(${\it Left}$) Invariant mass distribution of muon pairs passing the selection criteria. In the plot, $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu}$ candidates are required to have 5 $<$ $p_{\rm T}$ $<$ 7 $ {\mathrm{ Ge V /}c}$ and $3.0<y<3.5$. The solid (dashed) vertical lines indicate the signal (sideband) regions. (${\it Right}$) Pseudo decay-time significance ($S_{\tau}$) distribution for background subtracted $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu}$ candidates in the same kinematic bin. The solid vertical lines indicate the $S_\tau$ selection region. The right tail of the distribution is due to $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu}$ production through the decay of $b$ hadrons.

Global efficiency (area normalized to unity) as a function of (top) $\cos \theta$ and (bottom) $\phi$ for (left) 3 $<$ $p_{\rm T}$ $<$ 4 $ {\mathrm{ Ge V /}c}$ and for (right) 7 $<$ $p_{\rm T}$ $<$ 10 $ {\mathrm{ Ge V /}c}$ of $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu}$ mesons in the helicity frame. The efficiency is determined from simulation.

(Left) Distributions of $\cos\theta$ in the helicity frame for $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu}$ mesons from $B^+ \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K^+$ decays in data (open circles) and simulated sample (open squares) after the weighting based on the $B^{+}$ and $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu}$ kinematics and (right) their ratio.

Measurements of $\lambda_{\theta}$ in bins of $p_{\rm T}$ for five rapidity bins in (left) the helicity frame and (right) the Collins-Soper frame. The error bars represent the statistical and systematic uncertainties added in quadrature. The data points are shifted slightly horizontally for different rapidities to improve visibility.

Comparison of LHCb and ALICE results for $\lambda_{\theta}$ in different $p_{\rm T}$ bins integrating over the rapidity range $2.5 < y < 4.0$ in (left) the helicity frame and (right) the Collins-Soper frame. Error bars represent the statistical and systematic uncertainties added in quadrature.

Comparison of LHCb prompt $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu}$ polarization measurements of $\lambda_{\theta}$ with direct NLO color singlet (magenta diagonal lines \cite{TheoryMathias}) and three different NLO NRQCD (blue diagonal lines (1) \cite{TheoryMathias}, red vertical lines (2) \cite{Gong:2012ug} and green hatched (3) \cite{Chao:2012iv,*Shao2012fs}) predictions as a function of the $p_{\rm T}$ of the $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu}$ meson in the rapidity range $2.5<y<4.0$ in the helicity frame.

Differential cross-section of prompt $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu}$ production as a function of $p_{\rm T}$ and in bins of $y$. The vertical error bars show the quadratic sum of the statistical and systematic uncertainties.

Animated gif made out of all figures.

Main contributions to the absolute systematic uncertainty on the parameter $\lambda_\theta$ in the helicity and Collins-Soper frames. While the systematic uncertainties are evaluated separately for all $p_{\rm T}$ and $y$ bins, we give here only the average, the minimum and the maximum values of all bins.

Measured $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu}$ polarization parameters in bins of $p_{\rm T}$ and $y$ in the helicity frame. The first uncertainty is statistical (from the fit and the background subtraction) while the second is the systematic uncertainty.

Measured $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu}$ polarization parameters in bins of $p_{\rm T}$ and $y$ in Collins-Soper frame. The first uncertainty is statistical (from the fit and the background subtraction) while the second is the systematic uncertainty.

Double-differential cross-section $d ^{2} \sigma/ d p_{\rm T} dy$ in nb/( $ {\mathrm{ Ge V /}c}$ ) for prompt $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu}$ production in bins of $p_{\rm T}$ and $y$, with statistical, systematic and polarization uncertainties.

This ZIP file contains supplemetary material for the publication LHCb-PAPER-2013-008. The files are: LHCB-PAPER-2013-008-additional.pdf: In this file we present extra results in figures and also explicitly in tables, short discussions are made. *.pdf *.eps *.png *.C : The figures used in the file LHCB-PAPER-2013-008-additional.pdf mycommands_italic.tex: predefined symbols for tex