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 $275~pmathrm{b}^{-1}$. 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*} begin{split} sigma(mbox{prompt }psi(2S),13~mathrm{TeV}) &= {1.430 pm 0.005(mathrm{stat}) pm 0.099 (mathrm{syst})mumathrm{b}}, sigma(psi(2S)mathrm{-from-}b,13~mathrm{TeV})&={0.426 pm 0.002(mathrm{stat}) pm0.030 (mathrm{syst})mumathrm{b}}. end{split} 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 $614~{pmathrm{b}^{-1}}$.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*} begin{split} sigma(mbox{prompt }psi(2S),7~mathrm{TeV}) &={0.471 pm0.001 (mathrm{stat}) pm 0.025 (mathrm{syst})mumathrm{b}}, sigma(psi(2S)mathrm{-from-}b,7~mathrm{TeV}) &={0.126pm0.001 (mathrm{stat}) pm0.008 (mathrm{syst})mumathrm{b}}. end{split} end{equation*} All results show reasonable agreement with theoretical calculations.
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