Falsifying leptogenesis for a TeV scale $W_R^{\pm }$ at the LHC

We point out that the discovery of a right-handed charged gauge boson $W_R^{\pm }$ with mass of around a few TeV, for example through a signal of two leptons and two jets that has been reported by CMS to have a 2.8$\sigma$ local excess or through a signal of a resonance decaying into a pair of standard model (SM) gauge bosons showing a local excess of 3.4$\sigma$ (2.5$\sigma$ global) reported by ATLAS search, will rule out all possibilities of leptogenesis in all classes of the left-right symmetric extensions of the Standard Model (LRSM) with both triplet and doublet Higgs scalars due to the unavoidable fast gauge mediated $B-L$ violating interactions $e_{R}^{\pm} W_{R}^{\mp} \rightarrow e_{R}^{\mp} W_{R}^{\pm}$. Our conclusions are very general in the sense that they do not necessarily demand for a lepton number violating detection signal of $W_R^{\pm }$.