Lepton number violation at hadron colliders via pseudo-Dirac heavy neutral leptons
Symmetry-protected low-scale seesaw models can account for the observed neutrino flavour oscillations without fine-tuning, while yielding collider-accessible signatures through pseudo-Dirac heavy neutral leptons (HNLs). Seesaw frameworks generically predict lepton number (LN) violation, which provides a powerful discovery channel. In symmetry-protected realisations, however, the amplitudes for LN violation are strongly suppressed by destructive interference between the contributions of the two quasi-degenerate HNLs within the usual QFT plane-wave treatment. We demonstrate that damped heavy neutrino-antineutrino oscillations significantly alleviate this suppression. We compare the sensitivities to pseudo-Dirac HNLs in both LN-blind and LN-violating channels at the LHC and future hadron colliders such as the FCC-$hh$ and the S$pp$C. We find that, although searches for LN violation outperform their LN-blind counterparts, small mass splittings in the pseudo-Dirac HNL pair can drastically reduce the sensitivities in these channels. We further show that combining LN-blind and LN-violating searches can distinguish a pseudo-Dirac HNL pair from the double-Majorana limit in the intermediate regime where LN violation is observable but not yet saturated.