$B-L$ gauge symmetry is motivated by the successful generation of the seesaw mechanism and leptogenesis. We show that if the $B-L$ gauge boson constitutes a small fraction of dark matter (DM) it can explain the Galactic 511 keV emission via decay into an electron-positron pair. We find the model parameter space that is consistent with the seesaw mechanism, is cosmologically viable, and accounts for the amplitude of the Galactic positron line. From this parameter space, we derive an upper bound on the gauge boson mass and a bound on the positron injection energy $\lesssim 3\mathrm{MeV}$. This derived energy bound is consistent with the observational upper limit of the injection energy. The resultant model predicts the $B-L$ breaking scale to be in a relatively narrow range, i.e., $V_{B-L}\sim {10}^{15}–{10}^{16}\mathrm{GeV}$, which is consistent with a grand unification scale seesaw mechanism. The model is consistent in several phenomenologies, suggesting that they have a common origin in $B-L$ symmetry breaking.

• Received 23 May 2022
• Accepted 12 September 2022

DOI:https://doi.org/10.1103/PhysRevD.106.075012

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Published by the American Physical Society