If the lightest neutrino mass is the dark-energy scale: a narrow window for neutrinoless double-beta decay

Abstract

The dark-energy density fixes a mass scale ρ_Λ^{1/4} ≃ 2.25 meV, of the same order as the neutrino mass splittings. Numerical proximity is not evidence; we only map consequences. Taking the sharpest arithmetic reading as a scenario — m₁ = 2.25 meV with normal ordering — and evaluating the standard m_ββ map at that single point gives three contributions (1.52, 2.67, 1.10) meV, m_ββ ∈ [0.04, 5.30] meV, and Σm_ν = 61.3 meV. The lower edge is an unprotected 1.7% accident: it exists only because the middle term exceeds the other two by 0.045 meV and vanishes entirely for m₁ ≳ 2.32 meV; it has no observational weight. The nearer referee is cosmology: the mass sum sits just inside current combined limits and will be graded there first. Laboratory discrimination is secondary. Minimal normal ordering cannot exceed 3.69 meV, while this scenario reaches 5.30 meV and occupies the gap between them 32% of the time. One planned experiment overlaps that gap only at the favourable end of its matrix-element range, and only 10.8% of phases put m_ββ above the corresponding threshold; a detection there would favour the scenario over minimal ordering, while a detection above 5.30 meV excludes it. A null result constrains nothing, at any sensitivity. The m_ββ band itself is textbook; only the placement at this m₁ is at issue.