Falsifying leptogenesis for a TeV scale $W^{\pm}_{R}$ 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 $W_R^\pm$.
