Two-loop radiative seesaw, LFV, muon \(g-2\), and dark matter

Abstract

The quartic scalar coupling \(\lambda_5\) term, which violates the lepton-number by two units in the Ma's model, is phenomenologically small when the sizable lepton-flavor violation (LFV) processes are considered. In order to dynamically generate the \(\lambda_5\) parameter through quantum loop effects, in order to enhance the muon \(g-2\) and to explain the dark matter (DM) relic density (\(\Omega_{\rm DM}\)), we extend the Ma-model by adding a \(Z_2\)-odd vector-like lepton doublet and a \(Z_2\)-even Majorana singlet. With the new couplings to the Higgs and gauge bosons, the observed \(\Omega_{\rm DM}\) can be explained when the resulting DM-nucleon scattering cross sections satisfy the current upper limits. In addition to the neutrino data and LFV constraints, it is found that the DM relic density can significantly exclude the free parameter space. Nevertheless, in the model, muon \(g-2\) can be enhanced up to \(O(10^{-9})\), and \(BR(\tau\to \mu \gamma)\) can be as large as the current upper limit when the parameters are taken to suppress the rare \(\mu\to (e \gamma, 3 e)\) decays.