  It is well recognized that looking for new physics at lower energy colliders
is a tendency which is complementary to high energy machines such as LHC. Based
on large database of BESIII, we may have a unique opportunity to do a good job.
In this paper we calculate the branching ratios of semi-leptonic processes
$D^+_s \to K^+ e^-e^+$, $D^+_s \to K^+ e^-\mu^+$ and leptonic processes $D^0
\to e^-e^+$, $D^0 \to e^-\mu^+$ in the frames of $U(1)'$ model, 2HDM and
unparticle separately. It is found that both the $U(1)'$ and 2HDM may influence
the semi-leptonic decay rates, but only the $U(1)'$ offers substantial
contributions to the pure leptonic decays and the resultant branching ratio of
$D^0 \to e^-\mu^+$ can be as large as $10^{-7}\sim10^{-8}$ which might be
observed at the future super $\tau$-charm factory.
