  In this work, we calculate the form factors for $J/\psi\to \bar{D}^{(*)0}$
induced by the flavor changing neutral currents (FCNC) in terms of the QCD sum
rules. Making use of these form factors, we further calculate the branching
fractions of semileptonic decays $J/\psi \to \bar{D}^{(*)0} l ^+ l^-$ ($l=e,
\mu$). In particular, we formulate the matrix element $<J/\psi|T_{\mu\nu}|
\bar{D}^{*0}>$ with $T_{\mu\nu}$ being a tensor current, which was not fully
discussed in previous literature. Our analysis indicates that if only the
standard model (SM) applies, the production of single charmed mesons at the
present electron-positron colliders is too small to be observed even the
resonance effects are included, therefore if an anomalous production rates are
observed, it would be a hint of new physics beyond SM. Even though the
predicted branching ratios are beyond the reach of present facilities which can
be seen from a rough order estimate, the more accurate formulation of the three
point correlation function derived in this work has theoretical significance
and the technique can also be applied to other places. In analog to some
complicated theoretical derivations which do not have immediate
phenomenological application yet, if the future experiments can provide
sufficient luminosity and accuracy, the results would be helpful.
