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

TL;DR

This paper investigates how final state interactions can explain the unexpectedly large non-Dar D decay component of the $\psi(3770)$ particle, showing that secondary processes significantly contribute to these decays.

Contribution

The study introduces a model accounting for final state interactions to explain the non-Dar D decay component of $\psi(3770)$, providing quantitative estimates of its branching ratios.

Findings

Final state interactions can account for up to 1.1% of non-Dar D decays.

Calculated branching ratios depend on parameters like $I$ and $\alpha$.

FSI effects are significant and should not be neglected in decay analyses.

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 $\psi(3770)\to D\bar D\to J/\psi\eta, \rho\pi, \omega\eta, K^*K$. Our results show that the branching ratio of $\psi(3770)\to \mathrm{non}-D\bar{D}$ can reach up to $\mathcal{B}_{\mathrm{non}-D\bar{D}}^{FSI}=(0.2\sim1.1)%$ 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.