  We perform the first global and unitary analysis of $e^+e^-\to b\bar{b}$
cross sections. We analyze exclusive cross sections in the $B\bar{B}$, $B^*
\bar{B}(+c.c.)$, $B^*\bar{B}^*$, $B_s^*\bar{B}_s^*$, $\Upsilon(nS)\pi^+\pi^-$
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 $\Upsilon(4S)$, $\Upsilon(10750)$,
$\Upsilon(5S)$ (or $\Upsilon(10860)$), and $\Upsilon(6S)$ (or
$\Upsilon(11020)$). We find strong evidence for the new $\Upsilon(10750)$
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 parameterizations or ratios of cross
sections. We also compare our results with a selection of theoretical
calculations for the vector bottomonium spectrum.
