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

that also set the decay length of the heavy neutral fermion

$$N_2$$ N 2

; in the compressed regime a separate, much smaller Yukawa entry

$$\sim \mathcal {O}(10^{-6})$$ ∼ O ( 10 - 6 )

additionally renders the charged scalar

$$\tilde{\eta }^{\pm }$$ η ~ ±

long-lived. We study the compressed-spectrum regime of its two-inert-doublet variant (

$$\varDelta M_{\textrm{comp}}= m_{\tilde{\eta }^\pm }- m_{N_2}\simeq 200\,\text {MeV}$$ Δ M comp = m η ~ ± - m N 2 ≃ 200 MeV

), in which small Yukawa entries render both the charged scalar

$$\tilde{\eta }^{\pm }$$ η ~ ±

and the heavy neutral fermion

$$N_2$$ N 2

long-lived and produce a nested cascade at the High-Luminosity LHC (HL-LHC):

$$\tilde{\eta }^{\pm }$$ η ~ ±

leaves a disappearing track (DT), decays to an invisible

$$N_2$$ N 2

, which travels macroscopically before forming a displaced dilepton vertex (DV). The two slow flights combine into a 4D time-of-flight delay

$$\varDelta t\sim 200$$ Δ t ∼ 200

–

$$800\,\text {ps}$$ 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

$$B\sim 10^{-5}$$ B ∼ 10 - 5

–

$$10^{-3}$$ 10 - 3

events, and the discovery remains

$$5\sigma $$ 5 σ

-significant for any background up to

$$B\sim 10$$ B ∼ 10

events. At the benchmark (

$$m_{N_2}=150\,\text {GeV}$$ m N 2 = 150 GeV

and proper decay lengths

$$c\tau _{\tilde{\eta }^\pm }=300\,\text {mm}$$ c τ η ~ ± = 300 mm

,

$$c\tau _{N_2}=189\,\text {mm}$$ c τ N 2 = 189 mm

) the strategy yields

$$N_s\approx 1212$$ N s ≈ 1212

signal events at

$$3000\,\text {fb}^{-1}$$ 3000 fb - 1

and establishes sensitivity across

$$15\,\text {mm}\lesssim c\tau _{\tilde{\eta }^\pm }\lesssim 300\,\text {mm}$$ 15 mm ≲ c τ η ~ ± ≲ 300 mm

,

$$10\,\text {mm}\lesssim c\tau _{N_2}\lesssim 1000\,\text {mm}$$ 10 mm ≲ c τ N 2 ≲ 1000 mm

, a correlated region left uncovered by any standalone DT or DV search. Because the

$$N_2$$ N 2

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.