}=7 {\mathrm{TeV}}$. The first uncertainty is statistical and the second systematic. Table_13.pdf [1 KiB] HiDef png [0 KiB] Thumbnail [0 KiB] tex code Values of $\uplambda_{\theta}$, $\uplambda_{\theta\phi}$, $\uplambda_{\phi}$ and $\tilde \uplambda$ measured in the CS frame for the $\Upsilon(2\mathrm{S})$ produced at $\sqrt{s}=8 {\mathrm{TeV}}$. The first uncertainty is statistical and the second systematic. Table_14.pdf [1 KiB] HiDef png [0 KiB] Thumbnail [0 KiB] tex code Values of $\uplambda_{\theta}$, $\uplambda_{\theta\phi}$, $\uplambda_{\phi}$ and $\tilde \uplambda$ measured in the GJ frame for the $\Upsilon(2\mathrm{S})$ produced at $\sqrt{s}=7 {\mathrm{TeV}}$. The first uncertainty is statistical and the second systematic. Table_15.pdf [44 KiB] HiDef png [342 KiB] Thumbnail [171 KiB] tex code Values of $\uplambda_{\theta}$, $\uplambda_{\theta\phi}$, $\uplambda_{\phi}$ and $\tilde \uplambda$ measured in the GJ frame for the $\Upsilon(2\mathrm{S})$ produced at $\sqrt{s}=8 {\mathrm{TeV}}$. The first uncertainty is statistical and the second systematic. Table_16.pdf [1 KiB] HiDef png [0 KiB] Thumbnail [0 KiB] tex code Values of $\uplambda_{\theta}$, $\uplambda_{\theta\phi}$ and $\uplambda_{\phi}$ measured in the HX, CS and GJ frames for the $\Upsilon(2\mathrm{S})$ produced at $\sqrt{s}=7 {\mathrm{TeV}}$ in the rapidity range $2.2< y^{\Upsilon} <4.5$. The first uncertainty is statistical and the second systematic. Table_17.pdf [1 KiB] HiDef png [0 KiB] Thumbnail [0 KiB] tex code Values of $\uplambda_{\theta}$, $\uplambda_{\theta\phi}$ and $\uplambda_{\phi}$ measured in the HX, CS and GJ frames for the $\Upsilon(2\mathrm{S})$ produced at $\sqrt{s}=8 {\mathrm{TeV}}$ in the rapidity range $2.2< y^{\Upsilon} <4.5$. The first uncertainty is statistical and the second systematic. Table_18.pdf [44 KiB] HiDef png [287 KiB] Thumbnail [146 KiB] tex code Values of $\tilde \uplambda$ measured in the HX, CS and GJ frames for the $\Upsilon(2\mathrm{S})$ produced at $\sqrt{s}=7$ and $8 {\mathrm{TeV}}$ in the rapidity range $2.2< y^{\Upsilon} <4.5$. The first uncertainty is statistical and the second systematic. Table_19.pdf [37 KiB] HiDef png [251 KiB] Thumbnail [122 KiB] tex code Values of $\uplambda_{\theta}$, $\uplambda_{\theta\phi}$, $\uplambda_{\phi}$ and $\tilde \uplambda$ measured in the HX frame for the $\Upsilon(3\mathrm{S})$ produced at $\sqrt{s}=7 {\mathrm{TeV}}$. The first uncertainty is statistical and the second systematic. Table_20.pdf [44 KiB] HiDef png [341 KiB] Thumbnail [170 KiB] tex code Values of $\uplambda_{\theta}$, $\uplambda_{\theta\phi}$, $\uplambda_{\phi}$ and $\tilde \uplambda$ measured in the HX frame for the $\Upsilon(3\mathrm{S})$ produced at $\sqrt{s}=8 {\mathrm{TeV}}$. The first uncertainty is statistical and the second systematic. Table_21.pdf [44 KiB] HiDef png [343 KiB] Thumbnail [171 KiB] tex code Values of $\uplambda_{\theta}$, $\uplambda_{\theta\phi}$, $\uplambda_{\phi}$ and $\tilde \uplambda$ measured in the CS frame for the $\Upsilon(3\mathrm{S})$ produced at $\sqrt{s}=7 {\mathrm{TeV}}$. The first uncertainty is statistical and the second systematic. Table_22.pdf [44 KiB] HiDef png [339 KiB] Thumbnail [170 KiB] tex code Values of $\uplambda_{\theta}$, $\uplambda_{\theta\phi}$, $\uplambda_{\phi}$ and $\tilde \uplambda$ measured in the CS frame for the $\Upsilon(3\mathrm{S})$ produced at $\sqrt{s}=8 {\mathrm{TeV}}$. The first uncertainty is statistical and the second systematic. Table_23.pdf [44 KiB] HiDef png [340 KiB] Thumbnail [170 KiB] tex code Values of $\uplambda_{\theta}$, $\uplambda_{\theta\phi}$, $\uplambda_{\phi}$ and $\tilde \uplambda$ measured in the GJ frame for the $\Upsilon(3\mathrm{S})$ produced at $\sqrt{s}=7 {\mathrm{TeV}}$. The first uncertainty is statistical and the second systematic. Table_24.pdf [44 KiB] HiDef png [338 KiB] Thumbnail [170 KiB] tex code Values of $\uplambda_{\theta}$, $\uplambda_{\theta\phi}$, $\uplambda_{\phi}$ and $\tilde \uplambda$ measured in the GJ frame for the $\Upsilon(3\mathrm{S})$ produced at $\sqrt{s}=8 {\mathrm{TeV}}$. The first uncertainty is statistical and the second systematic. Table_25.pdf [44 KiB] HiDef png [339 KiB] Thumbnail [171 KiB] tex code Values of $\uplambda_{\theta}$, $\uplambda_{\theta\phi}$ and $\uplambda_{\phi}$ measured in the HX, CS and GJ frames for the $\Upsilon(3\mathrm{S})$ produced at $\sqrt{s}=7 {\mathrm{TeV}}$ in the rapidity range $2.2< y^{\Upsilon} <4.5$. The first uncertainty is statistical and the second systematic. Table_26.pdf [44 KiB] HiDef png [288 KiB] Thumbnail [147 KiB] tex code Values of $\uplambda_{\theta}$, $\uplambda_{\theta\phi}$ and $\uplambda_{\phi}$ measured in the HX, CS and GJ frames for the $\Upsilon(3\mathrm{S})$ produced at $\sqrt{s}=8 {\mathrm{TeV}}$ in the rapidity range $2.2< y^{\Upsilon} <4.5$. The first uncertainty is statistical and the second systematic. Table_27.pdf [44 KiB] HiDef png [282 KiB] Thumbnail [146 KiB] tex code Values of $\tilde \uplambda$ measured in the HX, CS and GJ frames for the $\Upsilon(3\mathrm{S})$ produced at $\sqrt{s}=7$ and $8 {\mathrm{TeV}}$ in the rapidity range $2.2< y^{\Upsilon} <4.5$. The first uncertainty is statistical and the second systematic. Table_28.pdf [38 KiB] HiDef png [247 KiB] Thumbnail [122 KiB] tex code

## Supplementary Material [file]

 Supplementary material full pdf supple[..].pdf [499 KiB] Fig1_supp.pdf [15 KiB] HiDef png [492 KiB] Thumbnail [273 KiB] *C file Fig2_supp.pdf [97 KiB] HiDef png [388 KiB] Thumbnail [281 KiB] *C file Fig3_supp.pdf [97 KiB] HiDef png [385 KiB] Thumbnail [278 KiB] *C file Fig4a_supp.pdf [25 KiB] HiDef png [165 KiB] Thumbnail [113 KiB] *C file Fig4b_supp.pdf [28 KiB] HiDef png [181 KiB] Thumbnail [117 KiB] *C file Fig4c_supp.pdf [30 KiB] HiDef png [255 KiB] Thumbnail [150 KiB] *C file Figure[..].pdf [151 KiB] HiDef png [518 KiB] Thumbnail [350 KiB] *C file Figure[..].pdf [286 KiB] HiDef png [472 KiB] Thumbnail [406 KiB] *C file Figure[..].pdf [260 KiB] HiDef png [469 KiB] Thumbnail [404 KiB] *C file Figure[..].pdf [226 KiB] HiDef png [309 KiB] Thumbnail [253 KiB] *C file

Created on 18 October 2019.