Search for squarks and gluinos in <i>pp</i> collisions at √<i>s</i> = 13 TeV and 13.6 TeV in events with <i>τ</i>-leptons, jets and missing transverse momentum using the ATLAS detector

A search for R-parity-conserving supersymmetry in events with large missing transverse momentum, jets and at least one hadronically decaying <i>τ</i>-lepton is presented. Both gluino and squark pair production are considered, with the cascade decay of each gluino or squark producing either a <i>τ</i>-slepton or a <i>τ</i>-sneutrino. Three channels are examined, requiring either exactly one hadronically decaying <i>τ</i>-lepton and no other leptons, exactly one hadronically decaying <i>τ</i>-lepton and at least one other lepton, or two or more hadronically decaying <i>τ</i>-leptons. Analyses in the three channels are optimised independently and combined statistically. Two separate analysis strategies, either a cut-and-count or machine-learning approach, are used. The search uses 140 fb^-1 and 51.8 fb^-1 of <i>pp</i> collision data recorded by the ATLAS detector at the Large Hadron Collider during 2015-2018 at √<i>s</i> = 13 TeV and 2022-2023 at √<i>s</i> = 13.6 TeV, respectively. Gluino masses below 2.25 TeV and squark masses up to 1.7 TeV are excluded.