Effects of vectorlike leptons on $h\to 4\mathrm{\ell }$ and the connection to the muon g-2 anomaly

The mixing of new vectorlike leptons with leptons in the standard model can generate flavor violating couplings of $h$, $W$ and $Z$ between heavy and light leptons. Focusing on the couplings of the muon, the partial decay width of $h\to e_4^{\pm }{\mu }^{\mp }$, where $e_4$ is the new lepton, can be significant when this process is kinematically allowed. Subsequent decays $e_4^{\pm }\to Z{\mu }^{\pm }$ and $e_4^{\pm }\to W^{\pm }\nu$ lead to the same final states as $h \to ZZ^* \to Z \mu^+\mu^-$and$h \to WW^* \to W \mu\nu$, thus possibly affecting measurements of these processes. We calculate $h\to e_4 \ell_i \to Z\ell_i\ell_j$,where$\ell_{i,j}$ are standard model leptons, including the possibility of off-shell decays, interference with $h\to ZZ^* \to Z \ell_i \ell_i$,andthemasseffectof$\ell_{i,j}$ which are important when the mass of $e_4$ is close to the mass of the Higgs boson. We derive constraints on masses and couplings of the heavy lepton from the measurement of $h\to 4\mathrm{\ell }$. We focus on the couplings of the muon and discuss possible effects on $h\to ZZ^*$ from the region of parameters that can explain the anomaly in the measurement of the muon g-2.