Evidence for<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:mi>ϕ</mml:mi><mml:mi>ϕ</mml:mi></mml:math>Decay and Measurements of Branching Ratio and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi>C</mml:mi><mml:mi>P</mml:mi></mml:mrow></mml:msub></mml:math>for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>B</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:mo>→</mml:mo><mml:mi>ϕ</mml:mi><mml:msup><mml:mi>K</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:math>

We present the first evidence of charmless decays of the ${B}_{s}^{0}$ meson, the decay ${B}_{s}^{0}\ensuremath{\rightarrow}\ensuremath{\phi}\ensuremath{\phi}$, and a measurement of the branching ratio $\mathrm{BR}({B}_{s}^{0}\ensuremath{\rightarrow}\ensuremath{\phi}\ensuremath{\phi})$ using $180\text{ }\text{ }{\mathrm{pb}}^{\ensuremath{-}1}$ of data collected by the CDF II experiment at the Fermilab Tevatron collider. In addition, the BR and direct $CP$ asymmetry for the ${B}^{+}\ensuremath{\rightarrow}\ensuremath{\phi}{K}^{+}$ decay are measured. We obtain $\mathrm{BR}({B}_{s}^{0}\ensuremath{\rightarrow}\ensuremath{\phi}\ensuremath{\phi})=[{14}_{\ensuremath{-}5}^{+6}(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}6(\mathrm{syst})]\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$, $\mathrm{BR}({B}^{+}\ensuremath{\rightarrow}\ensuremath{\phi}{K}^{+})=[7.6\ifmmode\pm\else\textpm\fi{}1.3(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.6(\mathrm{syst})]\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$, and ${A}_{CP}({B}^{+}\ensuremath{\rightarrow}\ensuremath{\phi}{K}^{+})=\ensuremath{-}0.07\ifmmode\pm\else\textpm\fi{}0.17(\mathrm{stat})\genfrac{}{}{0}{}{+0.03}{\ensuremath{-}0.02}(\mathrm{syst})$. Both decays are governed in the standard model by second order (penguin) $b\ensuremath{\rightarrow}s\overline{s}s$ amplitudes.

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