  In this paper, we try to reveal the structure of the $Y(4660)$ from the
light-quark perspective. We study the dipion invariant mass spectrum and the
helicity angular distributions of the $e^+ e^- \to Y(4660) \to \psi(2S)
\pi^+\pi^-$ process. In particular, we consider the effects of different
light-quark SU(3) eigenstates inside the $Y(4660)$. The strong pion-pion
final-state interactions as well as the $K\bar{K}$ coupled channel in the
$S$-wave are taken into account model independently by using dispersion theory.
We find that the light-quark SU(3) octet state plays a significant role in this
transition, implying that the $Y(4660)$ contains a large light-quark component
and thus cannot be a conventional charmonium state. In the fit scheme
considering both the SU(3) singlet and SU(3) octet states, two solutions are
found. One solution differs significantly from the pure $[cs][\bar{c}\bar{s}]$
type fourquark scenario of the $Y(4660)$, while the result of the other
solution agrees with the pure $[cs][\bar{c}\bar{s}]$ type fourquark scenario of
the $Y(4660)$ within error bars. New measurement data with higher statistics in
the future will be helpful to better distinguish these two solutions.
