# First observation of $B^{+} \to D_s^{+}K^{+}K^{-}$ decays and a search for $B^{+} \to D_s^{+}\phi$ decays

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## Abstract

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 centre-of-mass 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.

## Figures and captions

 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 [42 KiB] Thumbnail [10 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 [150 KiB] Thumbnail [54 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 [243 KiB] Thumbnail [82 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 [223 KiB] Thumbnail [66 KiB] *.C file Fig4b.eps [67 KiB] HiDef png [226 KiB] Thumbnail [65 KiB] *.C file Projections of the background-subtracted two-body 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 [125 KiB] Thumbnail [57 KiB] *.C file Fig5b.eps [19 KiB] HiDef png [168 KiB] Thumbnail [77 KiB] *.C file Confidence bands produced using the Feldman-Cousins approach. The green and yellow bands represent the statistical-only 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 [191 KiB] Thumbnail [67 KiB] *.C file Animated gif made out of all figures. PAPER-2017-032.gif Thumbnail

## Tables and captions

 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 [52 KiB] HiDef png [35 KiB] Thumbnail [6 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 [52 KiB] HiDef png [41 KiB] Thumbnail [7 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 [55 KiB] HiDef png [70 KiB] Thumbnail [11 KiB] tex code

Created on 16 February 2019.Citation count from INSPIRE on 21 February 2019.