Precision $e^{-}$ Beam Polarimetry at an $e^{+}{e}^{-}$ B Factory using Tau-Pair Events

We present a new technique, `Tau Polarimetry’, for measuring the longitudinal beam polarization present in an $e^{+}{e}^{-}$ collider through the analysis of $e^{+}{e}^{-}\to {\tau }^{+}{\tau }^{-}$ events. By exploiting the sensitivity of $\tau$ decay kinematics to the longitudinal polarization of the beams, we demonstrate that the longitudinal polarization can be measured with a 3 per mil systematic uncertainty at the interaction point using a technique that is independent of spin and beam transport modeling. Using 424.2$\pm$1.8 fb${}^{-1}$ of BABAR data at $\sqrt{s}=10.58$ GeV, the average longitudinal polarization of the PEP-II $e^{+}{e}^{-}$ collider has been measured to be $⟨P⟩=0.0035\pm {0.0024}_{\text{stat}}\pm {0.0029}_{\text{sys}}$. The systematic uncertainty studies are described in detail, which can serve as a guide for future applications of Tau Polarimetry. A proposed $e^{-}$ beam longitudinal polarization upgrade to the SuperKEKB $e^{+}{e}^{-}$ collider would benefit from this technique.