Chromopolarizability of charmonium and $\pi \pi$ final state interaction revisited

Abstract

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 $\kappa =0.139\pm \mathrm{0.005.}$ Our results could be useful in studying the interactions of charmonium with light hadrons.

8 pages, 1 figure

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• Deciphering the mechanism of $J/\psi$-nucleon scattering
• Chromopolarizability of charm-beauty quarkonium from $B_c(2S)\to B_c\pi \pi$ transition