A precise measurement of the $\tau$ polarisation at LEP-1

The DELPHI Collaboration:     P.Abreu - et al.

doi:doi:10.1007/s100520000363

2021 Impact factor 4.991

Particles and Fields

Eur. Phys. J. C 14, 585-611
DOI 10.1007/s100520000363

A precise measurement of the $\tau$ polarisation at LEP-1

The DELPHI Collaboration

P.Abreu²²

²² LIP, IST, FCUL - Av. Elias Garcia, 14-1^o, 1000 Lisboa Codex, Portugal

Received: 1 December 1999 / Revised version: 2 February 2000 /
Published online: 14 April 2000 - © Springer-Verlag 2000

Abstract
The $\tau$ polarisation has been studied with the $\mbox{\rm e}^+ \mbox{\rm e}^-\rightarrow \tt$ data collected by the DELPHI detector at LEP in 1993, 1994 and 1995 around the $\mbox{\boldmath Z}$ resonance firstly through the exclusive decay channels $\mbox{\rm e}\nu\bar{\nu}$ , $\mu\nu\bar{\nu}$ , $\pi\nu$ , $\rho\nu$ and $\mbox{\rm a}_1\nu$ and secondly with an inclusive hadronic analysis which benefits from a higher efficiency and a better systematic precision. The results have been combined with those previously published on 1990 to 1992 DELPHI data, to produce results which reflect the full LEP-1 statistics. The fit of the $\tau$ polarisation dependence on the production angle yielded the polarisation parameters ${\cal A}_{_{\scriptstyle \!\tau}}=0.1359 \pm 0.0096$ and ${\cal A}_{_{\scriptstyle \!e}}=0.1382 \pm 0.0116$ . From these results the ratio of the vector and axial-vector effective couplings $\bar{v}_{\tau} / \bar{a}_{\tau} = 0.0683\pm0.0048$ and $\bar{v}_{\mbox{\footnotesize e}} / \bar{a}_{\mbox{\footnotesize e}} = 0.0694\pm0.0058$ have been derived, compatible with e $-\tau$ universality. With the assumption of lepton universality, the ratio of vector to axial-vector effective couplings for leptons $\bar{v}_l / \bar{a}_l = 0.0687\pm0.0037$ was obtained, implying a value of the effective weak mixing angle $\sin^{2}\theta^{\mbox{\scriptsize lept}}_{\mbox{\scriptsize eff}} = 0.23282\pm0.00092$ .