  In contrast with $B^0-\bar B^0$, $B_s-\bar B_s$ mixing where the standard
model (SM) contributions overwhelm that of new physics beyond standard model
(BSM), a measured relatively large $D^0-\bar D^0$ mixing where the SM
contribution is negligible, definitely implies the existence of new physics
BSM. It is natural to consider that the rare decays of D meson might be more
sensitive to new physics, and the rare decay $D^0\to \mu^+\mu^-$ could be an
ideal area to search for new physics because it is a flavor changing process.
In this work we look for a trace of new physics BSM in the leptonic decays of
$D^0$, concretely we discuss the contributions of unparticle or an extra gauge
boson $Z'$ while imposing the constraints set by fitting the $D^0-\bar D^0$
mixing data. We find that the long-distance SM effects for $D^0\to l\bar l$
still exceed those contributions of the BSM under consideration, but for a
double-flavor changing process such as $D^0\to \mu^{\pm}e^{\mp}$, the new
physics contribution would be significant.
