Further understanding of the non-$D\bar D$ decays of $\psi(3770)$

TL;DR

This paper investigates the non-Dar D decays of 3770 into light vector and pseudoscalar mesons, emphasizing the dominant role of long-distance strong interactions via intermediate charmed meson loops, and relates these decays to those of 3686 to constrain the model.

Contribution

It provides a detailed analysis of the non-Dar D decays of 3770, highlighting the significance of long-distance strong interactions and linking these decays to 3686 decays for parameter constraints.

Findings

Long-distance strong interactions via intermediate meson loops are crucial in 3770 decays.

Electromagnetic interactions have minimal impact on these decay processes.

The decay mechanisms of 3770 can be related to those of 3686, aiding in understanding the decay dynamics.

Abstract

We provide details of the study of $\psi(3770)$ non-$D\bar D$ decays into $VP$, where $V$ and $P$ denote light vector meson and pseudoscalar meson, respectively. We find that the electromagnetic (EM) interaction plays little role in these processes, while the strong interaction dominates. The strong interaction can be separated into two parts, i.e. the short-distance part probing the wave function at origin and the long-distance part reflecting the soft gluon exchanged dynamics. The long-distance part is thus described by the intermediate charmed meson loops. We show that the transition of $\psi(3770)\to VP$ can be related to $\psi(3686)\to VP$ such that the parameters in our model can be constrained by comparing the different parts in $\psi(3770)\to VP$ to those in $\psi(3686)\to VP$. Our quantitative results confirm the findings of [Zhang {\it et al.}, Phys. Rev. Lett. 102, 172001 (2009)] that the OZI-rule-evading long-distance strong interaction via the IML plays an important role in $\psi(3770)$ decays, and could be a key towards a full understanding of the mysterious $\psi(3770)$ non-$D\bar{D}$ decay mechanism.