The compressed-spectrum regime of the scotogenic model, where the inert charged state η ˜ ± and the dark matter candidate N 1 are nearly mass-degenerate (Δ M ≲ 20 GeV), remains largely inaccessible to current ATLAS and CMS displaced-lepton searches, which impose lepton p T ≳ 20–30 GeV requirements (and historically up to 65 GeV) that the soft decay products cannot satisfy. We propose a dedicated signal region, SR-SDL, targeting the process p p → η ˜ ± η ˜ 0 at s = 13.6 TeV , which produces a single soft displaced lepton ( p T > 5 GeV, | d 0 | ∈ [5, 300] mm) together with large missing transverse energy from the invisible η ˜ 0 → ν N 1 decay and initial-state radiation recoil. The key discriminating variables are a large-radius tracking requirement on the lepton impact parameter, a b -jet veto to suppress heavy-flavour backgrounds, and a signal E T miss threshold at the trigger efficiency plateau. Against an estimated SM background of B = 66 ± 24 events at 300 fb − 1 , eight of nine benchmark points with m η ˜ ± = 150 –500 GeV and c τ = 10 –300 mm satisfy the 95% CL exclusion criterion N sig > N 95 % CL excl ≃ 18 , with the Yukawa coupling excluded in the range | Y | ≲ ( 0.4 -- 1.4 ) × 10 − 6 (depending on m η ˜ ± , from 500 to 150 GeV), corresponding to proper decay lengths cτ ≳ 10 mm that place the η ˜ ± decay within the displaced-track acceptance window. The same Yukawa couplings that place the η ˜ ± decay length inside the ATLAS inner detector also reproduce the observed sub-eV neutrino masses via the scotogenic one-loop mechanism, making the SR-SDL search a direct probe of the radiative mass-generation scale.

