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 $e^+e^-\rightarrow\tau^+\tau^-$ 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 $\langle P\rangle=0.0035 \pm 0.0024_{\textrm{stat}}\pm 0.0029_{\textrm{sys}}$. 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.