Study of $t\bar{t}H$ and $tH$ production in the $H\to\tau\tau$ channel in $pp$ collisions at $\sqrt{s}=13$ TeV and 13.6 TeV with the ATLAS detector
A study of the production of the Higgs boson in association with either a top-quark pair ($t\bar{t}H$) or a single top quark ($tH$) in the $\tau$-lepton-pair decay channel is presented. The analysis relies on final states featuring fully hadronic decays of the top quarks and the $\tau$-leptons. It employs data samples of proton--proton collisions at $\sqrt{s}=13$ and 13.6 TeV recorded with the ATLAS detector at the CERN Large Hadron Collider and corresponding to integrated luminosities of 140 fb$^{-1}$ and 161 fb$^{-1}$, respectively. The measured signal strength ($\mu$), defined as the measured cross-section normalised to the Standard Model prediction, is $\mu_{t\bar{t}H}=1.51^{+0.71}_{-0.62}$ for $t\bar{t}H$ and $\mu_{tH}=-0.4^{+5.6}_{-5.1}$ for $tH$. Additionally, the $t\bar{t}H$ cross-section is measured differentially in three bins of the Higgs boson transverse momentum in the simplified template cross-section framework.