  A search has been performed for pair production of heavy vector-like
down-type ($B$) quarks. The analysis explores the lepton-plus-jets final state,
characterized by events with one isolated charged lepton (electron or muon),
significant missing transverse momentum and multiple jets. One or more jets are
required to be tagged as arising from $b$-quarks, and at least one pair of jets
must be tagged as arising from the hadronic decay of an electroweak boson. The
analysis uses the full data sample of $pp$ collisions recorded in 2012 by the
ATLAS detector at the LHC, operating at a center-of-mass energy of 8 TeV,
corresponding to an integrated luminosity of 20.3 fb$^{-1}$. No significant
excess of events is observed above the expected background. Limits are set on
vector-like $B$ production, as a function of the $B$ branching ratios, assuming
the allowable decay modes are $B \rightarrow Wt/Zb/Hb$. In the chiral limit
with a branching ratio of 100% for the decay $B \rightarrow Wt$, the observed
(expected) 95% CL lower limit on the vector-like $B$ mass is 810 GeV (760 GeV).
In the case where the vector-like $B$ quark has branching ratio values
corresponding to those of an $SU(2)$ singlet state, the observed (expected) 95%
CL lower limit on the vector-like $B$ mass is 640 GeV (505 GeV). The same
analysis, when used to investigate pair production of a colored, charge 5/3
exotic fermion $T_{5/3}$, with subsequent decay $T_{5/3} \rightarrow Wt$, sets
an observed (expected) 95% CL lower limit on the $T_{5/3}$ mass of 840 GeV (780
GeV).
