  This Letter presents a search for a hidden-beauty counterpart of the
$X(3872)$ in the mass ranges 10.05--10.31 GeV and 10.40--11.00 GeV, in the
channel $X_b \to \pi^{+} \pi^{-} \Upsilon(1 \rm S)(\rightarrow\mu^+\mu^-)$,
using 16.2 fb$^{-1}$ of $\sqrt{s}=8$ TeV $pp$ collision data collected by the
ATLAS detector at the LHC. No evidence for new narrow states is found, and
upper limits are set on the product of the $X_b$ cross section and branching
fraction, relative to those of the $\Upsilon(2 \rm S)$, at the 95% confidence
level using the CL$_S$ approach. These limits range from 0.8% to 4.0%,
depending on mass. For masses above 10.1 GeV, the expected upper limits from
this analysis are the most restrictive to date. Searches for production of the
$\Upsilon(1^3 \rm{D}$$_J)$, $\Upsilon(10860)$, and $\Upsilon(11020)$ states
also reveal no significant signals.
