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Measurement of the $\eta_c(1S)$ production cross-section in $pp$ collisions at $\sqrt{s} = 13$ TeV

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Abstract

Using a data sample corresponding to an integrated luminosity of $2.0 fb^{-1}$, collected by the LHCb experiment, the production of the $\eta_c(1S)$ state in proton-proton collisions at a centre-of-mass energy of $\sqrt{s}=13 \text{ TeV}$ is studied in the rapidity range ${2.0 < y < 4.5}$ and in the transverse momentum range ${6.5 < p_{T} < 14.0\text{ GeV}}$. The cross-section for prompt production of $\eta_c(1S)$ mesons relative to that of the $J/\psi$ meson is measured using the ${p\bar{p}}$ decay mode and is found to be ${\sigma_{\eta_c(1S)}/\sigma_{J/\psi} = 1.69 \pm 0.15 \pm 0.10 \pm 0.18}$. The quoted uncertainties are, in order, statistical, systematic and due to uncertainties on the branching fractions of the ${J/\psi\to p \bar{p}}$ and ${\eta_c\to p \bar{p}}$ decays. The prompt $\eta_c(1S)$ production cross-section is determined to be ${\sigma_{\eta_c(1S)} = 1.26 \pm 0.11\pm 0.08 \pm 0.14 \mu b}$, where the last uncertainty includes that on the ${J/\psi}$ meson cross-section. The ratio of the branching fractions of $b$-hadron decays to the $\eta_c(1S)$ and ${J/\psi}$ states is measured to be ${\mathcal{B}_{b\to\eta_c X}/\mathcal{B}_{b\to J/\psi X} = 0.48 \pm 0.03 \pm 0.03 \pm 0.05}$, where the last uncertainty is due to those on the branching fractions of the ${J/\psi \to p \bar{p}}$ and ${\eta_c\to p \bar{p}}$ decays. The difference between the ${J/\psi}$ and $\eta_c(1S)$ masses is also determined to be ${113.0 \pm 0.7 \pm 0.1\text{ MeV}}$, which is the most precise single measurement of this quantity to date.

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Invariant-mass distribution of the $ p $ $\overline p $ candidates for (top left) prompt-enriched and (top right) $ b $ -hadron-enriched samples in the entire $ p_{\mathrm{T}}$ range, $6.5< p_{\mathrm{T}} <14.0 \text{ Ge V} $. The solid blue lines represent the total fit result. The dashed magenta and dotted red lines show the signal and background components, respectively. Signal distributions with the background components from the fit subtracted are shown on the bottom plots for the two samples.

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The prompt $\eta _ c $ production cross-section as a function of centre-of-mass energy. (Left) Relative $\eta _ c $ prompt production cross-section. (Right) Absolute $\eta _ c $ (black rectangles) and $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu}$ (blue circles) prompt production cross-sections. The error bars show uncertainties due to statistical, systematic, and to the $\eta _ c \rightarrow p \overline p $ and $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \rightarrow p \overline p $ branching fractions and $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu}$ production cross-section.

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Relative $\eta _ c $ to $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu}$ differential production cross-sections for (left) prompt production and (right) production in $ b $ -hadron inclusive decays. The uncertainties are statistical, systematic, and due to the $\eta _ c \rightarrow p \overline p $ and $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \rightarrow p \overline p $ branching fractions, respectively. For the relative prompt production cross-section, the result of a fit with a linear function is overlaid.

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Differential production cross-sections of $\eta _ c $ (red rectangles) and $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu}$ (blue circles) for (left) prompt production and (right) production in $ b $ -hadron inclusive decays. The uncertainties for $\eta _ c $ production are statistical, systematic, and due to the $\eta _ c \rightarrow p \overline p $ and $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \rightarrow p \overline p $ branching fractions and $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu}$ production cross-section. For the prompt production cross-sections, the results of fits with an exponential function are overlaid. The $ p_{\mathrm{T}}$ values of the data points correspond to the average values of the fit function over the bins.

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Distribution of the $ p \overline p $ invariant mass. The solid line represents the fit result, while the dashed line shows the $\eta _ c $ and $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu}$ signal contributions.

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Invariant mass distributions of the $ p $ $\overline p $ candidates for seven bins of $t_z$ for the $ p_{\mathrm{T}}$ -integrated sample $6.5< p_{\mathrm{T}} <14.0 \text{ Ge V} $. The solid blue lines represent the total fit result. Dashed magenta and dotted red lines show the signal and background components, respectively. The distributions with the background component of the fit subtracted are shown below.

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Distributions of $t_z$ for (left) $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu}$ and (right) $\eta _ c $ mesons for the entire $ p_{\mathrm{T}}$ range ${6.5< p_{\mathrm{T}} <14.0 \text{ Ge V} }$ and the result of the simultaneous $\chi^2$ fit. The solid blue lines show the fit function, the red dashed areas show the prompt components, the green dotted areas show the contributions from inclusive $ b $ -hadron decays, the grey lines show contributions from the events with wrongly associated PV. The $t_z$ values of the data points correspond to the average values of the fit function over the bins.

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Relative $\eta _ c $ to $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu}$ differential production cross-sections for (left) prompt production and (right) production in $ b $ -hadron inclusive decays obtained using the alternative technique (points) and the baseline technique (red boxes). The uncertainties shown are statistical, systematic, and the uncertainty due to the $\eta _ c \rightarrow p \overline p $ and $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \rightarrow p \overline p $ branching fractions.

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Animated gif made out of all figures.

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Tables and captions

Yield of $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu}$ mesons and the $\eta _ c $ -to- $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu}$ yield ratio for prompt and $ b $ -hadron decay production, corrected for the cross-feed, in bins of transverse momentum.

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Relative uncertainties (in %) on the ratio of prompt cross-sections $\sigma^{\text{prompt}}_{\eta _ c }/\sigma^{\text{prompt}}_{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} }$. Uncertainties on $\mathcal{B} _{\eta _ c \rightarrow p \overline p }$ and $\mathcal{B} _{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \rightarrow p \overline p }$ are considered separately and given in the text.

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Relative uncertainties (in %) on the ratio of cross-sections for production in inclusive $ b $ -hadron decays $\sigma^{b}_{\eta _ c }/\sigma^{b}_{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} }$. Uncertainties on $\mathcal{B} _{\eta _ c \rightarrow p \overline p }$ and $\mathcal{B} _{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \rightarrow p \overline p }$ are considered separately and given in the text.

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Systematic uncertainties on the measurement of the $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu}$ --$\eta _ c $ mass difference.

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Relative $ p_{\mathrm{T}}$ -differential $\eta _ c $ prompt production cross-section.

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Differential $\eta _ c $ prompt production cross-section.

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Relative $ p_{\mathrm{T}}$ -differential $\eta _ c $ production cross-section in inclusive $ b $ -hadron decays.

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The $ p_{\mathrm{T}}$ -differential $\eta _ c $ production cross-section in inclusive $ b $ -hadron decays.

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Supplementary Material [file]

Supplementary material full pdf

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This ZIP file contains supplementary material for the publication LHCb-PAPER-2019-024. The files are: Supplementary.pdf : An overview of the extra figures supplementary.tex : tex-file of supplementary material, needs to be imported to main.tex) *.pdf, *.png, *.eps : The figures in various formats

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Created on 05 March 2021.