Search for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>D</mml:mi><mml:mn>0</mml:mn></mml:msup><mml:mtext mathvariant="normal">−</mml:mtext><mml:msup><mml:mover accent="true"><mml:mi>D</mml:mi><mml:mo stretchy="true">¯</mml:mo></mml:mover><mml:mn>0</mml:mn></mml:msup></mml:math>mixing using semileptonic decay modes

Based on an $87\mathrm{\text{\ensuremath{-}}}{\mathrm{f}\mathrm{b}}^{\ensuremath{-}1}$ data set collected by the BABAR detector at the PEP-II asymmetric-energy $B$ Factory, a search for ${D}^{0}\mathrm{\text{\ensuremath{-}}}{\overline{D}}^{0}$ mixing has been made using the semileptonic decay modes ${D}^{*+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{D}^{0}$, ${D}^{0}\ensuremath{\rightarrow}{K}^{(*)}e\ensuremath{\nu}$ (+c.c.). The use of these modes allows unambiguous flavor tagging and a combined fit of the ${D}^{0}$ decay time and ${D}^{*+}\mathrm{\text{\ensuremath{-}}}{D}^{0}$ mass difference ($\ensuremath{\Delta}M$) distributions. The high-statistics sample of unmixed semileptonic ${D}^{0}$ decays is used to model the $\ensuremath{\Delta}M$ distribution and time dependence of mixed events directly from the data. Neural networks are used to select events and reconstruct the ${D}^{0}$. A result consistent with no charm mixing has been obtained, ${R}_{\mathrm{m}\mathrm{i}\mathrm{x}}=0.0023\ifmmode\pm\else\textpm\fi{}0.0012\ifmmode\pm\else\textpm\fi{}0.0004$. This corresponds to an upper limit of ${R}_{\mathrm{m}\mathrm{i}\mathrm{x}}<0.0042$ (90% C.L.).

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