Probing lepton flavor mixing in $W_R$ searches with machine learning at the LHC

Right-handed lepton flavor mixing in the left-right symmetric model directly affects the production and decay of heavy Majorana neutrinos $N_R$, yet its impact on collider searches remains less explored. Using a deep neural network (DNN), we analyze the Keung-Senjanović process $pp\to W_R\to {\mathrm{\ell }}_{\alpha }{N}_R\to {\mathrm{\ell }}_{\alpha }{\mathrm{\ell }}_{\beta }jj$ with ${\mathrm{\ell }}_{\alpha ,\beta }=e,\mu$ at LHC Run~2 and the HL-LHC, considering both same-sign and opposite-sign dilepton channels. We adopt three benchmark mixing scenarios: unmixed, maximal-mixing, and PMNS-like. In the unmixed scenario, the DNN improves the expected significance over the cut-based analyses performed by ATLAS, leading to stronger exclusion limits. For the combined $\mathrm{\ell }\mathrm{\ell }$ analysis, the HL-LHC can exclude $m_{W_R}$ and $m_{N_R}$ up to $6.7$ ($6.3$)~TeV and $4.4$ ($4.1$)~TeV, respectively, under maximal (PMNS-like) mixing. LHC Run~2 already excludes a significant portion of the $\mathrm{\mid }{V}_{e1}\mathrm{\mid }\text{–}\mathrm{\mid }{V}_{\mu 1}\mathrm{\mid }$ plane, and the HL-LHC will probe even smaller mixing values, possibly ruling out both the maximal and PMNS-like patterns. Finally, we investigate complementarities with low-energy charged lepton flavor violation processes, where future searches can overlap with or exceed the LHC reach.