# Observation of $\eta_{c}(2S) \to p \bar p$ and search for $X(3872) \to p \bar p$ decays

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## Abstract

The first observation of the decay $\eta_{c}(2S) \to p \bar p$ is reported using proton-proton collision data corresponding to an integrated luminosity of $3.0\rm \, fb^{-1}$ recorded by the LHCb experiment at centre-of-mass 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*}

## Figures and captions

 Invariant mass spectrum of the $p \bar{p} K^+$ candidates. The total fit curve and individual fit components are superimposed on the data. Fig1.pdf [32 KiB] HiDef png [252 KiB] Thumbnail [66 KiB] 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. Fig2.pdf [62 KiB] HiDef png [207 KiB] Thumbnail [57 KiB] Animated gif made out of all figures. PAPER-2016-016.gif Thumbnail

## Tables and captions

 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 non-resonant 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. Table_1.pdf [45 KiB] HiDef png [153 KiB] Thumbnail [23 KiB] tex code 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. Table_2.pdf [30 KiB] HiDef png [51 KiB] Thumbnail [8 KiB] tex code 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. Table_3.pdf [52 KiB] HiDef png [45 KiB] Thumbnail [7 KiB] tex code

Created on 19 April 2019.Citation count from INSPIRE on 24 April 2019.