The polarisation of prompt $\psi(2S)$ mesons is measured by performing an angular analysis of $\psi(2S)\rightarrow \mu^{+} \mu^{}$ decays using protonproton collision data, corresponding to an integrated luminosity of 1.0 fb$^{1}$, collected by the LHCb detector at a centreofmass energy of 7 TeV. The polarisation is measured in bins of transverse momentum $p_\mathrm{T}$ and rapidity $y$ in the kinematic region $3.5<p_\mathrm{T}<15$ GeV$/c$ and $2.0<y<4.5$, and is compared to theoretical models. No significant polarisation is observed.
Invariant mass distribution of $\psi {(2S)}$ candidates in the kinematic region $5< p_{\rm T} <7 {\mathrm{ Ge V /}c} $ and $2.5<y<3.0$. The solid blue line is the total fit function, the dotdashed green line represents the linear background function and the red dashed line is the combination of the two CB functions. 
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Detection efficiency in arbitrary units as a function of $\cos \theta$ and $\phi$ in the helicity frame for $\psi {(2S)}$ mesons in the range $5< p_{\rm T} <7 {\mathrm{ Ge V /}c} $ and $2.5<y<3.0$. 
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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 (filled triangles) and in the simulated sample (open circles) and (right) their ratio after the weighting based on the $ B ^+ $ and $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu}$ kinematic properties. 
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Polarisation parameters for prompt $\psi {(2S)}$ mesons as a function of $p_{\rm T}$ , in five rapidity intervals, (top left) $\lambda_\theta $ and (bottom) $\lambda_{\mathrm{inv}} $, measured in the helicity frame, and (top right) $\lambda_\theta $ in the CollinsSoper frame. The uncertainties on data points are the sum in quadrature of statistical and systematic uncertainties. The horizontal bars represent the width of the $p_{\rm T}$ bins for the $\psi {(2S)}$ meson. The data points for each rapidity interval are displaced horizontally to improve visibility. 
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Polarisation parameter $\lambda_\theta$ of the prompt $\psi {(2S)}$ meson in the helicity frame as a function of $p_{\rm T}$ , in the rapidity range $2.5<y<4$. The predictions of NLO CSM [39] and three NLO NRQCD models (1) [39], (2) [40] and (3) [41] are also shown. Uncertainties on data are the sum in quadrature of the statistical and systematic uncertainties. The horizontal bars represent the width of $p_{\rm T}$ bins for the $\psi {(2S)}$ meson. 
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Animated gif made out of all figures. 
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Sources of systematic uncertainties on the polarisation parameter $\lambda_\theta$ in the helicity and CollinsSoper frames. For each type of uncertainty, the average and the range over all $\psi {(2S)}$ kinematic bins are shown. 
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Measured prompt $\psi {(2S)}$ polarisation parameters $\lambda_\theta$ , $\lambda_{\theta\phi}$ , $\lambda_{\phi}$ and $\lambda_{\mathrm{inv}}$ in bins of $p_{\rm T}$ and $y$ in the helicity frame. The first uncertainty is statistical and the is second systematic. 
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Measured prompt $\psi {(2S)}$ polarisation parameters $\lambda_\theta$ , $\lambda_{\theta\phi}$ , $\lambda_{\phi}$ and $\lambda_{\mathrm{inv}}$ in bins of $p_{\rm T}$ and $y$ in the CollinsSoper frame. The first uncertainty is statistical and the second is systematic. 
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Created on 19 February 2021.