K-matrix Analysis of $e^{+}{e}^{-}$ Annihilation in the Bottomonium Region

Abstract

We perform the first global and unitary analysis of $e^{+}{e}^{-}\to b\bar{b}$ cross sections. We analyze exclusive cross sections in the $B\bar{B}$, $B^{\ast }\bar{B}(+c.c.)$, $B^{\ast }{\bar{B}}^{\ast }$, $B_s^{\ast }{\bar{B}}_s^{\ast }$, ${\rm Y}(nS){\pi }^{+}{\pi }^{-}$ and $h_b(nP){\pi }^{+}{\pi }^{-}$ channels as well as the total inclusive cross section for $b\bar{b}$ production. Pole positions and residues are determined for four vector states, which we associate with the ${\rm Y}(4S)$, ${\rm Y}(10750)$, ${\rm Y}(5S)$ (or ${\rm Y}(10860)$), and ${\rm Y}(6S)$ (or ${\rm Y}(11020)$). We find strong evidence for the new ${\rm Y}(10750)$ recently claimed by Belle, although with parameters not well constrained by the data. Results presented here cast doubt on the validity of branching ratios reported earlier using Breit-Wigner parameterizations or ratios of cross sections. We also compare our results with a selection of theoretical calculations for the vector bottomonium spectrum.

arXiv comment24 pages, 12 figures

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• Hidden-bottom hadronic transitions of ${\rm Y}(10753)$
• Status and Prospects of Exotic Hadrons at Belle II
• Production of $D^{(\ast )}{\bar{D}}^{(\ast )}$ near the thresholds in $e^{+}{e}^{-}$ annihilation
• Bottomonia in an unquenched quark model
• Measurement of the $e^{+}{e}^{-}\to B_s^0{\bar{B}}_s^{0}X$ cross section in the energy range from $10.63$ to $11.02$ GeV using inclusive $D_s^{\pm }$ and $D^0$ production
• Exotic hadrons associated with $b$-quark
• Amplitude analysis of $\psi (3686)\to \gamma K_S^0{K}_S^0$
• Search for $e^{+}{e}^{-}\to \gamma {\chi }_{bJ}$ ($J$ = 0, 1, 2) near $\sqrt{s}=10.746$ GeV at Belle II
• Improved measurement of Born cross sections for ${\chi }_{bJ}\omega$ and ${\chi }_{bJ}({\pi }^{+}{\pi }^{-}{\pi }^0{)}_{\mathrm{non}-\omega }$ ($J$ = 0, 1, 2) at Belle and Belle II