Lepton flavor violating τ → 3μ decay in the type-III two Higgs doublet model

We study the current structure of the lepton flavor violating tau -> 3 mu decay in the Type-III 2HDM. This model has many coupling constants that affect this decay. We find that each coupling constant corresponds to a different final-state momentum distribution and vice versa. Using this fact, we suggest how to determine the current structure. We also find the upper limit vertical bar eta(E)(23)eta(E)(22)vertical bar < 0.00022 in the case that all Higgs bosons except for the lighter CP even neutral h(0) are decoupled, M-h(0) = 115 GeV and cos beta = 1/root 2. The observable difference between the MSSM and Type-III 2HDM is also discussed.