7 keV sterile neutrino dark matter from split flavor mechanism

The recently discovered X-ray line at about $3.5\,$keV can be explained by sterile neutrino dark matter with mass, $m_s \simeq 7\,$keV, and the mixing, $\sin^2 2\theta \sim 10^{-10}$. Such sterile neutrino is more long-lived than estimated based on the seesaw formula, which strongly suggests an extra flavor structure in the seesaw sector. We show that one can explain both the small mass and the longevity based on the split flavor mechanism where the breaking of flavor symmetry is tied to the breaking of the $B-L$ symmetry. In a supersymmetric case we find that the $7\,$keV sterile neutrino implies the gravitino mass about $100\,$TeV.