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 $\tau$-$\mu$ pair at a linear collider. We study the significance of the signal process, $e^+e^- \to Z^\ast \to Z h^0 \to Z \tau^\pm \mu^\mp$, against the backgrounds such as $e^{+}e^{-} \to Z \tau^{+}\tau^{-} \to Z \tau^{\pm}\mu^{\mp}+$ 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 $h^0 \to \tau^\pm \mu^\mp$ is larger than about $10^{-4}$. In a Minimal Supersymmetric Standard Model scenario, the effective coupling of $h^0 \tau^\pm \mu^\mp$ can be generated at 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 $h^0 \to \tau^\pm \mu^\mp$ can reach to a few times $10^{-3}$ within the available experimental bound, so that we can obtain larger significance.