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A search is presented for single production of a vector-like $B$ quarkdecaying into a Standard Model $b$-quark and a Standard Model Higgs boson,which decays into a $b\bar{b}$ pair. The search is carried out in 139 fb$^{-1}$of $\sqrt{s} = 13$ TeV proton-proton collision data collected by the ATLASdetector at the LHC between 2015 and 2018. No significant deviation from theStandard Model background prediction is observed, and mass-dependent exclusionlimits at the 95% confidence level are set on the resonance productioncross-section in several theoretical scenarios determined by the couplings$c_W$, $c_Z$ and $c_H$ between the $B$ quark and the Standard Model $W$, $Z$and Higgs bosons, respectively. For a vector-like $B$ occurring as an isospinsinglet, the search excludes values of $c_W$ greater than 0.45 for a $B$resonance mass ($m_B$) between 1.0 and 1.2 TeV. For 1.2 TeV < $m_B$ < 2.0 TeV,$c_W$ values larger than 0.50-0.65 are excluded. If the $B$ occurs as part of a$(B,Y)$ doublet, the smallest excluded $c_Z$ coupling values range between 0.3and 0.5 across the investigated resonance mass range 1.0 TeV < $m_B$ < 2.0 TeV.

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Search for single vector-like $B$ quark production and decay via  $B\rightarrow bH(b\bar{b})$ in $pp$ collisions at $\sqrt{s} = 13$ TeV with  the ATLAS detector