Are there the VP couplings in the psi(3770) non-charmed decays hidden behind the current experiment measurements?

A global analysis of the full amplitudes for $e^+e^- \to$ VP (Vector and Pseudoscalar) channels at $\sqrt{s}$ =3.773 GeV and 3.670 GeV, which were measured by the CLEO-c Collaboration, shows that those measurements are essentially nontrivial for searching for the $\psi(3770)$ non-$D\bar D$ decays. Unlike the nearly negative verdict on the $\psi(3770)$ strong decays to the VP channels in the original analysis of the CLEO-c data, there exist some unusual solutions that predict the remarkable strength of SU(3) symmetry VP decay of $\psi(3770)$ resonance, which give some clue to understand the mechanism of $\psi(3770)$ non-$D\bar D$ decays and to reexplain the well-known $\rho-\pi$ puzzle in the J/$\psi$ and $\psi(3686)$ decays.