Quasi-Dirac neutrinos at the LHC

Lepton number violation is searched for at the LHC using same-sign leptons plus jets. The standard lore is that the ratio of same-sign lepton to opposite-sign lepton events, $R_{ll}$, is equal to $R_{ll}=1$ ($R_{ll}=0$) for Majorana (Dirac) neutrinos. We argue that for "quasi-Dirac" neutrinos, $R_{ll}$ can have any value between 0 and 1, the precise value being controlled by the mass splitting versus the width of the quasi-Dirac resonances. A measurement of $R_{ll}\neq 0,1$ would then contain valuable information about the origin of neutrino masses. We consider as an example the inverse seesaw mechanism in a left-right symmetric scenario, which is phenomenologically particularly interesting since all the heavy states in the high energy completion of the model could be within experimental reach. A prediction of this scenario is a correlation between the values of $R_{ll}$ and the ratio between the rates for heavy neutrino decays into standard model gauge bosons, and into three body final states $ljj$ mediated by off-shell $W_R$ exchange.