# 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.

## Figures and captions

 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. Fig1.pdf [302 KiB] HiDef png [238 KiB] Thumbnail [213 KiB] *.C file 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. Fig2.pdf [318 KiB] HiDef png [94 KiB] Thumbnail [100 KiB] *.C file 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. Fig3.pdf [384 KiB] HiDef png [118 KiB] Thumbnail [121 KiB] *.C file 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. Fig4.pdf [384 KiB] HiDef png [123 KiB] Thumbnail [117 KiB] *.C file 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. Fig5.pdf [332 KiB] HiDef png [115 KiB] Thumbnail [108 KiB] *.C file 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. Fig6.pdf [553 KiB] HiDef png [1 KiB] Thumbnail [0 KiB] *.C file 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. Fig7.pdf [1 MiB] HiDef png [238 KiB] Thumbnail [162 KiB] *.C file 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. Fig8.pdf [1 MiB] HiDef png [132 KiB] Thumbnail [135 KiB] *.C file Animated gif made out of all figures. PAPER-2019-024.gif Thumbnail

## 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. Table_1.pdf [75 KiB] HiDef png [67 KiB] Thumbnail [34 KiB] tex code 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. Table_2.pdf [71 KiB] HiDef png [84 KiB] Thumbnail [39 KiB] tex code 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. Table_3.pdf [70 KiB] HiDef png [79 KiB] Thumbnail [37 KiB] tex code Systematic uncertainties on the measurement of the ${ J \mskip -3mu/\mskip -2mu\psi \mskip 2mu}$ --$\eta _ c$ mass difference. Table_4.pdf [71 KiB] HiDef png [101 KiB] Thumbnail [47 KiB] tex code Relative $p_{\mathrm{T}}$ -differential $\eta _ c$ prompt production cross-section. Table_5.pdf [66 KiB] HiDef png [65 KiB] Thumbnail [32 KiB] tex code Differential $\eta _ c$ prompt production cross-section. Table_6.pdf [89 KiB] HiDef png [67 KiB] Thumbnail [34 KiB] tex code Relative $p_{\mathrm{T}}$ -differential $\eta _ c$ production cross-section in inclusive $b$ -hadron decays. Table_7.pdf [65 KiB] HiDef png [70 KiB] Thumbnail [33 KiB] tex code The $p_{\mathrm{T}}$ -differential $\eta _ c$ production cross-section in inclusive $b$ -hadron decays. Table_8.pdf [88 KiB] HiDef png [70 KiB] Thumbnail [36 KiB] tex code

## Supplementary Material [file]

 Supplementary material full pdf supple[..].pdf [874 KiB] 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 Fig1S.pdf [482 KiB] HiDef png [104 KiB] Thumbnail [100 KiB] *C file Fig2S.pdf [391 KiB] HiDef png [282 KiB] Thumbnail [179 KiB] *C file Fig3S.pdf [372 KiB] HiDef png [243 KiB] Thumbnail [192 KiB] *C file Fig4S.pdf [347 KiB] HiDef png [244 KiB] Thumbnail [184 KiB] *C file Fig5S.pdf [347 KiB] HiDef png [255 KiB] Thumbnail [221 KiB] *C file Fig6S.pdf [284 KiB] HiDef png [256 KiB] Thumbnail [204 KiB] *C file

Created on 05 March 2021.