  The production of the resonance $X(3823)$, identified as the charmonium
$^3D_2$ state, in the process $e^+e^- \to \pi \pi X(3823)$ has been recently
reported by BESIII. It is pointed out that this process is fully described, up
to one overall coupling constant, in the soft pion limit. An interpretation of
the available and possible future data within the discussed theoretical
framework may reveal new features of the charmoniumlike states. In particular,
the observed relative yield for this process at different energies strongly
suggests a very significant enhancement of the amplitude at the charmoniumlike
peak near 4.36\,GeV.
