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

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