Abstract : A search for flavour-changing neutral current decays of a top quark to an up-type quark ($q=u, c$) and the Standard Model Higgs boson, where the Higgs boson decays to $b\bar{b}$, is presented. The analysis searches for top quark pair events in which one top quark decays to $Wb$, with the $W$ boson decaying leptonically, and the other top quark decays to $Hq$. The search is based on $pp$ collisions at $\sqrt{s}=8$ TeV recorded in 2012 with the ATLAS detector at the CERN Large Hadron Collider and uses an integrated luminosity of 20.3 fb$^{-1}$. Data are analysed in the lepton-plus-jets final state, characterised by an isolated electron or muon and at least four jets. The search exploits the high multiplicity of $b$-quark jets characteristic of signal events, and employs a likelihood discriminant that uses the kinematic differences between the signal and the background, which is dominated by $t\bar{t} \to WbWb$ decays. No significant excess of events above the background expectation is found, and observed (expected) 95% CL upper limits of 0.56% (0.42%) and 0.61% (0.64%) are derived for the $t\to Hc$ and $t\to Hu$ branching ratios respectively. The combination of this search with other ATLAS searches in the $H \to \gamma\gamma$ and $H\to WW^*, \tau\tau$ decay modes significantly improves the sensitivity, yielding observed (expected) 95% CL upper limits on the $t\to Hc$ and $t\to Hu$ branching ratios of 0.46% (0.25%) and 0.45% (0.29%) respectively. The corresponding combined observed (expected) upper limits on the $|\lambda_{tcH}|$ and $|\lambda_{tuH}|$ couplings are 0.13 (0.10) and 0.13 (0.10) respectively. These are the most restrictive direct bounds on $tqH$ interactions measured so far.
