Chromopolarizabilities of bottomonia from the ${\rm Y}(2S,3S,4S)\to {\rm Y}(1S,2S)\pi \pi$ transitions

Abstract

The dipion transitions ${\rm Y}(2S,3S,4S)\to {\rm Y}(1S,2S)\pi \pi$ are systematically studied by considering the mechanisms of the hadronization of soft gluons, exchanging the bottomoniumlike $Z_b$ states, and the bottom-meson loops. The strong pion-pion final-state interaction, especially including the channel coupling to $K\bar{K}$ in the $S$-wave, is taken into account in a model-independent way using the dispersion theory. Through fitting to the available experimental data, we extract values of the transition chromopolarizabilities $|{\alpha }_{{\rm Y}(mS){\rm Y}(nS)}|$, which measure the chromoelectric couplings of the bottomonia with soft gluons. It is found that the $Z_b$ exchange has a slight impact on the extracted chromopolarizablity values, and the obtained $|{\alpha }_{{\rm Y}(2S){\rm Y}(1S)}|$ considering the $Z_b$ exchange is $(0.29\pm 0.20){\text{GeV}}^{-3}$. Our results could be useful in studying the interactions of bottomonium with light hadrons.

Comments: 14 pages, 3 figures, more discussions added