The nature of X(3900) and recognition of open charm effects

We identify open charm effects in a direct production process $e^+e^-\to J/\psi \pi^0$\mathrm{.}Auniquefeatureofthisprocessisthatthe$D\bar{D}^*+c.c.$thresholdislocatedatarelativelyisolatedenergyregion,i\mathrm{.}e\mathrm{.}$\sim 3.876
$\mathrm{G}\mathrm{e}\mathrm{V}$$,whichisfarawayfromthewell-establishedcharmonia$\psi(3770)$and$\psi(4040)$. Therefore, the cross section line-shape of this reaction provides an opportunity for singling out the open charm effects. A model-independent narrow enhancement between the thresholds of $D^0{\bar{D}}^{\ast 0}+c\mathrm{.}c\mathrm{.}$ and $D^{+}{D}^{\ast -}+c\mathrm{.}c\mathrm{.}$ is predicted. This study can also help understand the X(3900) enhancement recently observed by the Belle and BaBar Collaboration in $e^{+}{e}^{-}\to D\bar{D}+c\mathrm{.}c\mathrm{.}$ We also show that the open charm effects play a crucial role for our understanding of the long-standing “$\rho \pi$ puzzle”.