Chromopolarizability of charm-beauty quarkonium from $B_c(2S)\to B_c\pi \pi$ transition

The chromopolarizability of a charm-beauty quarkonium characterizes its interaction with soft gluonic fields and can be probed through heavy quarkonium decays. Using the dispersion theory which considers the $\pi \pi$ final state interaction model-independently, we analyze the transition $B_c(2S)\to B_c{\pi }^{+}{\pi }^{-}$ and determine the chromopolarizability ${\alpha }_{B_c(2S)B_c}=(0.66\pm 0.25)$ GeV${}^{-3}$ and the parameter $\kappa =-0.02\pm 0.13$. Our results indicate that the transitional chromopolarizability of the $c\bar{b}$ state lies between the transitional chromopolarizabilities of the $c\bar{c}$ and $b\bar{b}$ states. These findings provide valuable insights into the interactions of charm-beauty quarkonium with light hadrons.