Pair Production and Correlated Decay of Heavy Majorana Neutrinos in $e^+e^-$ Collisions

We consider the process $e^+e^-\to N_1N_2$, where $N_1$ and $N_2$ are heavy Majorana particles, with relative $CP$ given by $\eta_{CP}=+1$ or $-1$, decaying subsequently via $N_1,N_2\to W^{\pm}e^{\mp}$. We derive the energy and angle correlation of the dilepton final state, both for like-sign ($e^{\mp}e^{\mp}$) and unlike-sign ($e^-e^+$) configurations. Interesting differences are found between the cases $\eta_{CP}=+1$ and $-1$. The characteristics of unlike-sign $e^+e^-$ dileptons originating from a Majorana pair $N_1N_2$ are contrasted with those arising from the reaction $e^+e^-\to N\bar{N}\to W^+e^-W^-e^+$, where $N\bar{N}$ is a Dirac particle-antiparticle pair.