An improved search for the electric dipole moment of the $\tau$ lepton

We report a measurement of the electric dipole moment of the $\tau$ lepton ($d_\tau$) using an 833 fb$^{-1}$ data sample collected near the $\Upsilon(4S)$ resonance, with the Belle detector at the KEKB asymmetric-energy $e^+ e^-$ collider. Using an optimal observable method, we obtain the real and imaginary parts of $d_\tau$ as ${\rm Re}(d_\tau) = ( -0.62 \pm 0.63 ) \times 10^{-17} ~e{\rm cm}$ and ${\rm Im}(d_\tau) = ( -0.40 \pm 0.32 ) \times 10^{-17} ~e{\rm cm}$, respectively. These results are consistent with no electric dipole moment at the present level of experimental sensitivity and improve the sensitivity by about a factor of three.