Lepton flavor violation in Higgs boson decays under the rare tau decay results

We study lepton flavor violation (LFV) associated with tau leptons in the framework of the two Higgs doublet model, in which LFV couplings are introduced as a deviation from Model II Yukawa interaction. Parameters of the model are constrained from experimental results and also from requirements of theoretical consistencies such as vacuum stability and perturbative unitarity. Current data for rare tau decays provide substantial upper limits on the LFV Yukawa couplings in the large $\tan\beta$ region ($\tan\beta \gtrsim 30 $), which are comparable with predictions in fundamental theories. Here $\tan\beta$ is the ratio of vacuum expectation values of the two Higgs doublets. We show that a search for the LFV decays $\phi^{0} \to \tau^\pm \mu^\mp$ $(\tau^\pm e^\mp)$ of neutral Higgs bosons ($\phi^{0} =h,H$ and $A$) at future collider experiments can be useful to further constrain the LFV couplings especially in the relatively small $\tan\beta$ region ($\tan\beta \lesssim 30 $), where rare tau decay data cannot give any strong limit.