$D$ wave bottomonia production from $Z_b^{(\prime )}$ decay

Abstract

In the present work, we investigate the dipion transitions between ${\rm Y}(5S)$ and ${{\rm Y}}_J(1D)$ with $J=1,2,3$. Our analysis indicates that the dominant sources of the anomalously large widths of ${\rm Y}(5S)\to {{\rm Y}}_J(1D){\pi }^{+}{\pi }^{-}$ should be $Z_b^{(\prime )}$, i.e., the dipion transitions occur via the cascade decays ${\rm Y}(5S)\to Z_b^{(\prime )\pm }{\pi }^{\mp }\to {{\rm Y}}_J(1D){\pi }^{+}{\pi }^{-}$. With the assumption that all the short ranged dynamics could be absorbed in a single cutoff with a model parameter $\alpha$, the present estimations indicate that in a reasonable parameter range the measured branching ratios of ${\rm Y}(5S)\to {{\rm Y}}_J(1D){\pi }^{+}{\pi }^{-}$ can be reproduced in magnitude, which further proves that the decays via $Z_b^{(\prime )}$ dominate the dipion transitions of ${\rm Y}(5S)$ to ${{\rm Y}}_J(1D)$. Moreover, we also predict the ratios of the branching fractions of $Z_b^{(\prime )}\to {{\rm Y}}_J(1D)\pi$, which in our calculations are largely independent of the parameter $\alpha$ and could be tested by further experiments in Belle II.

Comments: 9 pages, 5 figures, accepted for publication in the Phys.Rev.D