6533b821fe1ef96bd127ae1b

RESEARCH PRODUCT

A Precise Measurement of the $\tau$ Polarisation at LEP-1

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The $\tau$ polarisation has been studied with the ${\rm e^+e^-}\to \tau^+\tau^-$ data collected by the DELPHI detector at LEP in 1993, 1994 and 1995 around the Z resonance firstly through the exclusive decay channels ${\rm e}\nu\bar{\nu}$ , $\mu\nu\bar{\nu}$ , $\pi\nu$ , $\rho\nu$ and ${\rm a}_1\nu$ 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 $\bar{v}_{\rm e} / \bar{a}_{\rm e} = 0.0694\pm0.0058$ 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 $\sin^{2}\theta^{\rm lept}_{\rm eff} = 0.23282\pm0.00092$ .