The first observation of the $B^0_s\to\eta'\eta'$ decay is reported. The study is based on a sample of protonproton collisions corresponding to $3.0$ ${\rm fb^{1}}$ of integrated luminosity collected with the LHCb detector. The significance of the signal is $6.4$ standard deviations. The branching fraction is measured to be $[3.31 \pm 0.64 {\rm (stat)} \pm 0.28 {\rm (syst)} \pm 0.12 {\rm (norm)}]\times10^{5}$, where the third uncertainty comes from the $B^{\pm}\to\eta' K^{\pm}$ branching fraction that is used as a normalisation. In addition, the charge asymmetries of $B^{\pm}\to\eta' K^{\pm}$ and $B^{\pm}\to\phi K^{\pm}$, which are control channels, are measured to be $(0.2 \pm1.3)\%$ and $(+1.7\pm1.3)\%$, respectively. All results are consistent with theoretical expectations.
Distributions of the (top) $\eta ^{\prime} \eta ^{\prime} $, (bottom) $(\pi\pi\gamma )_1$ and $(\pi\pi\gamma )_2$ invariant masses for the $ B ^0_ s \rightarrow \eta ^{\prime} \eta ^{\prime} $ candidates with fit results overlaid. The $(\pi\pi\gamma )_1$ and $(\pi\pi\gamma )_2$ mass distributions are shown for the candidates with an $\eta ^{\prime} \eta ^{\prime} $ invariant mass within three standard deviations of the $ B ^0_ s $ mass. The components are the following: (dashed red curves) $ B ^0_ s \rightarrow \eta ^{\prime} \eta ^{\prime} $ signal, (longdashed blue curves) combinatorial background without an $\eta ^{\prime} $ resonance in the final state, (dotlongdashed black curves) partially reconstructed background without an $\eta ^{\prime} $ resonance, (shortdashed red, shortdashed blue curves) combinatorial background with one $\eta ^{\prime} $ resonance, and (dotdashed green, dotdashed black curves) partially reconstructed background with one $\eta ^{\prime} $ resonance. The total fit function is shown as the solid blue curves. 
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Distributions of the (top) $\eta ^{\prime} K ^\pm $ and (bottom) $\pi ^+ \pi ^ \gamma$ invariant masses for the $ B ^\pm \rightarrow \eta ^{\prime} K ^\pm $ candidates with fit results overlaid. The components are the following: (dashed red curves) $ B ^\pm \rightarrow \eta ^{\prime} K ^\pm $ signal, (longdashed blue curves) combinatorial background without an $\eta ^{\prime} $ resonance in the final state, and (dotted blue curves) combinatorial background with an $\eta ^{\prime} $ resonance. The total fit function is shown as the solid blue curves. 
fig2.pdf [30 KiB] HiDef png [347 KiB] Thumbnail [273 KiB] *.C file 

Distributions of the (top) $\phi K ^\pm $ and (bottom) $ K ^+ K ^ $ invariant masses for the $ B ^\pm \rightarrow \phi K ^\pm $ candidates with fit results overlaid The components are the following: (dashed red curves) $ B ^\pm \rightarrow \phi K ^\pm $ signal, (longdashed red curves) nonresonant $ B ^\pm \rightarrow K ^+ K ^ K ^\pm $ background, partially reconstructed $b$hadron background (longdashed blue curves) with or (dotdashed blue curves) without a $\phi$ resonance in the decay chain. The combinatorial background with or without a $\phi$ resonance is too small to be visible. The total fit function is shown as the solid blue curves. 
fig3.pdf [34 KiB] HiDef png [364 KiB] Thumbnail [289 KiB] *.C file 

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Created on 08 August 2020.