Search for the rare decay<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:msup><mml:mi>μ</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>μ</mml:mi><mml:mo>−</mml:mo></mml:msup></mml:math>with the D0 detector

We present a search for the flavor-changing neutral current decay ${B}_{s}^{0}\ensuremath{\rightarrow}\ensuremath{\phi}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ using about $0.45\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of data collected in $p\overline{p}$ collisions at $\sqrt{s}=1.96\text{ }\text{ }\mathrm{TeV}$ with the D0 detector at the Fermilab Tevatron Collider. We find an upper limit on the branching ratio of this decay normalized to ${B}_{s}^{0}\ensuremath{\rightarrow}J/\ensuremath{\psi}\ensuremath{\phi}$ of $\frac{\mathcal{B}({B}_{s}^{0}\ensuremath{\rightarrow}\ensuremath{\phi}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}})}{\mathcal{B}({B}_{s}^{0}\ensuremath{\rightarrow}J/\ensuremath{\psi}\ensuremath{\phi})}<4.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ at the 95% C.L. Using the central value of the world average branching fraction of ${B}_{s}^{0}\ensuremath{\rightarrow}J/\ensuremath{\psi}\ensuremath{\phi}$, the limit corresponds to $\mathcal{B}({B}_{s}^{0}\ensuremath{\rightarrow}\ensuremath{\phi}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}})<4.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ at the 95% C.L., the most stringent upper bound to date.

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