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

Abstract

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 $\Ntwo$; in the compressed regime a separate, much smaller Yukawa entry $\sim\mathcal{O}(10^{-6})$ additionally renders the charged scalar $\etapm$ long-lived. We study the compressed-spectrum regime of its two-inert-doublet variant ($\DMcomp = \mHpm - \mNtwo \simeq 200\MeV$), in which small Yukawa entries render both the charged scalar $\etapm$ and the heavy neutral fermion $\Ntwo$ long-lived and produce a nested cascade at the High-Luminosity LHC~(HL-LHC): $\etapm$ leaves a disappearing track~(DT), decays to an invisible $\Ntwo$, which travels macroscopically before forming a displaced dilepton vertex~(DV). The two slow flights combine into a 4D time-of-flight delay $\dt\sim200$--$800\ps$ 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 $B\sim10^{-5}$--$10^{-3}$ events, and the discovery remains $5σ$-significant for any background up to $B\sim10$ events. At the benchmark ($\mNtwo=150\GeV$ and proper decay lengths $\ctauH=300\mm$, $\ctauN=189\mm$) the strategy yields $N_s\approx1212$ signal events at $3000\ifb$ and establishes sensitivity across $15\mm\lesssim\ctauH\lesssim300\mm$, $10\mm\lesssim\ctauN\lesssim1000\mm$, a correlated region left uncovered by any standalone DT or DV search. Because the $\Ntwo$ 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.