  Some models of leptogenesis involve a nearly-degenerate pair of heavy
Majorana neutrinos $N_{1,2}$ whose masses can be small, $O({\rm GeV})$. There
can be heavy-light neutrino mixing parametrized by $|B_{\ell N}|^2 = 10^{-5}$,
which leads to the rare lepton-number-violating decay $W^\pm \to \ell_1^\pm
\ell_2^\pm (q'{\bar q})^\mp$. With contributions to this decay from both $N_1$
and $N_2$, a CP-violating rate difference between the decay and its
CP-conjugate can be generated. In this talk, I describe the prospects for
measuring such a CP asymmetry $A_{\rm CP}$ at the LHC. I consider three
versions of the LHC -- HL-LHC, HE-LHC, FCC-hh -- and show that, for $5~{\rm
GeV} \le M_N \le 80~{\rm GeV}$, small values of the CP asymmetry can be
measured at $3\sigma$, in the range $1\%\le A_{\rm CP} \le 15\%$.
