Heavy Majorana Neutrinos from $Wγ$ Fusion at Hadron Colliders

Vector boson fusion processes become increasingly more important at higher collider energies and for probing larger mass scales due to collinear logarithmic enhancements of the cross section. In this context, we revisit the production of a hypothetic heavy Majorana neutrino $(N)$ at hadron colliders. Particular attention is paid to the fusion process $W\gamma \rightarrow N\ell^{\pm}$. We systematically categorize the contributions from an initial state photon in the elastic, inelastic, and deeply inelastic channels. Comparing with the leading channel via the Drell-Yan production $q \bar{q}'\rightarrow W^{*}\rightarrow N\ell^{\pm}$ at NNLO in QCD, we find that the $W\gamma$ fusion process becomes relatively more important at higher scales, surpassing the DY mechanism at $m_{N} \sim 1 \text{TeV} \ (770 \text{GeV})$ at the 14 TeV LHC (100 TeV VLHC). We investigate the inclusive heavy Majorana neutrino signal, including QCD corrections, and quantify the Standard Model backgrounds at future hadron colliders. We conclude that, with the currently allowed mixing $| V_{\mu N}| ^2<6\times 10^{-3}$, a $5\sigma$ discovery can be made via the same-sign dimuon channel for $m_N = 530 (1070)$ GeV at the 14 TeV LHC (100 TeV VLHC) after 1 ab$^{-1}$. Reversely, for $m_N = 500$ GeV and the same integrated luminosity, a mixing $| V_{\mu N}|^2$ of the order $1.1\times10^{-3} (2.5\times10^{-4})$ may be probed.