Top Quark Polarization in Polarized $e^+e^-$ Annihilation near Threshold

Abstract

Top quark polarization in $e^+e^-$ annihilation into $t\bar t$ is calculated for linearly polarized beams. The Green function formalism is applied to this reaction near threshold. The Lippmann--Schwinger equations for the $S$-wave and $P$-wave Green functions are solved numerically for the QCD chromostatic potential given by the two-loop formula for large momentum transfer and Richardson's ansatz for intermediate and small momenta. $S$-$P$--wave interference contributes to all components of the top quark polarization vector. Rescattering of the decay products is considered. The mean values $\langle n \ell \rangle$ of the charged lepton four-momentum projections on appropriately chosen directions $n$ in semileptonic top decays are proposed as experimentally observable quantities sensitive to top quark polarization. The results for $\langle n \ell \rangle$ are obtained including $S$-$P$--wave interference and rescattering of the decay products. It is demonstrated that for the longitudinally polarized electron beam a highly polarized sample of top quarks can be produced.

LaTeX2e, 46 pages, 18 postscript figures included. Uses epsf. The complete paper, including figures, is also available via anonymous ftp at ftp://www-ttp.physik.uni-karlsruhe.de/ , or via www at http://www-ttp.physik.uni-karlsruhe.de/cgi-bin/preprints