  One of the most important tasks in high energy physics is search for the
exotic states, such as glueball, hybrid and multi-quark states. The transitions
$\psi(ns)\to \psi(ms)+\pi\pi$ and $\Upsilon(ns)\to \Upsilon(ms)+\pi\pi$ attract
great attentions because they may reveal characteristics of hybrids. In this
work, we analyze those transition modes in terms of the theoretical framework
established by Yan and Kuang. It is interesting to notice that the intermediate
states between the two gluon-emissions are hybrids, therefore by fitting the
data, we are able to determine the mass spectra of hybrids. The ground hybrid
states are predicted as 4.23 GeV (for charmonium) and 10.79 GeV (for bottonium)
which do not correspond to any states measured in recent experiments, thus it
may imply that very possibly, hybrids mix with regular quarkonia to constitute
physical states. Comprehensive comparisons of the potentials for hybrids whose
parameters are obtained in this scenario with the lattice results are
presented.
