Search for flavour-changing neutral-current couplings between the top quark and the Higgs boson in multi-lepton final states in 13 TeV $pp$ collisions with the ATLAS detector

A search is presented for flavour-changing neutral-current interactions involving the top quark, the Higgs boson and an up-type quark ($q=u,c$) with the ATLAS detector at the Large Hadron Collider. The analysis considers leptonic decays of the top quark along with Higgs boson decays into two $W$ bosons, two $Z$ bosons or a ${\tau }^{+}{\tau }^{-}$ pair. It focuses on final states containing either two leptons (electrons or muons) of the same charge or three leptons. The considered processes are $t\bar{t}$ and $Ht$ production. For the $t\bar{t}$ production, one top quark decays via $t\to Hq$. The proton-proton collision data set analysed amounts to 140 fb${}^{-1}$ at $\sqrt{s}=13$ TeV. No significant excess beyond Standard Model expectations is observed and upper limits are set on the $t\to Hq$ branching ratios at 95% confidence level, amounting to observed (expected) limits of $\mathcal{B}(t\to Hu)<2.8(3.0)\times {10}^{-4}$ and $\mathcal{B}(t\to Hc)<3.3(3.8)\times {10}^{-4}$. Combining this search with other searches for $tHq$ flavour-changing neutral-current interactions previously conducted by ATLAS, considering $H\to b\bar{b}$ and $H\to \gamma \gamma$ decays, as well as $H\to {\tau }^{+}{\tau }^{-}$ decays with one or two hadronically decaying $\tau$-leptons, yields observed (expected) upper limits on the branching ratios of $\mathcal{B}(t\to Hu)<2.6(1.8)\times {10}^{-4}$ and $\mathcal{B}(t\to Hc)<3.4(2.3)\times {10}^{-4}$.