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.
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