<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>K</mml:mi></mml:mrow></mml:math>-matrix analysis of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup><mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math> annihilation in the bottomonium region
N. Hüsken, R. E. Mitchell, Eric S. Swanson
Abstract
We perform the first global and unitary analysis of ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}b\overline{b}$ cross sections. We analyze exclusive cross sections in the $B\overline{B}$, ${B}^{*}\overline{B}(+\mathrm{c}.\mathrm{c}.)$, ${B}^{*}{\overline{B}}^{*}$, ${B}_{s}^{*}{\overline{B}}_{s}^{*}$, $\mathrm{\ensuremath{\Upsilon}}(nS){\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$, and ${h}_{b}(nP){\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ channels as well as the total inclusive cross section for $b\overline{b}$ production. Pole positions and residues are determined for four vector states, which we associate with the $\mathrm{\ensuremath{\Upsilon}}(4S)$, $\mathrm{\ensuremath{\Upsilon}}(10750)$, $\mathrm{\ensuremath{\Upsilon}}(5S)$ [or $\mathrm{\ensuremath{\Upsilon}}(10860)$], and $\mathrm{\ensuremath{\Upsilon}}(6S)$ [or $\mathrm{\ensuremath{\Upsilon}}(11020)$]. We find strong evidence for the new $\mathrm{\ensuremath{\Upsilon}}(10750)$ 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 parametrizations or ratios of cross sections. We also compare our results with a selection of theoretical calculations for the vector-bottomonium spectrum.