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.

arXiv comment14 pages, 3 figures, more discussions added

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• Hunting for $X_b$ via hidden bottomonium decays $X_b\to \pi \pi {\chi }_{bJ}$
• Predictions of ${\rm Y}(4S)\to h_b(1P,2P){\pi }^{+}{\pi }^{-}$ transitions
• Study of the $Y(4660)$ from a light-quark perspective
• Canonical interpretation of $Y(10750)$ and ${\rm Y}(10860)$ in the ${\rm Y}$ family
• $\varphi (2170)$ decaying to $\varphi \pi \pi$ and $\varphi K\bar{K}$
• Chromopolarizability of charm-beauty quarkonium from $B_c(2S)\to B_c\pi \pi$ transition
• Unified study of $B_s^0\to X(3872){\pi }^{+}{\pi }^{-}(K^{+}{K}^{-})$ and $B_s^0\to \psi (2S){\pi }^{+}{\pi }^{-}(K^{+}{K}^{-})$ processes
• Exotic hadrons associated with $b$-quark