Heavy neutrino-antineutrino oscillations at the FCC-ee

We discuss the impact of heavy neutrino-antineutrino oscillations (NN¯Os\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \textrm{N}\overline{\textrm{N}}\textrm{Os} $$\end{document}) on heavy neutral lepton (HNL) searches at proposed electron-positron colliders such as the future circular e+e− collider (FCC-ee). During the Z pole run, HNLs can be produced alongside a light neutrino or antineutrino that escapes detection and can decay into a charged lepton or antilepton together with an off-shell W boson. In this case, signals of lepton number violation (LNV) only show up in the final state distributions. We discuss how NN¯Os\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \textrm{N}\overline{\textrm{N}}\textrm{Os} $$\end{document}, a typical feature of collider-testable low-scale seesaw models where the heavy neutrinos form pseudo-Dirac pairs, modify such final state distributions. For example, the forward-backward asymmetry (FBA) of the reconstructed heavy (anti)neutrinos develops an oscillatory dependence on the HNL lifetime. We show that these oscillations can be resolvable for long-lived HNLs. We also discuss that when the NN¯Os\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \textrm{N}\overline{\textrm{N}}\textrm{Os} $$\end{document} are not resolvable, they can nevertheless significantly modify the theory predictions for FBAs and observables such as the ratio of the total number of HNL decays into ℓ− over ones into ℓ+, in an interval of the angle θ between the HNL and the beam axis. Our results show that NN¯Os\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \textrm{N}\overline{\textrm{N}}\textrm{Os} $$\end{document} should be included in collider simulations of HNLs at the FCC-ee.