Leading diagram corresponding to $ B ^0_ s \rightarrow \eta _ c \phi$ and $ B ^0_ s \rightarrow \eta _ c \pi ^+ \pi ^- $ decays, where the $\pi ^+ \pi ^- $ pair may arise from the decay of the $f_0(980)$ resonance.

Distribution of $p\bar p$ invariant-mass for $ B ^0_ s \rightarrow p\bar{p}\pi ^+ \pi ^- $ candidates obtained by the $_s{\cal P}lot$ technique. The solid black curve is the projection of the total fit result. The full blue, tight-cross-hatched red and wide-cross-hatched black histograms show the $\eta _ c $ , $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu}$ and nonresonant $p\bar p$ contributions, respectively. The structure visible around $3.15 $GeV is found to be consistant with a statistical fluctuation.

One-dimensional scan of $-2 \Delta \ln L$ as a function of the $\eta _ c $ yield in the fit to the $p\bar{p}$ invariant-mass distribution for $ B ^0_ s \rightarrow p\bar{p}\pi ^+ \pi ^- $ candidates. The dotted red and solid blue curves correspond to the result of the scan including statistical only and summed (statistical and systematic) uncertainties, respectively.

Distribution of the $p\bar p$ and each of the $4h$ invariant-mass spectra for $ B ^0_ s \rightarrow p\bar{p}(4h)\phi$ candidates obtained by the $_s{\cal P}lot$ technique. The solid black curve is the total result of the simultaneous fit. The full blue and tight-cross-hatched red histograms show the $\eta _ c $ and $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu}$ contributions, respectively. In addition, for each of the $4h$ modes, the wide-cross-hatched and dotted black histograms show the $4h_{\rm NR}$ and $4h_{\rm bkg}$ contributions, respectively. The dashed blue curves show the interference between $ B ^0_ s \rightarrow \eta _ c (\rightarrow 4h)\phi$ and $ B ^0_ s \rightarrow (4h)_{\rm NR}\phi$ amplitudes.

Distribution of the $p\bar{p}\pi ^+ \pi ^- $ invariant mass. Points with error bars show the data. The solid curve is the projection of the total fit result. The short-dashed blue, the dashed-double-dotted green, the dashed-single-dotted yellow and medium-dashed red curves show the $ B ^0_ s \rightarrow p\bar{p}\pi ^+ \pi ^- $, $ B ^0 \rightarrow p\bar{p}\pi ^+ \pi ^- $, $ B ^0 \rightarrow p\bar{p} K ^+ \pi ^- $ and combinatorial background contributions, respectively.

Distribution of the $p\bar{p} K ^+ K ^- $ (top) and $ K ^+ K ^- $ (bottom) invariant masses. Points with error bars show the data. The solid black curve is the projection of the total fit result. The short-dashed and dotted blue curves show the $ B ^0_ s \rightarrow p\bar{p}\phi$ and $ B ^0_ s \rightarrow p\bar{p} K ^+ K ^- $ contributions, respectively. The long-dashed and medium-dashed red curves show the contributions of the combinatorial background with prompt $\phi$ and NR $ K ^+ K ^- $, respectively. The dashed-double-dotted green, dashed-triple-dotted green and dashed-single-dotted-yellow curves show the $ B ^0 \rightarrow p\bar{p}\phi$, $ B ^0 \rightarrow p\bar{p} K ^+ K ^- $ and $ B ^0 \rightarrow p\bar{p} K ^+ \pi ^- $ contributions, respectively.

Distribution of the $2K2\pi K ^+ K ^- $ (top) and $ K ^+ K ^- $ (bottom) invariant masses. Points with error bars show the data. The solid black curve is the projection of the total fit result. The short-dashed and dotted blue curves show the $ B ^0_ s \rightarrow 2K2\pi\phi$ and $ B ^0_ s \rightarrow 2K2\pi K ^+ K ^- $ contributions, respectively. The long-dashed and medium-dashed red curves show the contributions of the combinatorial background with prompt $\phi$ and NR $ K ^+ K ^- $, respectively. The dashed-double-dotted and dashed-triple-dotted green curves show the $ B ^0 \rightarrow 2K2\pi\phi$ and $ B ^0 \rightarrow 2K2\pi K ^+ K ^- $ contributions, respectively.

Distribution of the $4\pi K ^+ K ^- $ (top) and $ K ^+ K ^- $ (bottom) invariant masses. Points with error bars show the data. The solid black curve is the projection of the total fit result. The short-dashed and dotted blue curves show the $ B ^0_ s \rightarrow 4\pi\phi$ and $ B ^0_ s \rightarrow 4\pi K ^+ K ^- $ contributions, respectively. The long-dashed and medium-dashed red curves show the contributions of the combinatorial background with prompt $\phi$ and NR $ K ^+ K ^- $, respectively. The dashed-double-dotted and dashed-triple-dotted green curves show the $ B ^0 \rightarrow 4\pi\phi$ and $ B ^0 \rightarrow 4\pi K ^+ K ^- $ contributions, respectively.

Distribution of the $4K K ^+ K ^- $ (top) and $ K ^+ K ^- $ (bottom) invariant masses. Points with error bars show the data. The solid black curve is the projection of the total fit result. The short-dashed and dotted blue curves show the $ B ^0_ s \rightarrow 4K\phi$ and $ B ^0_ s \rightarrow 4K K ^+ K ^- $ contributions, respectively. The long-dashed and medium-dashed red curves show the contributions of the combinatorial background with prompt $\phi$ and NR $ K ^+ K ^- $, respectively. The dashed-double-dotted and dashed-triple-dotted green curves show the $ B ^0 \rightarrow 4K\phi$ and $ B ^0 \rightarrow 4K K ^+ K ^- $ contributions, respectively.

Animated gif made out of all figures.

Ratio of efficiencies between the normalisation and signal channels for each final state.

Yields of the different final states as obtained from the fit to the $p\bar{p}\pi ^+ \pi ^- $ invariant-mass distribution and from the 2D fits in the $p\bar{p}(4h) K ^+ K ^- \times K ^+ K ^- $ invariant-mass planes. Only statistical uncertainties are reported. The abbreviation "n/a" stands for "not applicable".

Results of the fit to the $p\bar p$ invariant-mass spectra weighted for $ B ^0_ s \rightarrow p\bar{p}\pi ^+ \pi ^- $ candidates. Uncertainties are statistical only. The parameter $N_{\rm NR}$ corresponds to the yield of $B^0_s \rightarrow (p\bar p)_{\rm NR} \pi^+ \pi^-$ candidates. The $\eta _ c $ yield does not appear since it is parametrised as a function of $\mathcal{B} ( B ^0_ s \rightarrow \eta _ c \pi ^+ \pi ^- )$, the measured value of which is reported in Eq. 22.

Result of the simultaneous fit to the $p\bar{p}$ and $4h$ invariant-mass spectra. Uncertainties are statistical only. The $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu}$ and $\eta _ c $ magnitudes do not appear since they are set to unity as reference and parametrised as a function of $\mathcal{B} ( B ^0_ s \rightarrow \eta _ c \phi)$, respectively. In the simultaneous fit, the $m_{\eta _ c }$ and $m_{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} }$ parameters are shared across the four modes. The measured value of $\mathcal{B} ( B ^0_ s \rightarrow \eta _ c \phi)$ is reported in Eq. 23. The abbreviation "n/a" stands for "not applicable".

Fit fractions obtained from the parameters of the simultaneous fit to the $p\bar{p}$ and $4h$ invariant-mass spectra. Uncertainties are statistical only. Due to interference between $ B ^0_ s \rightarrow \eta _ c (\rightarrow 4h) \phi$ and $ B ^0_ s \rightarrow (4h)_{\rm NR} \phi$ amplitudes, for the $4h$ final states the sum of fit fractions, $\sum_k {\rm FF}_k $, may be different from unity. The abbreviation "n/a" stands for "not applicable".

Summary of systematic uncertainties. The "Sum" of systematic uncertainties is obtained from the quadratic sum of the individual sources, except the external branching fractions, which are quoted separately. All values are in $\%$ of the measured branching fractions. The abbreviation "n/a" stands for "not applicable".

Statistical correlation matrix for the parameters from the simultaneous fit to the $p\bar{p}$ and $4h$ invariant-mass spectra for $ B ^0_ s \rightarrow p\bar{p}\phi$ and $ B ^0_ s \rightarrow 4h\phi$ candidates.