Measurement of the $\tau$ electric dipole moment using longitudinal polarization of $e^{+}{e}^{-}$ beams

Abstract

Certain CP-odd momentum correlations in the production and subsequent decay of $\tau$ 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 $d_{\tau }^{\gamma }$, the electric dipole moment of the $\tau$. 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 $\tau$ decays. If 42\% average polarization of each beam is achieved, as proposed for the tau-charm factories, with equal integrated luminosities for each sign of polarization and a total yield of $2\cdot 10^7$ ${\tau }^{+}{\tau }^{-}$ pairs, it is possible to attain sensitivities for $|\delta \mathrm{Re}{d}_{\tau }^{\gamma }|$ of $8\cdot 10^{-19}$, $1\cdot 10^{-19}$, $1\cdot 10^{-19}$ $e$ cm respectively and for $|\delta \mathrm{Im}{d}_{\tau }^{\gamma }|$ of $4\cdot 10^{-14}$, $6\cdot 10^{-15}$, $5\cdot 10^{-16}$ $e$ 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 posible weak dipole form factor $d_{\tau }^Z$ are negligible as is the case when it is of the same order of magnitude as $d_{\tau }^{\gamma }$. 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 programme at the tau-charm factory appears warranted.

Comments: 30 pages, latex, no figures