  The chromopolarizability of a quarknonium describes the quarknonium's
interaction with soft gluonic fields and can be measured in the heavy
quarkonium decays. Within the framework of dispersion theory which consider the
$\pi\pi$ final state interaction (FSI) model-independently, we analyze the
transition $\psi^\prime\to J/\psi\pi^+\pi^-$ and obtain the
chromopolarizability $\alpha_{\psi^\prime \psi}$ and the parameter $\kappa$. It
is found that the $\pi\pi$ FSI plays an important role in extracting the
chromopolarizability from the experimental data. The obtained
chromopolarizability with the FSI is reduced to about 1/2 of that without the
FSI. With the FSI, we determine the chromopolarizability
$|\alpha_{\psi^\prime\psi}|=(1.44\pm 0.02)$ GeV$^{-3}$ and the parameter
$\kappa=0.139\pm 0.005.$ Our results could be useful in studying the
interactions of charmonium with light hadrons.
