  We present a search for a neutral, long-lived particle $L$ that is produced
in $e^+e^-$ collisions and decays at a significant distance from the $e^+e^-$
interaction point into various flavor combinations of two oppositely charged
tracks. The analysis uses an $e^+e^-$ data sample with a luminosity of $489.1
\rm{fb}^{-1}$ collected by the BaBar detector at the $\Upsilon$(4S),
$\Upsilon$(3S), and $\Upsilon$(2S) resonances and just below the
$\Upsilon$(4S). Fitting the two-track mass distribution in search of a signal
peak, we do not observe a significant signal, and set 90% confidence level
upper limits on the product of the $L$ production cross section, branching
fraction, and reconstruction efficiency for six possible two-body $L$ decay
modes as a function of the $L$ mass. The efficiency is given for each final
state as a function of the mass, lifetime, and transverse momentum of the
candidate, allowing application of the upper limits to any production model. In
addition, upper limits are provided on the branching fraction $Br(B\to X_s L)$,
where $X_s$ is a strange hadronic system.
