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

TL;DR

This paper investigates the decay mechanisms of $S$ bottomonium states into $J(1D)$ states via $Z_b^{( extprime)}$ intermediaries, showing that these cascade decays dominate and predicting testable branching ratios.

Contribution

It introduces a model explaining the dominant decay pathway of $S$ to $J(1D)$ bottomonia through $Z_b^{( extprime)}$ states, with parameter-independent predictions for branching ratios.

Findings

Decay via $Z_b^{( extprime)}$ explains large widths.

Model reproduces experimental branching ratios.

Predicts branching fraction ratios testable by Belle II.

Abstract

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