Effect of $Z_b$ states on $Υ(3S)\toΥ(1S)ππ$ decays

Abstract

Within the framework of dispersion theory, we analyze the dipion transitions between the lightest $Υ$ states, $Υ(nS) \rightarrow Υ(mS) ππ$ 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 $ππ$ 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 $ππ$ mass spectrum of the decay $Υ(3S) \rightarrow Υ(1S) ππ$. 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 $Υ(nS)π$, which is only possible if a Flatté-like parametrization is used in the data analysis for the $Z_b$ states.

21 pages, 6 figures. The final version published in Phys. Rev. D 93, 034030 (2016)