  The most recent experimental data for all measured production and decay
channels of the bottomonium-like states $Z_b(10610)$ and $Z_b(10650)$ are
analysed simultaneously using solutions of the Lippmann-Schwinger equations
which respect constraints from unitarity and analyticity. The interaction
potential in the open-bottom channels $B^{(*)}\bar{B}^{*}+\mbox{c.c.}$ contains
short-range interactions as well as one-pion exchange. It is found that the
long-range interaction does not affect the line shapes as long as only $S$
waves are considered. Meanwhile, the line shapes can be visibly modified once
$D$ waves, mediated by the strong tensor forces from the pion exchange
potentials, are included. However, in the fit they get balanced largely by a
momentum dependent contact term that appears to be needed also to render the
results for the line shapes independent of the cut-off. The resulting line
shapes are found to be insensitive to various higher-order interactions
included to verify stability of the results. Both $Z_b$ states are found to be
described by the poles located on the unphysical Riemann sheets in the vicinity
of the corresponding thresholds. In particular, the $Z_b(10610)$ state is
associated with a virtual state residing just below the $B\bar{B}^{*}/\bar
B{B}^{*}$ threshold while the $Z_b(10650)$ state most likely is a shallow state
located just above the $B^*\bar{B}^{*}$ threshold.
