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 $⟨n\ell ⟩$ 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 $⟨n\ell ⟩$ 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.

Comments: 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