Measurement of the τ electric dipole moment using longitudinal polarization of e⁺e⁻ beams

Abstract

Certain CP-odd momentum correlations in the production and subsequent decay of τ pairs in e⁺e⁻ collisions are enhanced significantly when the e⁺ and e⁻ beams are longitudinally polarized. These may be used to probe the real and imaginary parts of d_τγ, the electric dipole moment of the τ. Closed-form expressions for these "vector correlations" and the standard deviation of the operators defining them due to standard model interactions are presented for the two-body final states of τ decays. If 42% average polarization of each beam is achieved, as proposed for the τ-charm factories, with equal integrated luminosities for each sign of polarization and a total yield of 2×10⁷ τ⁺τ⁻ pairs, it is possible to attain sensitivities for ||δ Red_τγ|| of 8×10⁻¹⁹, 1×10⁻¹⁹, 1×10⁻¹⁹e cm, respectively, and for ||δ Imd_τγ|| of 4×10⁻¹⁴, 6×10⁻¹⁵, 5×10⁻¹⁶e cm, respectively, at the three operating center-of-mass energies of 3.67, 4.25, and 10.58 GeV. These bounds emerge when the effects of a possible weak dipole form factor d_τZ are negligible as is the case when it is of the same order of magnitude as d_τZ. Furthermore, in such a polarization experiment where different polarizations are possible, a model-independent disentangling of their individual effects is possible, and a technique to achieve this is described. A strong longitudinal polarization physics program at the τ-charm factory appears warranted.