$Z_b/Z_b^\prime \to \Upsilon\pi$ and $h_b \pi$ decays in intermediate meson loops model

Abstract

With the recent measurement of $Z_b(10610)$ and $Z_b(10650)\to B\bar{B}^*+c.c.$ and $B^*\bar{B}^*$, we investigate the transitions from the $Z_b(10610)$ and $Z_b(10650)$ to bottomonium states with emission of a pion via intermediate $B \ {B}^*$ meson loops. The experimental data can be reproduced in this approach with a commonly accepted range of values for the form factor cutoff parameter $\alpha$. The $\Upsilon(3S)\pi$ decay channels appear to experience obvious threshold effects which can be understood by the property of the loop integrals. By investigating the $\alpha$-dependence of partial decay widths and ratios between different decay channels, we show that the intermediate $B \ {B}^*$ meson loops are crucial for driving the transitions of $Z_b/Z_b'\to \Upsilon(nS)\pi$ with $n = 1, 2, 3$, and $h_b(mP)\pi$ with $m = 1$ and 2.