Manifestation of the electric dipole moment in the decays of $\tau$ leptons produced in $e^+e^-$ annihilation

Abstract

\mbox{CP}-odd asymmetries in the processes $e^+e^-\rightarrow \tau^+\pi^-\nu_\tau$, $e^+e^-\rightarrow \pi^+\tau^-\bar\nu_ \tau$, $e^+e^-\rightarrow \tau^+\rho^-\nu_\tau$, and $e^+e^-\rightarrow \rho^+\tau^-\bar\nu_\tau$ are investigated with account for longitudinal polarization of electrons (or positrons). These asymmetries is a manifestation of electric dipole form factor $F_3^\tau\equiv b$ in the $\gamma\tau^+\tau^-$ vertex. It is shown that to measure \mbox{Im}\,b, polarization is not needed, and to measure \mbox{Re}\,b, the polarization is not necessary, but simplifies the measurement of \mbox{Re}\,b.Comment: 12 pages, 1 figur