  Heavy Majorana neutrinos beyond the standard model can simultaneously explain
the origin of tiny neutrino masses and matter-antimatter asymmetry in our
Universe. The existence of heavy Majorana neutrinos will also lead to lepton
number violation and the rare lepton-number-violating $W$ decays are possible.
With contributions from two different Majorana neutrinos, a nonzero CP
asymmetry may be generated from the rate difference between $W$ decay and its
CP-conjugate process. The aim of this paper is to investigate the prospects for
measuring CP violation in rare $W$ decays via Majorana neutrinos at the LHC.
Our calculations show that the induced CP asymmetry is independent of the
Majorana neutrino mass for $10~ \rm GeV < m_N < 70 ~\rm GeV$. Such a CP
asymmetry if observed, would in turn provide unambiguous evidence of new
physics beyond the standard model.
