Renjie Wang
The ultra-compressed scotogenic regime, in which a 2\,GeV mass splitting between the charged inert scalar and the dark-matter fermion is motivated by and compatible with co-annihilation to the observed relic density for suitable choices of the remaining model parameters, produces decay leptons for which existing LHC displaced-lepton and disappearing-track searches retain only partial, unoptimised acceptance, leaving room for a dedicated timing-assisted strategy. We propose exploiting the 30\,ps timing resolution of the HL-LHC precision timing detectors as a fourth observable, converting the macroscopic scalar decay length of 100--1000\,mm into an arrival-time delay of 70--700\,ps---more than three orders of magnitude above the sub-picosecond delays of all prompt Standard Model backgrounds. Operating at the level of a low-$p_T$ disappearing-track stub matched to a delayed timing hit, without requiring full lepton reconstruction, our 4D timing strategy achieves signal efficiencies of 12--36\% across the probed mass range (14\% at the 200\,GeV benchmark) and zero background across $4.20\times10^6$ simulated prompt SM events, projecting 95\%\,C.L.\ exclusion up to scalar masses of $\simeq\!670$\,GeV at 3000\,fb$^{-1}$ under conservative background assumptions. The scalar lifetime is set by the Yukawa coupling $y$ through $cτ\propto y^{-2}$, while sub-eV neutrino masses constrain only the product $y^2λ_5$; the small couplings that place the charged scalar in the optimal timing window are therefore compatible with, though not uniquely fixed by, the radiative neutrino-mass mechanism, making the co-annihilation corridor---conventionally the most elusive regime---an accessible target for 4D spacetime tracking at the HL-LHC.