Effect of $Z_b$ states on $\Upsilon(3S)\to\Upsilon(1S)\pi\pi$ decays

TL;DR

This paper investigates how bottomoniumlike $Z_b$ states influence the dipion decay spectrum of $S$ to $
S$ states, showing that these exotic states can explain observed anomalies in the decay's two-peak structure.

Contribution

It demonstrates that including $Z_b$ states within dispersion theory explains the peculiar decay spectrum, highlighting the importance of proper coupling extraction using Flatté-like parametrization.

Findings

$Z_b$ states can explain the two-peak $S o
S \,
ext{S}$ decay spectrum.

Dispersion theory combined with $Z_b$ states reproduces experimental anomalies.

Proper coupling extraction requires Flatté-like parametrization.

Abstract

Within the framework of dispersion theory, we analyze the dipion transitions between the lightest $\Upsilon$ states, $\Upsilon(nS) \rightarrow \Upsilon(mS) \pi\pi$ with $m < n \leq 3$. In particular, we consider the possible effects of two intermediate bottomoniumlike exotic states $Z_b(10610)$ and $Z_b(10650)$. The $\pi\pi$ rescattering effects are taken into account in a model-independent way using dispersion theory. We confirm that matching the dispersive representation to the leading chiral amplitude alone cannot reproduce the peculiar two-peak $\pi\pi$ mass spectrum of the decay $\Upsilon(3S) \rightarrow \Upsilon(1S) \pi\pi$. The existence of the bottomoniumlike $Z_b$ states can naturally explain this anomaly. We also point out the necessity of a proper extraction of the coupling strengths for the $Z_b$ states to $\Upsilon(nS)\pi$, which is only possible if a Flatt\'e-like parametrization is used in the data analysis for the $Z_b$ states.