The polarisation of prompt $\psi(2S)$ mesons is measured by performing an angular analysis of $\psi(2S)\rightarrow \mu^{+} \mu^{-}$ decays using proton-proton collision data, corresponding to an integrated luminosity of 1.0 fb$^{-1}$, collected by the LHCb detector at a centre-of-mass 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.
The differential cross-section for the inclusive production of $\psi(2S)$ mesons in $pp$ collisions at $\sqrt{s}$ =7 TeV has been measured with the LHCb detector. The data sample corresponds to an integrated luminosity of 36 pb$^{-1}$ collected during 2010. The $\psi(2S)$ mesons are reconstructed in the decay channels $\psi(2S) \rightarrow \mu^{+} \mu^{-}$ and $\psi(2S)$ $\rightarrow$ $J$/$\psi \pi^{+}\pi^{-}$, with the $J$/$\psi$ meson decaying into two muons. Results are presented both for promptly produced $\psi(2S)$ mesons and for those originating from $b$-hadron decays. In the kinematic range $p_{\rm T}(\psi(2S))$ $\leq$ 16 GeV/$c$ and 2 < $y$($\psi(2S))$ $\leq$ 4.5 we measure \begin{eqnarray*} \sigma_{\rm prompt}(\psi(2S)) &=& 1.44 \pm 0.01~(\text{stat})\pm 0.12~(\text{syst})^{+0.20}_{-0.40}~(\text{pol})~{\rm \mu b}, \\ \sigma_{b}(\psi(2S)) &=& 0.25 \pm 0.01~(\text{stat}) \pm 0.02~(\text{syst})~{\rm \mu b}, \end{eqnarray*} where the last uncertainty on the prompt cross-section is due to the unknown $\psi(2S)$ polarization. Recent QCD calculations are found to be in good agreement with our measurements. Combining the present result with the LHCb $J$/$\psi$ measurements we determine the inclusive branching fraction \begin{equation*} \mathcal{B}(b \rightarrow \psi(2S) X) = (2.73 \pm 0.06~(\text{stat}) \pm 0.16~(\text{syst}) \pm 0.24~(\text{BF})) \times 10^{-3}, \end{equation*} where the last uncertainty is due to the $\mathcal{B}(b \rightarrow J/\psi X)$, $\mathcal{B}(J/\psi \rightarrow \mu^+ \mu^-)$ and $\mathcal{B}(\psi(2S) \rightarrow e^+ e^-)$ branching fraction uncertainties. All above results are corrected by an erratum included as an appendix.
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