We consider low-scale leptogenesis via right-handed neutrinos $N$ coupled to
a $Z'$ boson, with gauged $U(1)_{B-L}$ as a simple realization. Keeping the
neutrinos sufficiently out of equilibrium puts strong bounds on the $Z'$
coupling strength and mass, our focus being on light $Z'$ and $N$, testable in
the near future by SHiP, HPS, Belle II, and at the LHC. We show that
leptogenesis could be robustly falsified in a large region of parameter space
by the double observation of $Z'$ and $N$, e.g. in the channel $pp\to Z' \to
NN$ with displaced $N$-decay vertex, and by several experiments searching for
light $Z'$, according to the mass of $N$.Comment: 9 pages, 8 figures; added one figure and minor clarifications,
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