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Decay of Free Polarized Top Quarks

Detailed studies of the decay of free polarized top quarks have already been available including the full ${\cal O}(\alpha_s)$ corrections [12,13,14]. The best example is the energy-angular distribution of charged leptons l+ in the semi-leptonic decay of the top quark. At leading order, the l+ distribution has a form where the energy and angular dependences are factorized [15,16]:

$\displaystyle \frac{d\Gamma_{t \to bl^+\nu}
({\bf {S}})}
{dE_l d\Omega_l}
= h(E...
...}\vert \cos \theta_l ) ~~ + ~~
[ \, {\cal O}(\alpha_s)~\mbox{correction} \, ] .$     (4.4)

Here El, $\Omega_l$, and $\theta_l$denote, respectively, the l+ energy, the solid angle of l+, and the angle between the l+ direction and the top polarization vector ${\bf {S}}$, all of which are defined in the top-quark rest frame. Hence, we may measure the top-quark polarization with maximal sensitivity using the l+ angular distribution.

ACFA Linear Collider Working Group