The puzzle of excessive non-$D\bar{D}$ component of the inclusive $\psi (3770)$ decay and the long-distant contribution

Abstract

In this letter we suggest that the obvious discrepancy between theoretical prediction on the $\mathrm{non}-D\bar{D}$ decays of $\psi (3770)$ and data is to be alleviated by taking final state interaction (FSI) into account. By assuming that $\psi (3770)$ overwhelmingly dissociates into $D\bar{D}$, then the final state interaction induces a secondary process, we calculate the branching ratios of $\psi (3770)\to D\bar{D}\to J/\psi \eta ,\rho \pi ,\omega \eta ,K^{\ast }K$. Our results show that the branching ratio of $\psi (3770)\to \mathrm{non}-D\bar{D}$ can reach up to ${\mathcal{B}}_{\mathrm{non}-D\bar{D}}^{FSI}=(0.2\sim 1.1)$ while typical parameters $I=0.4$ GeV${}^{-2}$ and $\alpha =0.8\sim 1.3$ are adopted. This indicates that the FSI is obviously non-negligible.

Comments: 6 pages, 4 figures, 1 tables. More references and discussions added, typos corrected. Accepted by Phys. Lett. B