Search for compressed electroweak SUSY production in final states with two $\tau$-leptons in $\sqrt{s}=13$ and $13.6$ TeV $pp$ collisions with the ATLAS detector

Searches for the production of $\tau$-sleptons ($\tilde{\tau }$), charginos (${\tilde{\chi }}_1^{\pm }$), and neutralinos (${\tilde{\chi }}_2^0$) in events with at least one hadronically decaying $\tau$-lepton are presented, targeting compressed mass spectra scenarios. For charginos and neutralinos, the cascade decays producing either a $\tau$-slepton or a $\tau$-sneutrino are considered. Two final selections are studied, requiring either one hadronically decaying $\tau$-lepton and one other charged lepton, or two or more hadronically decaying $\tau$-leptons. To enhance sensitivity to the compressed mass spectra, production modes with initial-state radiation (ISR) jets are considered. The searches use 140 ${\mathrm{f}\mathrm{b}}^{-1}$ and 53 ${\mathrm{f}\mathrm{b}}^{-1}$ of proton-proton collision data recorded by the ATLAS detector at the Large Hadron Collider during 2015-2018 at a centre-of-mass energy of $\sqrt{s}=13$ TeV and 2022-2023 at a centre-of-mass energy of $\sqrt{s}=13.6$ TeV, respectively. The searches provide sensitivity to the compressed mass spectra scenarios with light $\tau$-sleptons. The results are generally consistent with the Standard Model, although several deviations with local significances of $2.1-2.4\sigma$ are observed. These deviations weaken the observed exclusion limits. For direct $\tau$-slepton production, in the ISR channel alone the limits are set for $\mathrm{\Delta }m(\tilde{\tau },{\tilde{\chi }}_1^0)=30$ GeV for $\tau$-slepton masses up to $115$ GeV at 95% confidence level. Given the observed data, no exclusion limits are set for direct $\tau$-sleptons production when statistically combining all considered channels. For electroweakino production, limits are set for $\mathrm{\Delta }m({\tilde{\chi }}_2^0,{\tilde{\chi }}_1^0)=30$ GeV for ${\tilde{\chi }}_2^0$ masses up to $200$ GeV. For pure chargino pair-production, limits are set for chargino masses up to $175$ GeV for the same mass splitting.