Lepton Flavor Violating Dilepton Dijet Signatures from Sterile Neutrinos at Proton Colliders

In this article we investigate the prospects of searching for sterile neutrinos in lowscale seesaw scenarios via the lepton flavour violating (but lepton number conserving) dilepton dijet signature. In our study, we focus on the final state $e^pm mu^mp jj$ at the HL-LHC and the FCC-hh (or the SppC). We perform a multivariate analysis at the detector level including the dominant SM backgrounds from di-top, di-boson, and tri-boson. Under the assumption of the active-sterile neutrino mixings $|V_{ l N}|^2=|theta_e|^2=|theta_mu|^2$ and $|V_{ tau N}|^2 = |theta_tau|^2=0$, the sensitivities on the signal production cross section times branching ratio $sigma(p p to l^pm N)times {rm BR} (N to l^{ mp} jj)$ and on $|V_{ l N}|^2$ for sterile neutrino mass $M_N$ between 200 and 1000 GeV are derived. For the benchmark $M_N=500$ GeV, when ignoring systematic uncertainties at the HL-LHC (FCC-hh/SppC) with 3 (20) ${rm ab}^{-1}$ luminosity, the resulting 2-$sigma$ limits on $|V_{ l N}|^2$ are $4.9times 10^{-3}$ ($7.0times 10^{-5}$), while the 2 -$sigma$ limit on $sigma times {rm BR}$ are $4.4times10^{-2}$ ($1.6times10^{-2}$) fb, respectively. The effect of the systematic uncertainty is also studied and found to be important for sterile neutrinos with smaller masses. We also comment on searches with $tau^pm mu^mp jj$ and $tau^pm e^mp jj$ final states.