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Measurement of $J/\psi$ polarization in $pp$ collisions at $\sqrt{s}=7$ TeV

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Abstract

An angular analysis of the decay $J/\psi \rightarrow \mu^{+} \mu^{-}$ is performed to measure the polarization of prompt $J/\psi$ mesons produced in $pp$ collisions at $\sqrt{s}=7\; \mathrm{TeV}$. The dataset corresponds to an integrated luminosity of 0.37 fb$^{-1}$ collected with the LHCb detector. The measurement is presented as a function of transverse momentum, $p_\mathrm{T}$, and rapidity, $y$, of the $J/\psi$ meson, in the kinematic region $2 < p_\mathrm{T} < 15\; \mathrm{GeV}/c$ and $2.0<y<4.5$.

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(${\it Left}$) 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.

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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.

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(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.

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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.

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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.

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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.

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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.

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Tables and captions

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.

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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.

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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.

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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.

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Supplementary Material [file]

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

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Created on 18 October 2019.