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 $ if mediated by a far off-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 $pp\rightarrow W_{\rm SM}^{\pm *} \rightarrow N \ell^\pm \rightarrow \ell^\pm \ell^\pm +nj$. In this context, we reinterpret $\sqrt{s}=8$ TeV LHC constraints on DP rates for the minimal LRSM. For $m_N = 200-500$ GeV and right-left coupling ratio $\kappa_R = g_R/g_L$, we find $(M_{W_R} / \kappa_R) > {1.1-1.8}$ 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 $(M_{W_R} / \kappa_R) < {7.9-8.9~(14-40)}$ TeV for $m_N = {100 - 700~(1200)}$ GeV. Findings in terms of gauge invariant dimension-six operators with heavy $N$ are also reported.