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

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Abstract

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

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Distributions of (left) the invariant mass $m_{\mu ^+\mu ^- }$ and (right) pseudo decay time $t_z$ of selected $\psi {(2S)}$ candidates in the kinematic bin of $5< p_{\mathrm{T}} <6\text{ Ge V /}c $ and $2.5<y<3.0$ in the $13\text{ Te V} $ data sample. Projections of the two-dimensional fit result are also shown. The solid (red) line is the total fit function, the shaded (green) area corresponds to the background component. The prompt $\psi {(2S)}$ contribution is shown in cross-hatched (blue) area, $\psi {(2S)}$ -from-$b$ in a solid (black) line and the tail contribution due to the association of $\psi {(2S)}$ with the wrong PV is shown in filled (magenta) area. The tail contribution is invisible in the invariant-mass plot.

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Double-differential production cross-sections of prompt $\psi {(2S)}$ as functions of $ p_{\mathrm{T}}$ in bins of $y$ at (left) $13\text{ Te V} $ and (right) $7\text{ Te V} $. The statistical and systematic uncertainties are added in quadrature. The $\psi {(2S)}$ meson is assumed to be produced unpolarised.

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Double-differential production cross-sections of $\psi {(2S)}$ -from- $ b $ as functions of $ p_{\mathrm{T}} $ in bins of $y$ at (left) $13\text{ Te V} $ and (right) $7\text{ Te V} $. The statistical and systematic uncertainties are added in quadrature. The $\psi {(2S)}$ meson is assumed to be produced unpolarised.

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Differential production cross-sections as functions of $ p_{\mathrm{T}}$ in the range $2.0<y<4.5$ for the (top) $13\text{ Te V} $ and (bottom) $7\text{ Te V} $ samples. The left-hand figures are for prompt $\psi {(2S)}$ and the results are compared with the NRQCD calculations \cite{Shao:2014yta}; the right-hand figures are for $\psi {(2S)}$ -from- $ b $ and the results are compared with the FONLL calculations \cite{Cacciari:1998it}.

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Differential production cross-sections as functions of $y$ (top) in the range $2< p_{\mathrm{T}} <20\text{ Ge V /}c $ for the $13\text{ Te V} $ sample and (bottom) in the range $3.5< p_{\mathrm{T}} <14\text{ Ge V /}c $ for the $7\text{ Te V} $ sample. The left figures are for prompt $\psi {(2S)}$ , the right figures are for $\psi {(2S)}$ -from- $ b $ compared with the FONLL calculations \cite{Cacciari:1998it}.

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Fractions of $\psi {(2S)} $-from-$ b $ in bins of $ p_{\mathrm{T}}$ and $y$ for the (left) $13\text{ Te V} $ and (right) $7\text{ Te V} $ samples. The uncertainties are statistical.

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Ratios of differential cross-sections between prompt $\psi {(2S)}$ and prompt $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu}$ mesons at $13\text{ Te V} $ as functions of (left) $ p_{\mathrm{T}}$ and (right) $y$. The NRQCD predicted ratio \cite{Shao:2014yta} is shown in the left panel for comparison.

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Ratios of differential cross-sections between $\psi {(2S)}$ -from- $ b $ and $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu}$ mesons from $ b $ -hadron decays at $13\text{ Te V} $ as functions of (left) $ p_{\mathrm{T}}$ and (right) $y$. The FONLL calculations \cite{Cacciari:2015fta} are shown for comparison.

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Ratio of differential production cross-sections between the $13\text{ Te V} $ and $7\text{ Te V} $ measurements as a function of (left) $ p_{\mathrm{T}}$ integrated over $y$, (right) $y$ integrated over $ p_{\mathrm{T}} $ for prompt $\psi {(2S)}$ production. Theoretical calculations of NRQCD \cite{Shao:2014yta} are compared to data on the left side.

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Ratio of differential production cross-sections between the $13\text{ Te V} $ and the $7\text{ Te V} $ measurements as a function of (left) $ p_{\mathrm{T}}$ integrated over $y$, (right) $y$ integrated over $ p_{\mathrm{T}} $ for $\psi {(2S)}$ -from- $ b $ . Theoretical FONLL calculations \cite{Cacciari:2015fta} are compared to the measured $\psi {(2S)}$ -from- $ b $ ratio.

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Tables and captions

Systematic uncertainties on the $\psi {(2S)}$ cross-section measurements. The uncertainty from the $t_z$ fit only affects the $\psi {(2S)} $-from-$b$ result. Uncertainties labelled with "$\ast$" are correlated between kinematic bins.

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Differential production cross-sections $\mathrm{d}\sigma/\mathrm{d} p_{\mathrm{T}} $ (in $\text{ nb}$ /( $ {\mathrm{Ge V /}c}$ )) of prompt $\psi {(2S)}$ and $\psi {(2S)}$ -from-$ b $ mesons at $13\text{ Te V} $. The first uncertainties are statistical and the second (third) are uncorrelated (correlated) systematic uncertainties amongst bins.

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Differential production cross-sections $\mathrm{d}\sigma/\mathrm{d} y$ (in $\text{ nb}$ ) of prompt $\psi {(2S)}$ and $\psi {(2S)}$ -from-$ b $ mesons at $13\text{ Te V} $. The first uncertainties are statistical and the second (third) are uncorrelated (correlated) systematic uncertainties amongst bins.

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Differential cross-sections $\mathrm{d}\sigma/\mathrm{d} p_{\mathrm{T}} $ (in $\text{ nb}$ /( $ {\mathrm{Ge V /}c}$ )) of prompt $\psi {(2S)}$ and $\psi {(2S)}$ -from-$b$ mesons at $7\text{ Te V} $, integrated over $y$ between 2.0 and 4.5. The first uncertainties are statistical and the second (third) are uncorrelated (correlated) systematic uncertainties amongst bins.

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Differential cross-sections $\mathrm{d}\sigma/\mathrm{d} y$ (in $\text{ nb}$ ) of prompt $\psi {(2S)}$ and $\psi {(2S)}$ -from-$b$ mesons at $7\text{ Te V} $, integrated over $ p_{\mathrm{T}}$ between 3.5 and 14 $\text{ Ge V /}c$ . The first uncertainties are statistical and the second (third) are uncorrelated (correlated) systematic uncertainties amongst bins.

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Fractions of $\psi {(2S)}$ -from-$ b $ (in %) at $13\text{ Te V} $ in bins of $( p_{\mathrm{T}} ,y)$ of $\psi {(2S)}$ mesons. The uncertainties are statistical only. The systematic uncertainties are negligible. Adjacent bins with large statistical uncertainty have been merged.

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Fractions of $\psi {(2S)}$ -from-$ b $ (in %) at $7\text{ Te V} $ in bins of $( p_{\mathrm{T}} ,y)$ of $\psi {(2S)}$ mesons. The uncertainties are statistical only. The systematic uncertainties are negligible.

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Ratios of production cross-sections at $13\text{ Te V} $ between $\psi {(2S)}$ mesons and $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu}$ mesons in bins of $ p_{\mathrm{T}}$ for prompt productions and those from $ b $-hadron decays. The statistical and systematic uncertainties are added in quadrature.

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Ratios of production cross-sections between $\psi {(2S)}$ mesons and $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu}$ mesons at $13\text{ Te V} $ in bins of $y$ for prompt productions and those from $ b $-hadron decays. The statistical and systematic uncertainties are added in quadrature.

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Ratios of production cross-sections between $13\text{ Te V} $ and $7\text{ Te V} $ in bins of $ p_{\mathrm{T}}$ for prompt $\psi {(2S)}$ and $\psi {(2S)}$ -from-$ b $ mesons. The statistical and systematic uncertainties are added in quadrature.

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Ratios of cross-sections between measurements at $13\text{ Te V} $ and $7\text{ Te V} $ in different bins of $y$ for prompt $\psi {(2S)}$ and $\psi {(2S)}$ -from-$ b $ mesons. The statistical and systematic uncertainties are added in quadrature.

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Created on 20 August 2019.Citation count from INSPIRE on 20 August 2019.