Measurement of $\psi(2S)$ production cross-sections in proton-proton collisions at $\sqrt{s} = 7$ and 13 TeV

The cross-sections of $\psi(2S)$ meson production in proton-proton collisions at $\sqrt{s}=13~\mathrm{TeV}$ are measured with a data sample collected by the LHCb detector corresponding to an integrated luminosity of $275~p\mathrm{b}^{-1}$. The production cross-sections for prompt $\psi(2S)$ mesons and those for $\psi(2S)$ mesons from $b$-hadron decays ($\psi{(2S)}\mathrm{-from-}b$) are determined as functions of the transverse momentum, $p_{\mathrm{T}}$, and the rapidity, $y$, of the $\psi(2S)$ meson in the kinematic range $2<p_{\mathrm{T}}<20~\mathrm{GeV}/c$ and $2.0<y<4.5$. The production cross-sections integrated over this kinematic region are \begin{equation*} \sigma(\mbox{prompt }\psi(2S),13~\mathrm{TeV})={1.430\pm0.005(\mathrm{stat})\pm0.099(\mathrm{syst})\mu\mathrm{b}}, \end{equation*} \begin{equation*} \sigma(\psi(2S)\mathrm{-from-}b,13~\mathrm{TeV})={0.426\pm0.002(\mathrm{stat})\pm0.030(\mathrm{syst})\mu\mathrm{b}}. \end{equation*} A new measurement of $\psi(2S)$ production cross-sections in $pp$ collisions at $\sqrt{s}=7~\mathrm{TeV}$ is also performed using data collected in 2011, corresponding to an integrated luminosity of $614~{p\mathrm{b}^{-1}}$.The integrated production cross-sections in the kinematic range $3.5<p_{\mathrm{T}}<14~\mathrm{GeV}/c$ and $2.0<y<4.5$ are \begin{equation*} \sigma(\mbox{prompt }\psi(2S),7~\mathrm{TeV})={0.471\pm0.001(\mathrm{stat})\pm0.025(\mathrm{syst})\mu\mathrm{b}}, \end{equation*} \begin{equation*} \sigma(\psi(2S)\mathrm{-from-}b,7~\mathrm{TeV})={0.126\pm0.001(\mathrm{stat})\pm0.008(\mathrm{syst})\mu\mathrm{b}}. \end{equation*} All results show reasonable agreement with theoretical calculations.