Nested Disappearing-Track plus Displaced-Vertex Topology at the HL-LHC: A Dual Long-Lived-Particle Signature of the Scotogenic Model

The scotogenic model generates sub-eV neutrino masses radiatively through small Yukawa couplings $\sim \mathcal{O}({10}^{-3})$ that also set the decay length of the heavy neutral fermion $\text{Ntwo}$; in the compressed regime a separate, much smaller Yukawa entry $\sim \mathcal{O}({10}^{-6})$ additionally renders the charged scalar $\text{etapm}$ long-lived. We study the compressed-spectrum regime of its two-inert-doublet variant ($\text{DMcomp}=\text{mHpm}-\text{mNtwo}\simeq 200\text{MeV}$), in which small Yukawa entries render both the charged scalar $\text{etapm}$ and the heavy neutral fermion $\text{Ntwo}$ long-lived and produce a nested cascade at the High-Luminosity LHC~(HL-LHC): $\text{etapm}$ leaves a disappearing track~(DT), decays to an invisible $\text{Ntwo}$, which travels macroscopically before forming a displaced dilepton vertex~(DV). The two slow flights combine into a 4D time-of-flight delay $\text{dt}\sim 200$–$800\text{ps}$ resolvable by the CMS MIP Timing Detector, while the DT-to-DV displacement vector inherits the parent track direction, yielding a spatial back-pointing correlation with no SM analogue. These two handles are expected to suppress the background to $B\sim {10}^{-5}$–${10}^{-3}$ events, and the discovery remains $5\sigma$-significant for any background up to $B\sim 10$ events. At the benchmark ($\text{mNtwo}=150\text{GeV}$ and proper decay lengths $\text{ctauH}=300\text{mm}$, $\text{ctauN}=189\text{mm}$) the strategy yields $N_s\approx 1212$ signal events at $3000\text{ifb}$ and establishes sensitivity across $15\text{mm}\lesssim \text{ctauH}\lesssim 300\text{mm}$, $10\text{mm}\lesssim \text{ctauN}\lesssim 1000\text{mm}$, a correlated region left uncovered by any standalone DT or DV search. Because the $\text{Ntwo}$ decay length is controlled by the same Yukawa couplings that generate sub-eV neutrino masses, mapping this nested cascade turns the HL-LHC into a direct collider probe of the interaction responsible for neutrino mass.