Search for lepton flavor violation in the Higgs boson decay at a linear collider

We discuss possibility of direct search for lepton flavor violation (LFV) in Yukawa interaction by measuring the branching ratio for the decay of the lightest Higgs boson (h ⁰) into a τ-μ pair at a linear collider (LC). We study the significance of the signal process, e ⁺e ^-→Z*→Zh ⁰→Zτ ^±μ ^∓, against the backgrounds such as e ⁺e ^-→Zτ ⁺τ ^-→Zτ ^±μ ^∓+ missings. After taking appropriate kinematic cuts, the number of the background event is considerably reduced, so that the signal can be visible when the branching ratio of h ⁰→τ ^±μ ^∓ is larger than about 10 ^-4. In a minimal supersymmetric Standard Model scenario, the effective coupling of h ⁰τ ^±μ ^∓ can be generated at the loop level due to the slepton mixing. When supersymmetric mass parameters are larger than TeV scales, the branching ratio can be as large as several times 10 ^-4. Therefore, the signal can be marginally visible at a LC. In the general two-Higgs-doublet model, the possible maximal value for the branching ratio of h ⁰→τ ^±μ ^∓ can reach to a few times 10 ^-3 within the available experimental bound, so that we can obtain larger significance.