We report results on studies of the $e^{+}{e}^{-}$ annihilation into three-body $\mathrm{\Upsilon }(nS){\pi }^{+}{\pi }^{-}$ ($n=1,2,3$) final states including measurements of cross sections and the full amplitude analysis. The cross sections measured at $\sqrt{s}=10.866\mathrm{GeV}$ and corrected for the initial state radiation are $\sigma (e^{+}{e}^{-}\to \mathrm{\Upsilon }(1S){\pi }^{+}{\pi }^{-})=(2.27\pm 0.12\pm 0.14)\mathrm{pb}$, $\sigma (e^{+}{e}^{-}\to \mathrm{\Upsilon }(2S){\pi }^{+}{\pi }^{-})=(4.07\pm 0.16\pm 0.45)\mathrm{pb}$, and $\sigma (e^{+}{e}^{-}\to \mathrm{\Upsilon }(3S){\pi }^{+}{\pi }^{-})=(1.46\pm 0.09\pm 0.16)\mathrm{pb}$. Amplitude analysis of the three-body $\mathrm{\Upsilon }(nS){\pi }^{+}{\pi }^{-}$ final states strongly favors $I^G(J^P)=1^{+}(1^{+})$ quantum-number assignments for the two bottomonium-like $Z_b^{\pm }$ states, recently observed in the $\mathrm{\Upsilon }(nS){\pi }^{\pm }$ and $h_b(mP){\pi }^{\pm }$ ($m=1,2$) decay channels. The results are obtained with a $121.4{\mathrm{fb}}^{-1}$ data sample collected with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider.

• Received 7 March 2014

DOI:https://doi.org/10.1103/PhysRevD.91.072003