Bounds on LFV Higgs decays in a vector-like lepton model and searching for doubly charged leptons at the LHC

The Higgs-portal lepton flavor violation is studied in a vectorlike lepton model. For evading the constraints from rare $Z\to \ell^\pm_i \ell^\mp_j$ decays, we introduce two triplet vectorlike leptons, $(1,3)_{-1}$ and $(1,3)_{0}$. The resultant branching ratio for $h\to \mu \tau$ can be up to $10^{-4}$ when the constraints from the invisible $Z$ decays are applied. As a result, the signal strength for $\tau\tau$ channel has a $12\%$ deviation from the standard model prediction, while the muon $g-2$ is two-order of magnitude smaller than the data and $BR(\tau\to \mu \gamma)$ is of order of $10^{-12}$. A predicted doubly charged lepton in $pp$ collisions at $\sqrt{s}=13$ TeV is analyzed and it is found that the interesting production channels are $pp\to (\Psi^{--}_{1} \Psi^{++}_1, \Psi^{\pm\pm}_1 \Psi^\mp_1)$. Both single and pair production cross sections of $\Psi^{++}_1$ are comparable and can be a few hundred fb. The main decay channels for the doubly charged lepton are $\Psi^{\pm\pm} \to \ell^\pm W^\pm$ and for the heavy singly charged lepton are $\Psi^\pm_1 \to \nu W^\pm, \ell^\pm Z$. The numerical analysis is given at $13$ TeV LHC with $100$ fb$^{-1}$ luminosity.