The first observation of the decay $\eta_{c}(2S) \to p \bar p$ is reported using protonproton collision data corresponding to an integrated luminosity of $3.0\rm fb^{1}$ recorded by the LHCb experiment at centreofmass energies of 7 and 8 TeV. The $\eta_{c}(2S)$ resonance is produced in the decay $B^{+} \to [c\bar c] K^{+}$. The product of branching fractions normalised to that for the $J/\psi$ intermediate state, ${\cal R}_{\eta_{c}(2S)}$, is measured to be \begin{align*} {\cal R}_{\eta_{c}(2S)}\equiv\frac{{\mathcal B}(B^{+} \to \eta_{c}(2S) K^{+}) \times {\mathcal B}(\eta_{c}(2S) \to p \bar p)}{{\mathcal B}(B^{+} \to J/\psi K^{+}) \times {\mathcal B}(J/\psi\to p \bar p)} = & (1.58 \pm 0.33 \pm 0.09)\times 10^{2}, \end{align*} where the first uncertainty is statistical and the second systematic. No signals for the decays $B^{+} \to X(3872) (\to p \bar p) K^{+}$ and $B^{+} \to \psi(3770) (\to p \bar p) K^{+}$ are seen, and the 95% confidence level upper limits on their relative branching ratios are found to be ${\cal R}_{X(3872)}<0.25\times10^{2}$ and ${\cal R}_{\psi(3770))}<0.10$. In addition, the mass differences between the $\eta_{c}(1S)$ and the $J/\psi$ states, between the $\eta_{c}(2S)$ and the $\psi(2S)$ states, and the natural width of the $\eta_{c}(1S)$ are measured as \begin{align*} M_{J/\psi}  M_{\eta_{c}(1S)} = & 110.2 \pm 0.5 \pm 0.9 \rm MeV, M_{\psi(2S)} M_{\eta_{c}(2S)} = & 52.5 \pm 1.7 \pm 0.6 \rm MeV, \Gamma_{\eta_{c}(1S)} = & 34.0 \pm 1.9 \pm 1.3 \rm MeV. \end{align*}
Invariant mass spectrum of the $p \bar{p} K^+$ candidates. The total fit curve and individual fit components are superimposed on the data. 
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Invariant mass spectrum of the $p \bar{p}$ candidates. Background in the $B^{+} \rightarrow p \bar p K^{+}$ distribution is subtracted using the sPlot technique as described in the text. The total fit curve is superimposed. 
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Animated gif made out of all figures. 
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Signal yields from the fit to the $p \bar p$ mass spectrum in $B^{+} \rightarrow p \bar p K^{+}$ decays. The fit fractions of the $\eta_c(1S)$ and the nonresonant component in the $J=0$ amplitude are $25\%$ and $65\%$ respectively. The fit fractions do not include uncertainties due to the ambiguities in the relative phase of the interfering amplitudes. Uncertainties are statistical only. 
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Systematic uncertainties in units of $10^{4}$ on the $\eta_{c}(2S)$, $X(3872)$ and $\psi(3770)$ branching fraction measurements relative to that of the $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu}$ . The efficiency contribution includes both the PID efficiency variation and the statistical error due to the finite size of the simulated samples. 
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Systematic uncertainties on the mass differences $M_{ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} }  M_{\eta_c(1S)}$, $M_{\psi(2S)}  M_{\eta_c(2S)}$ and the $\Gamma_{\eta_c(1S)}$ measurements. The systematic uncertainty associated to the momentum scale calibration is negligible for the total width $\Gamma_{\eta_c(1S)}$ measurement. 
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Created on 05 March 2021.