Lepton number violation from Higgs/$Z$ decays into a pair of right-handed neutrinos

Abstract

We explore signatures of Lepton Number Violation (LNV) from decays of the discovered Higgs ($h$) and Z bosons into a pair of Right-Handed Neutrinos (RHNs). Due to the Majorana nature of RHNs, the final state can be the same-sign dilepton plus jets leading to 2 units of LNV. As a simple but plausible scenario, we investigate such a signal in models with a new $U(1)_X$ gauge symmetry which naturally introduces three RHNs for gauge anomaly cancellation, and is spontaneously broken down by a vacuum expectation value of an isospin singlet scalar field ($\phi$). In this scenario, $h$ and the Z boson can decay into a pair of RHNs via the $h$-$\phi$ mixing and the $Z$-$Z'$ mixing with $Z'$ being a new massive gauge boson, respectively. Estimating the LNV signal and corresponding backgrounds for the $\ell^{\pm} \ell^{\pm} 4j$ final states, we find bounds on the $h$-$\phi$ mixing and the $Z$-$Z^\prime$ mixing as a function of a mass of RHNs at Higgs factories, e.g., at High-Luminosity LHC with $\sqrt{s}=$ 14 TeV, future $e^-e^+$ colliders at $\sqrt{s}=$ 250 GeV, muon colliders at $\sqrt{s}=$ 125 GeV as well as at Z factories, e.g., CEPC and FCC-ee at $\sqrt{s}=$ 91.2 GeV. We also discuss limits on the scalar mixing at $e^-\mu^+$ and $\mu^+ \mu^+$ collisions ($\mu$TRISTAN) with $\sqrt{s}=$346 GeV/775 GeV and 2 TeV, respectively.