Precision neutral current asymmetry parameter measurements from the Tau polarization at LEP

Abstract.

Measurements of the $\tau$ lepton polarization and forward-backward polarization asymmetry near the Z$^0$ resonance using the OPAL detector are described. The measurements are based on analyses of $\tau \rightarrow{\rm e} \nu_e\nu_{\tau}, \tau\rightarrow \mu\nu_{\mu}\nu_{\tau}, \tau\rightarrow \pi\nu_{\tau}, \tau \rightarrow \rho\nu_{\tau}$ and $\tau\rightarrow{\rm a}_1\nu_{\tau}$ decays from a sample of 144,810 $\rm e^+e^-\rightarrow \tau^+\tau^-$ candidates corresponding to an integrated luminosity of 151 pb$^{-1}$. Assuming that the $\tau$ lepton decays according to V–A theory, we measure the average $\tau$ polarization near $\sqrt{s} ={\rm M}_{\mathrm{Z}}$ to be $\langle P_{\tau}\rangle= (-14.10 \pm 0.73 \pm 0.55)\%$ and the $\tau$ polarization forward-backward asymmetry to be $\rm A_{\mathrm{pol}}^{\mathrm{FB}} = (-10.55 \pm 0.76 \pm 0.25)\%$, where the first error is statistical and the second systematic. Taking into account the small effects of the photon propagator, photon-Z$^0$ interference and photonic radiative corrections, these results can be expressed in terms of the lepton neutral current asymmetry parameters:

\begin{eqnarray} {\cal A}_{\tau} & = & 0.1456 \pm 0.0076 \pm 0.0057, \nonumber {\cal A}_{\mathrm e}& = & 0.1454 \pm 0.0108 \pm 0.0036. \nonumber \end{eqnarray}

These measurements are consistent with the hypothesis of lepton universality and combine to give ${\cal A}_{\ell} = 0.1455 \pm 0.0073$. Within the context of the Standard Model this combined result corresponds to $=0.23172 \pm 0.00092$. Combing these results with those from the other OPAL neutral current measurements yields a value of $=0.23211 \pm 0.00068$.