Anomalous magnetic and electric moments of $\tau$ and lepton flavor mixing matrix in effective lagrangian approach

In an effective lagrangian approach [EM97] to new physics, the authors in ref. [HL99] pushed tau anomalous magnetic and electric dipole moments (AMDM and EDM) down to ${10}^{-11}$ and ${10}^{-25}ecm$ by using a Fritzsch-Xing lepton mass matrix ansatz. In this note, we find that, in this approach, there exists the connection between $\tau$ AMDM and EDM and the lepton flavor mixing matrix. By using the current neutrino oscillation experimental results, we investigate the parameter space of lepton mixing angles to $\tau$ AMDM and EDM. We can obtain the same or smaller bounds of $\delta a_{\tau }$ and $d_{\tau }$ acquired in ref. [HL99] and constrain ${\theta }_l$ (the mixing angle obtained by long-baseline neutrino oscillation experiments) from $\tau$ AMDM and EDM.