Effect of $Z_b$ states on ${\rm Y}(3S)\to {\rm Y}(1S)\pi \pi$ decays

Abstract

Within the framework of dispersion theory, we analyze the dipion transitions between the lightest ${\rm Y}$ states, ${\rm Y}(nS)\to {\rm Y}(mS)\pi \pi$ with $m<n\le 3$. 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 ${\rm Y}(3S)\to {\rm Y}(1S)\pi \pi$. 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 ${\rm Y}(nS)\pi$, which is only possible if a Flatté-like parametrization is used in the data analysis for the $Z_b$ states.

arXiv comment21 pages, 6 figures. The final version published in Phys. Rev. D 93, 034030 (2016)

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