Lepton Number Violation at Colliders from Kinematically Inaccessible Gauge Bosons

We reevaluate the necessity of $W_R$ gauge bosons being kinematically accessible to test the Left-Right Symmetric Model (LRSM) at hadron colliders. In the limit that $W_R$ are too heavy, resonant production of sub-TeV Majorana neutrinos $N$ can still proceed at the Large Hadron Collider (LHC) via the process $pp\rightarrow W_R^{\pm *}\rightarrow N \ell^\pm \to \ell^\pm \ell^\pm +nj $ifmediatedbyafaroff-shell$W_R$. Traditional searches strategies are insensitive to this regime as they rely on momenta of final states scaling with TeV-scale $M_{W_R}$. For such situations, the process is actually kinematically and topologically identical to the direct production (DP) process $pp\rightarrow W_{\rm SM}^{\pm *} \rightarrow N \ell^\pm \rightarrow \ell^\pm \ell^\pm +nj$\mathrm{.}Inthiscontext,wereinterpret$\sqrt{s}=8$ TeV LHC constraints on DP rates for the minimal LRSM. For $m_N=200-500$ GeV and right-left coupling ratio ${\kappa }_R=g_R\mathrm{/}{g}_L$, we find $(M_{W_R}\mathrm{/}{\kappa }_R)>1.1-1.8$ TeV at 95% CLs. Expected sensitivities to DP at 14 (100) TeV are also recast: with $\mathcal{L}=1(10){\text{ab}}^{-1}$, one can probe $(M_{W_R} / \kappa_R) < {7.9-8.9~(14-40)}$TeVfor$m_N = {100 - 700~(1200)}$ GeV. Findings in terms of gauge invariant dimension-six operators with heavy $N$ are also reported.