Flavor Tomography of Long-Lived Neutrino-Mass Mediators: Probing the Neutrino Mass Ordering at the HL-LHC

Abstract: The neutrino mass ordering remains unresolved because long-baseline oscillation measurements are entangled with the unknown CP phase $δ<em>{CP}$; a collider probe free of this degeneracy would provide a qualitatively different, complementary test. We show that when the long-lived charged particle producing a displaced-lepton signal at the High-Luminosity LHC is also the mediator responsible for Majorana neutrino masses---the \textit{shared-coupling condition}---the Casas--Ibarra parametrization determines the lepton flavor ratio $N_e/N</em>μ$ of time-delayed leptons in terms of Pontecorvo--Maki--Nakagawa--Sakata (PMNS) mixing parameters alone. Within the resulting \textit{shared-coupling class} of models the ratio is fixed by oscillation data, independent of all beyond-Standard-Model mass and coupling parameters up to calculable corrections bounded by charged-lepton-flavor-violation data, yielding $N_e/N_μ= 0.140$ for the Normal and $2.11$ for the Inverted Hierarchy---a separation of more than an order of magnitude between the two predictions. This prediction holds identically across the Scotogenic model, the Type-III seesaw, the inverse and linear seesaw, and lepton-portal dark matter, and is stable against oscillation-parameter uncertainties and detector-efficiency variations, which cancel in the ratio. A single efficiency-corrected decision criterion identifies the hierarchy, and explicit signal-yield estimates combined with an exact Poisson test show that $\mathcal{O}(25)$ displaced-lepton events suffice for a $3σ$ discrimination with the timing infrastructure already under construction at CMS and ATLAS---so that a positive long-lived-particle signal would simultaneously resolve the mass ordering, with no dependence on $δ_{CP}$.