Charged bottomonium-like states $Z_b(10610)$ and $Z_b(10650)$ and the $\Upsilon(5S)\to \Upsilon(2S)\pi^+\pi^-$ decay

Inspired by the newly observed two charged bottomonium-like states, we consider the possible contribution from the intermediate $Z_b(10610)$ and $Z_b(10650)$ states to the $\Upsilon(5S)\to \Upsilon(2S)\pi^+\pi^-$ decay process, which naturally explains Belle's previous observation of the anomalous $\Upsilon(2S)\pi^+\pi^-$ production near the peak of $\Upsilon(5S)$ at $\sqrt s=10.87$ GeV [K.F. Chen {\it et al}. (Belle Collaboration), Phys. Rev. Lett. {\bf 100}, 112001 (2008)]. The resulting $d\Gamma(\Upsilon(5S)\to \Upsilon(2S)\pi^+\pi^-)/dm_{\pi^+\pi^-}$ and $d\Gamma(\Upsilon(5S)\to \Upsilon(2S)\pi^+\pi^-)/d\cos\theta$ distributions agree with Belle's measurement after inclusion of these $Z_b$ states. This formalism also reproduces the Belle observation of the double-peak structure and its reflection in $\Upsilon(2S)\pi^+$ invariant mass spectrum of $\Upsilon(5S)\to \Upsilon(2S)\pi^+\pi^-$ decay.