Discovering heavy neutrino-antineutrino oscillations at the Z-pole

A bstract Collider-testable type I seesaw extensions of the Standard Model are generally protected by an approximate lepton number (LN) symmetry. Consequently, they predict pseudo-Dirac heavy neutral leptons (HNLs) composed of two nearly degenerate Majorana fields. The interference between the two mass eigenstates can induce heavy neutrino-antineutrino oscillations ( $$ N\overline{N}\textrm{Os} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> <mml:mover> <mml:mi>N</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>Os</mml:mi> </mml:math> ) leading to observable lepton number violation (LNV), even though the LN symmetry is approximately conserved. These $$ N\overline{N}\textrm{Os} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> <mml:mover> <mml:mi>N</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>Os</mml:mi> </mml:math> could be resolved in long-lived HNL searches at collider experiments, such as the proposed Future Circular e + e − Collider (FCC- ee ) or Circular Electron Positron Collider (CEPC). However, during their Z -pole runs, the LN carried away by the light (anti)neutrinos produced alongside the HNLs prevents LNV from being observed directly. Nevertheless, $$ N\overline{N}\textrm{Os} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> <mml:mover> <mml:mi>N</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>Os</mml:mi> </mml:math> materialise as oscillating signatures in final state distributions. We discuss and compare a selection of such oscillating observables, and perform a Monte Carlo simulation to assess the parameter space in which $$ N\overline{N}\textrm{Os} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> <mml:mover> <mml:mi>N</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>Os</mml:mi> </mml:math> could be resolved.