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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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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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Double-differential production cross-sections (in $\text{ nb}$ /( $ {\mathrm{Ge V /}c}$ )) of prompt $\psi {(2S)}$ mesons at $13\text{ Te V} $ in bins of ( $ p_{\mathrm{T}}$ , $y$). The first uncertainties are statistical, the second are the uncorrelated systematic uncertainties between bins, and the last are the correlated systematic uncertainties between bins. Adjacent bins with large statistical uncertainties have been merged.

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Double-differential production cross-sections (in $\text{ nb} /( {\mathrm{Ge V /}c} )$) of $\psi {(2S)}$ -from-$b$ mesons at $13\text{ Te V} $ in bins of ( $ p_{\mathrm{T}}$ ,$y$). The first uncertainties are statistical, the second are the uncorrelated systematic uncertainties between bins, and the last are the correlated systematic uncertainties between bins. Adjacent bins with large statistical uncertainties have been merged.

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Double-differential production cross-section in $\text{ nb}$ /( $ {\mathrm{Ge V /}c}$ ) of prompt $\psi {(2S)}$ mesons at $7\text{ Te V} $ in bins of ( $ p_{\mathrm{T}}$ ,$y$). The first uncertainty is statistical, the second is the uncorrelated systematic uncertainties shared between bins and the last is the correlated systematic uncertainties.

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Double-differential production cross-section in $\text{ nb}$ /( $ {\mathrm{Ge V /}c}$ ) of $\psi {(2S)}$ -from-$b$ mesons at $7\text{ Te V} $ in bins of ( $ p_{\mathrm{T}}$ ,$y$). The first uncertainties are statistical, the second are the uncorrelated systematic uncertainties shared between bins and the last are the correlated systematic uncertainties.

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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 10 July 2020.