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

In the present work, we investigate the dipion transitions between $\mathrm{{\rm Y}}(5S)$ and ${\mathrm{{\rm Y}}}_J(1D)$ with $J=1,2,3$. Our analysis indicates that the dominant sources of the anomalously large widths of $\Upsilon(5S)\to \Upsilon_J(1D) \pi^+ \pi^-$shouldbe$Z_b^{(\prime)}$, i.e., the dipion transitions occur via the cascade decays $\Upsilon(5S)\to Z_b^{(\prime)\pm} \pi^\mp \to \Upsilon_J(1D) \pi^+ \pi^-$. 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 $\mathrm{{\rm Y}}(5S)\to {\mathrm{{\rm Y}}}_J(1D){\pi }^{+}{\pi }^{-}$ can be reproduced in magnitude, which further proves that the decays via $Z_b^{(\mathrm{\prime })}$ dominate the dipion transitions of $\mathrm{{\rm Y}}(5S)$ to ${\mathrm{{\rm Y}}}_J(1D)$. Moreover, we also predict the ratios of the branching fractions of $Z_b^{(\mathrm{\prime })}\to {\mathrm{{\rm Y}}}_J(1D)\pi$, which in our calculations are largely independent of the parameter $\alpha$ and could be tested by further experiments in Belle II.