A discussion on the anomalous threshold enhancement of $J/\psi$ -- $\psi(3770)$ couplings and $X(6900)$ peak

Abstract

The attractive interaction between $J/\psi$ and $\psi(3770)$ has to be strong enough to form the molecular resonant structure, i.e., $X(6900)$. We argue that since $\psi(3770)$ decays predominantly into a $D\bar D$ pair, the interactions between $J/\psi$ and $\psi(3770)$ may be significantly enhanced due to the three point $D\bar D$ loop diagram. The enhancement comes from the anomalous threshold located at $t=-1.288$GeV$^2$, which effect propagates into the $s$-channel partial wave amplitude in the vicinity of $\sqrt{s}\simeq 6.9$GeV. This effect may be helpful in forming the $X(6900)$ peak.