Measurement of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>B</mml:mi><mml:mo>→</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mi>s</mml:mi></mml:msub><mml:msup><mml:mi>ℓ</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>ℓ</mml:mi><mml:mo>−</mml:mo></mml:msup></mml:math>Branching Fraction with a Sum over Exclusive Modes

We measure the branching fraction for the flavor-changing neutral-current process $B\ensuremath{\rightarrow}{X}_{s}{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ with a sample of $89\ifmmode\times\else\texttimes\fi{}{10}^{6}$ $\ensuremath{\Upsilon}(4S)\ensuremath{\rightarrow}B\overline{B}$ events recorded with the BABAR detector at the PEP-II ${e}^{+}{e}^{\ensuremath{-}}$ storage ring. The final state is reconstructed from ${e}^{+}{e}^{\ensuremath{-}}$ or ${\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ pairs and a hadronic system ${X}_{s}$ consisting of one ${K}^{\ifmmode\pm\else\textpm\fi{}}$ or ${K}_{S}^{0}$ and up to two pions, with at most one ${\ensuremath{\pi}}^{0}$. We observe a signal of $40\ifmmode\pm\else\textpm\fi{}10(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t})\ifmmode\pm\else\textpm\fi{}2(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t})$ events and extract the inclusive branching fraction $\mathcal{B}(B\ensuremath{\rightarrow}{X}_{s}{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}})=\mathbf{(}5.6\ifmmode\pm\else\textpm\fi{}1.5(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t})\ifmmode\pm\else\textpm\fi{}0.6(\mathrm{e}\mathrm{x}\mathrm{p}\text{ }\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t})\ifmmode\pm\else\textpm\fi{}1.1(\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{l}\text{ }\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t})\mathbf{)}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ for ${m}_{{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}}&gt;0.2\text{ }\mathrm{G}\mathrm{e}\mathrm{V}\mathrm{/}{c}^{2}$.

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