The puzzle of excessive non-$D\bar D$ component of the inclusive $ψ(3770)$ 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 $ψ(3770)$ and data is to be alleviated by taking final state interaction (FSI) into account. By assuming that $ψ(3770)$ overwhelmingly dissociates into $D\bar D$, then the final state interaction induces a secondary process, we calculate the branching ratios of $ψ(3770)\to D\bar D\to J/ψη, ρπ, ωη, K^*K$. Our results show that the branching ratio of $ψ(3770)\to \mathrm{non}-D\bar{D}$ can reach up to $\mathcal{B}_{\mathrm{non}-D\bar{D}}^{FSI}=(0.2\sim1.1)%$ while typical parameters $I=0.4$ GeV$^{-2}$ and $α=0.8\sim 1.3$ are adopted. This indicates that the FSI is obviously non-negligible.