Chromo-polarizability and pipi final state interaction

The chromo-polarizability of a quarkonium state is a measure of the amplitude of the $E1$-$E1$ chromo-electric interaction of the quarkonium with soft gluon fields and can be measured in the heavy quarkonium decays. Based on the chiral unitary approach, formulas with modification caused by the $S$ wave $\pi\pi$ final state interaction (FSI) for measuring the chromo-polarizabilities are given. It is shown that the effect of the $S$ wave $\pi\pi$ FSI is very important in extracting chromo-polarizabilities from the experimental data. The resultant values with the FSI are reduced to about 1/3 of those determined without the FSI. The consequences of the FSI correction in the $J/\psi$-nucleon scattering near the threshold are also discussed. The estimated lower bound of the total cross section is reduced from about 17 mb to 2.9 mb, which agrees with the experimental data point and is compatible with the previously estimated values in the literature. In order to understand the interaction of heavy quarkonia with light hadrons at low energies better and to obtain the chromo-polarizabilities of quarkonia accurately, more data should be accumulated. This can be done in the $J/\psi \to \pi^+\pi^-l^+l^-$ decay at BES-III and CLEO-c and in the $\Upsilon \to \pi^+\pi^-l^+l^-$ decay at B factories.