Measuring the heavy neutrino oscillations in rare W boson decays at the Large Hadron Collider

Majorana neutrinos in the seesaw model can have sizable mixings through which they can be produced at the Large Hadron Collider (LHC) and show a remarkable Lepton Number Violating (LNV) signature. In this article we study the LNV decay of the W boson via two almost degenerate heavy on-shell Majorana neutrinos $N_j$, into three charged leptons and a light neutrino. We consider the scenario where the heavy neutrino masses are within $1$ GeV $\le M_N\le 10$ GeV. We evaluated the possibility to measure a LNV oscillation process in such a scenario, namely, the modulation of the quantity $d\mathrm{\Gamma }\mathrm{/}dL$ for the process at the LHC where $W^{\pm} \to \mu^{\pm} N \to \mu^{\pm} \tau^{\pm} W^{\mp *}$ $\to {\mu }^{\pm }{\tau }^{\pm }{e}^{\mp }{\nu }_e$. $L$ is the distance within the detector between the two vertices of the process. We found out some realistic conditions under which such a modulation could be probed at the LHC.