CP Violation in Rare Lepton-Number-Violating $W$ Decays at the LHC

Some models of leptogenesis involve a quasi-degenerate pair of heavy neutrinos $N_{1,2}$ whose masses can be small, $O({rm GeV})$. Such neutrinos can contribute to the rare lepton-number-violating (LNV) decay $W^pm to ell_1^pm ell_2^pm (q{bar q})^mp$. If both $N_1$ and $N_2$ contribute, there can be a CP-violating rate difference between the LNV decay of a $W^-$ and its CP-conjugate decay. In this paper, we examine the prospects for measuring such a CP asymmetry $A_{rm CP}$ at the LHC. We assume a value for the heavy-light neutrino mixing parameter $|B_{ell N}|^2 = 10^{-5}$, which is allowed by the present experimental constraints, and consider $5~{rm GeV} le M_N le 80~{rm GeV}$. We consider thr