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

Abstract

CP-odd asymmetries in the processes e + e − → τ + π − ν τ , e + e − → π + τ − ντ , e + e − → τ + ρ − ν τ , and e + e − → ρ + τ − ντ are investigated with account for longitudinal polarization of electrons (or positrons). These asymmetries is a manifestation of electric dipole form factor F τ 3 ≡ b in the γτ + τ − vertex. It is shown that to measure Im b, polarization is not needed, and to measure Re b, the polarization is not necessary, but simplifies the measurement of Re b.