  We present the fully general, model independent study of a few rare
semileptonic $B$ decays that get dominant contributions from $W$-annihilation
and $W$-exchange diagrams, in particular $B^0 \to \bar{D}^0 \ell^+\ell^-$,
where $\ell = e,\mu$. We consider the most general Lagrangian for the decay,
and define three angular asymmetries in the Gottfried-Jackson frame, which are
sensitive to new physics. We show how these angular asymmetries can be easily
extracted from the distribution of events in the Dalitz plot for $B \to D
\ell^+ \ell^-$ decays. Especially a non-zero forward-backward asymmetry within
the frame would give the very first hint of possible new physics. These
observations are also true for related decay modes, such as $B^+ \to D^+ \ell^+
\ell^-$ and $B^0 \to D^0 \ell^+ \ell^-$. Moreover, these asymmetry signatures
are not affected by either $B^0$-$\bar{B}^0$ or $D^0$-$\bar{D}^0$ mixings.
Then, this implies that both $B^0 \to \bar{D}^0 \ell^+ \ell^-$ and $B^0 \to D^0
\ell^+ \ell^-$ as well as their CP conjugate modes can all be considered
together in our search for signature of new physics. Hence, it would be of
great importance to look for and study these decays in the laboratory, LHCb and
Belle II in particular.
