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.

Comments: 24 pages, 12 figures