Observation of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msubsup><mml:mi>B</mml:mi><mml:mi>s</mml:mi><mml:mn>0</mml:mn></mml:msubsup><mml:mo>→</mml:mo><mml:msup><mml:mi>K</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>K</mml:mi><mml:mo>−</mml:mo></mml:msup></mml:math>and Measurements of Branching Fractions of Charmless Two-Body Decays of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>B</mml:mi><mml:mn>0</mml:mn></mml:msup></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msubsup><mml:mi>B</mml:mi><mml:mi>s</mml:mi><mml:mn>0</mml:mn></mml:msubsup></mml:math>Mesons in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mover accent="true"><mml:mi>p</mml:mi><mml:mo>¯</mml:mo></mml:mover><mml:mi>p</mml:mi></mml:math>Collisions at<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msqrt><mml:mi>s</mml:mi></mml:msqrt><mml:mo>=</mml:mo><mml:mn>1.96</mml:mn><mml:mtext> </mml:mtext><mml:mtext> </mml:mtext><mml:mi>TeV</mml:mi></mml:math>

We search for decays of the type ${B}_{(s)}^{0}\ensuremath{\rightarrow}{h}^{+}{h}^{\ensuremath{'}\ensuremath{-}}$ (where $h,{h}^{\ensuremath{'}}=K$ or $\ensuremath{\pi}$) in $180\text{ }\text{ }{\mathrm{pb}}^{\ensuremath{-}1}$ of $\overline{p}p$ collisions collected at the Tevatron by the upgraded Collider Detector at Fermilab. We report the first observation of the new mode ${B}_{s}^{0}\ensuremath{\rightarrow}{K}^{+}{K}^{\ensuremath{-}}$ with a yield of $236\ifmmode\pm\else\textpm\fi{}32$ events, corresponding to $({f}_{s}/{f}_{d})\ifmmode\times\else\texttimes\fi{}\mathcal{B}({B}_{s}^{0}\ensuremath{\rightarrow}{K}^{+}{K}^{\ensuremath{-}})/\mathcal{B}({B}^{0}\ensuremath{\rightarrow}{K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}})=0.46\ifmmode\pm\else\textpm\fi{}0.08(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.07(\mathrm{syst})$, where ${f}_{s}/{f}_{d}$ is the ratio of production fractions of ${B}_{s}^{0}$ and ${B}^{0}$. We find results in agreement with world averages for the ${B}^{0}$ modes, and set the following new limits at 90% C.L.: $\mathcal{B}({B}_{s}^{0}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+})&lt;5.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ and $\mathcal{B}({B}_{s}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}})&lt;1.7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$.

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