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

Within the framework of dispersion theory, we analyze the dipion transitions between the lightest $��$ states, $��(nS) \rightarrow ��(mS) ����$ 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 $����$ 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 $����$ mass spectrum of the decay $��(3S) \rightarrow ��(1S) ����$. 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 $��(nS)��$, which is only possible if a Flatt��-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)