Lowest-order diagrams for the $ B ^0_ s \rightarrow \eta ^{\prime} \phi $ decay. The spectator quark can become part of either the $\eta ^{\prime} $ or the $\phi $ meson, forming two different amplitudes (called PV and VP in the text).

Distributions of the (top left) $\pi^+\pi^-\gamma$ and (top right) $\eta ^{\prime} K^+K^-$ masses of the selected $ B ^0_ s \rightarrow \eta ^{\prime} \phi $ candidates, as well as of the (bottom left) $\pi^+\pi^-\gamma$ and (bottom right) $\eta ^{\prime} K ^+ $ masses of the selected $ B ^+ \rightarrow \eta ^{\prime} K ^+ $ candidates. The solid blue curves represent the result of the simultaneous two-dimensional fit described in the text, with the following components: $ B ^0_ s \rightarrow \eta ^{\prime} \phi $ and $ B ^+ \rightarrow \eta ^{\prime} K ^+ $ signals (red dashed), combinatorial backgrounds (blue dot-dot-dashed), combinatorial backgrounds with real $\eta ^{\prime} $ (green dotted), and $ B ^0_ s \rightarrow \phi \phi $ background (black dot-dashed).

Animated gif made out of all figures.

Theoretical predictions for the $ B ^0_ s \rightarrow \eta ^{\prime} \phi $ branching fraction.

Relative systematic uncertainties on the efficiency ratio $\epsilon( B ^+ \rightarrow \eta ^{\prime} K ^+ ) / \epsilon( B ^0_ s \rightarrow \eta ^{\prime} \phi )$.

Systematic uncertainties $\sigma_N$ and $\sigma_R$ on the fitted yield $N( B ^0_ s \rightarrow \eta ^{\prime} \phi )$ and on the yield ratio $R= N( B ^0_ s \rightarrow \eta ^{\prime} \phi )/N( B ^+ \rightarrow \eta ^{\prime} K^+ )$, respectively. The last line gives the quadratic sum of the individual uncertainties.