A search for $B^{+} \to D_s^{+}K^{+}K^{}$ decays is performed using $pp$ collision data corresponding to an integrated luminosity of 4.8 fb$^{1}$, collected at centreofmass energies of 7, 8 and 13$ $TeV with the LHCb experiment. A significant signal is observed for the first time and the branching fraction is determined to be \begin{equation*} \mathcal{B}(B^{+} \to D_s^{+}K^{+}K^{} ) = (7.1 \pm 0.5 \pm 0.6 \pm 0.7) \times 10^{6}, \end{equation*} where the first uncertainty is statistical, the second systematic and the third due to the uncertainty on the branching fraction of the normalisation mode $B^{+} \to D_s^{+} \overline{ D}^{0}$. A search is also performed for the pure annihilation decay $B^{+} \to D_s^{+}\phi$. No significant signal is observed and a limit of \begin{equation*} \mathcal{B}(B^{+} \to D_s^{+}\phi) < 4.9 \times 10^{7} (4.2 \times 10^{7}) \end{equation*} is set on the branching fraction at 95$\%$ (90$\%$) confidence level.
Dominant diagram for the (left) $ B ^+ \rightarrow D ^+_ s K ^+ K ^ $ decay and (right) annihilation diagram for the $ B ^+ \rightarrow D ^+_ s \phi $ decay in the Standard Model. 
Fig1.pdf [41 KiB] HiDef png [43 KiB] Thumbnail [29 KiB] *.C file 

Distributions of (left) $\cos{\theta_{K}}$ and (right) $m( K ^+ K ^ )$ in $ B ^+ \rightarrow D ^+_ s \phi $ decays, as determined from simulated events. The vertical lines represent the limits of the two categories used for each variable. In the $m( K ^+ K ^ )$ distribution, the area within the dashed red lines represents the $\phi $ signal region, and the two areas between the dashed red and blue lines represent the $\phi $ sideband region. The $ B ^+ \rightarrow D ^+_ s \phi $ signal decays are seen to primarily contribute to the $\phi$ signal region and the $\cos{\theta_{K}} > 0.4$ category. 
Fig2.eps [14 KiB] HiDef png [145 KiB] Thumbnail [136 KiB] *.C file 

Mass distribution of $ B ^+ \rightarrow D ^+_ s K ^+ K ^ $ candidates. The result of the fit to the data using the model described in Sec. 4.1 is overlaid, with the PDF components given in the legend. 
Fig3.eps [249 KiB] HiDef png [196 KiB] Thumbnail [99 KiB] *.C file 

Mass distribution of $ B ^+ \rightarrow D ^+_ s \phi $ candidates in (top) the $\phi $ mass region, and (bottom) the $\phi $ mass sideband. The plots on the left are in the helicity bin $\cos{\theta_{K}}>0.4$ and the right are in $\cos{\theta_{K}}<0.4$. The result of the fit to the data using the model described in Sec. 4.1 is overlaid, with the PDF components given in the legend. The $ B ^+ \rightarrow D ^+_ s \phi $ decays (black) are expected to primarily contribute to the $\phi$ region with $\cos{\theta_{K}} > 0.4$. 
Fig4a.eps [71 KiB] HiDef png [182 KiB] Thumbnail [76 KiB] *.C file 

Fig4b.eps [67 KiB] HiDef png [183 KiB] Thumbnail [75 KiB] *.C file 

Projections of the backgroundsubtracted twobody invariant masses (left) $m( D ^+_ s K ^ )$ and (right) $m( K ^+ K ^ )$ for $ B ^+ \rightarrow D ^+_ s K ^+ K ^ $ decays. These plots are additionally weighted by a factor $1/\epsilon^{\text{ratio}}_{i}$ to correct for the efficiency variation across the phase space. An expansion of the $\phi $ region of $m( K ^+ K ^ )$ is inset where the same $\phi $ signal region and $\phi $ sideband region have been represented as in Fig. 2. 
Fig5a.eps [13 KiB] HiDef png [99 KiB] Thumbnail [55 KiB] *.C file 

Fig5b.eps [19 KiB] HiDef png [171 KiB] Thumbnail [179 KiB] *.C file 

Confidence bands produced using the FeldmanCousins approach. The green and yellow bands represent the statisticalonly 90% and 95% CL bands. The black dotted line represents the 95% limit including systematic uncertainties. The measured value of the branching fraction is shown by the vertical red line, and the corresponding 95% CL limits, with and without systematic uncertainties, are represented by the dotted red lines. 
Fig6.eps [13 KiB] HiDef png [193 KiB] Thumbnail [164 KiB] *.C file 

Animated gif made out of all figures. 
PAPER2017032.gif Thumbnail 
Fractions of $ B ^+ \rightarrow D ^+_ s \phi $ candidates expected in the helicity and $m( K ^+ K ^ )$ invariant mass categories of the simultaneous fit. 
Table_1.pdf [66 KiB] HiDef png [29 KiB] Thumbnail [13 KiB] tex code 

Fractions of $ B ^+ \rightarrow D ^+_ s K ^+ K ^ $ candidates assumed to contribute to each helicity and $m( K ^+ K ^ )$ invariant mass categories of the simultaneous fit. The uncertainties shown are calculated from the range of fractions obtained by assuming different contributing resonances, as detailed in Sec. 4.1. 
Table_2.pdf [66 KiB] HiDef png [34 KiB] Thumbnail [14 KiB] tex code 

Systematic uncertainties contributing to the measurements of $\mathcal{B}( B ^+ \rightarrow D ^+_ s \phi )$ and $\mathcal{B}( B ^+ \rightarrow D ^+_ s K ^+ K ^ )$. The systematic uncertainty from the normalisation branching fraction is also included. 
Table_3.pdf [70 KiB] HiDef png [59 KiB] Thumbnail [27 KiB] tex code 
Created on 14 January 2021.