Effects of vectorlike leptons on h →4 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→e4±μwhere e4 is the new lepton, can be significant when this process is kinematically allowed. Subsequent decays e4±→Zμ ± and e4±→W±ν lead to the same final states as h→ZZ*→Zμ+μ- and h→WW*→Wμν, thus possibly affecting measurements of these processes. We calculate h→e4i→Zij, where i,j are standard model leptons, including the possibility of off-shell decays, interference with h→ZZ*→Zii, and the mass effect of i,j which are important when the mass of e4 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→4. We focus on the couplings of the muon and discuss possible effects on h→ZZ* from the region of parameters that can explain the anomaly in the measurement of the muon g-2.