Amplitude analysis ofe+e−→ϒ(nS)π+π−ats=10.866 GeV

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Abstract

We report results on studies of the ${e}^{+}{e}^{\ensuremath{-}}$ annihilation into three-body $\mathrm{\ensuremath{\Upsilon}}(nS){\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ ($n=1,2,3$) final states including measurements of cross sections and the full amplitude analysis. The cross sections measured at $\sqrt{s}=10.866\text{ }\text{ }\mathrm{GeV}$ and corrected for the initial state radiation are $\ensuremath{\sigma}({e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\mathrm{\ensuremath{\Upsilon}}(1S){\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}})=\phantom{\rule{0ex}{0ex}}(2.27\ifmmode\pm\else\textpm\fi{}0.12\ifmmode\pm\else\textpm\fi{}0.14)\text{ }\text{ }\mathrm{pb}$, $\ensuremath{\sigma}({e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\mathrm{\ensuremath{\Upsilon}}(2S){\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}})=(4.07\ifmmode\pm\else\textpm\fi{}0.16\ifmmode\pm\else\textpm\fi{}0.45)\text{ }\text{ }\mathrm{pb}$, and $\ensuremath{\sigma}({e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\mathrm{\ensuremath{\Upsilon}}(3S){\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}})=\phantom{\rule{0ex}{0ex}}(1.46\ifmmode\pm\else\textpm\fi{}0.09\ifmmode\pm\else\textpm\fi{}0.16)\text{ }\text{ }\mathrm{pb}$. Amplitude analysis of the three-body $\mathrm{\ensuremath{\Upsilon}}(nS){\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ final states strongly favors ${I}^{G}({J}^{P})={1}^{+}({1}^{+})$ quantum-number assignments for the two bottomonium-like ${Z}_{b}^{\ifmmode\pm\else\textpm\fi{}}$ states, recently observed in the $\mathrm{\ensuremath{\Upsilon}}(nS){\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}$ and ${h}_{b}(mP){\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}$ ($m=1,2$) decay channels. The results are obtained with a $121.4\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ data sample collected with the Belle detector at the KEKB asymmetric-energy ${e}^{+}{e}^{\ensuremath{-}}$ collider.

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