Three searches for the direct production of $\tau$-sleptons or charginos and neutralinos in final states with at least two hadronically decaying $\tau$-leptons are presented. For chargino and neutralino production, decays via intermediate $\tau$-sleptons or $W$ and $h$ bosons are considered. The analysis uses a dataset of $pp$ collisions corresponding to an integrated luminosity of $139\,$fb$^{-1}$, recorded with the ATLAS detector at the Large Hadron Collider at a centre-of-mass energy of 13 TeV. No significant deviation from the expected Standard Model background is observed and supersymmetric particle mass limits at 95% confidence level are obtained in simplified models. For direct production of $\tilde~{\chi}^+_1\tilde~{\chi}^-_1$, chargino masses are excluded up to 970 GeV, while $\tilde~{\chi}^{\pm}_1$ and $\tilde~{\chi}^0_2$ masses up to 1160 GeV (330 GeV) are excluded for $\tilde~{\chi}^{\pm}_1\tilde~{\chi}^0_2$/$\tilde~{\chi}^+_1\tilde~{\chi}^-_1$ production with subsequent decays via $\tau$-sleptons ($W$ and $h$ bosons). Masses of $\tau$-sleptons up to 500 GeV are excluded for mass degenerate $\tilde~{\tau}_{L,R}$ scenarios and up to 425 GeV for $\tilde~{\tau}_L$-only scenarios. Sensitivity to $\tilde~{\tau}_R$-only scenarios from the ATLAS experiment is presented here for the first time, with $\tilde~{\tau}_R$ masses excluded up to 350 GeV.
Higgsinos with masses near the electroweak scale can solve the hierarchy problem and provide a dark matter candidate, while detecting them at the LHC remains challenging if their mass splitting is $\mathcal{O}(1 \text{GeV})$. This Letter presents a novel search for nearly mass-degenerate Higgsinos in events with an energetic jet, missing transverse momentum, and a low-momentum track with a significant transverse impact parameter using 140 fb$^{-1}$ of proton-proton collision data at $\sqrt{s}=13$ TeV collected by the ATLAS experiment. For the first time since LEP, a range of mass splittings between the lightest charged and neutral Higgsinos from $0.3$ GeV to $0.9$ GeV is excluded at 95$\%$ confidence level, with a maximum reach of approximately $170$ GeV in the Higgsino mass.
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