A possible symmetry of the $ν$MSM

TL;DR

The paper presents an almost symmetric νMSM where a global lepton-number symmetry $U(1)_L$, broken at ${\cal O}(10^{-4})$, enforces a mass pattern with a keV-scale dark-matter sterile neutrino and a nearly degenerate pair of heavier sterile neutrinos. This structure, together with symmetry breaking, yields active-neutrino masses via a seesaw with one zero eigenvalue, compatible with oscillation data, and fixes the heavy-light Yukawa couplings to align with observed mixing. The breaking scale $\epsilon$ supplies the CP-violating source needed for baryogenesis through sterile-neutrino oscillations, while permitting heavy-neutrino masses to lie below ${\cal O}(1)$ GeV and enabling experimental tests in meson and $\tau$ decays, as well as potential inflaton-related production pathways for dark matter. The framework thus links neutrino phenomenology, cosmology, and low-scale laboratory searches, predicting specific flavor structures and offering experimentally accessible signatures in forthcoming meson-decay and X-ray observations.

Abstract

To explain the dark matter and the baryon asymmetry of the Universe, the parameters of the $ν$MSM (an extension of the Minimal Standard Model by three singlet neutrinos with masses smaller than the electroweak scale) must be fine-tuned: one of the masses should be in the ${\cal O} (10)$ keV region to provide a candidate for the dark-matter particle, while two other masses must be almost the same to enhance the CP-violating effects in the sterile neutrino oscillations leading to the baryon asymmetry. We show that a specifically defined global lepton-number symmetry, broken on the level of ${\cal O} (10^{-4})$ leads to the required pattern of sterile neutrino masses being consistent with the data on neutrino oscillations. Moreover, the existence of this symmetry allows to fix the flavour structure of couplings of singlet fermions to the particles of the Standard Model and indicates that their masses are likely to be smaller than ${\cal O} (1)$ GeV, opening a possibility of their search in decays of charmed, beauty and even $K$ or $π$-mesons.