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The f\'eeton is the gauge boson of the $U(1)_{B-L}$ gauge theory. If thegauge coupling constant is extremely small, it becomes a candidate for darkmatter. We show that its decay to a pair of electron and positron explains theobserved Galactic 511-keV gamma-ray excess in a consistent manner. Thisf\'eeton dark matter decays mainly into pairs of neutrino and anti-neutrino.Future low-energy experiments with improved directional capability make itpossible to capture those neutrino signals. The seesaw-motivated parameterspace predicts a relatively short f\'eeton lifetime comparable to the currentcosmological constraint.

F\'eeton ($B-L$ Gauge Boson) Dark Matter for the 511-keV Gamma-Ray Excess and the Prediction of Low-energy Neutrino Flux