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]:

 

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

Here E_l, $\Omega_l$, 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.