TTP97-23 Final-State Interactions in e^+e^- \to t\bar t \to bl^+\nu\bar bW^- Near Top Quark Threshold

We calculate final-state interaction corrections to the energy-angular distribution of l^+ in semi-leptonic top quark decay, where the parent top quark is produced via e^+e^- \to t\bar{t} near threshold. These are the corrections due to gluon exchange between t and \bar{b} (\bar{t} and b) and between b and \bar{b}. Combining with previously known other corrections, we explicitly write down the l^+ energy-angular distribution including full O(\alpha_s)=O(\beta) corrections near threshold. Numerical analyses of the final-state interaction corrections are presented. We find that they deform the l^+ distribution typically at 10% level. Also we elucidate mechanisms of the various effects of the final-state interactions. We find that all qualitative features of the numerical results can be understood from intuitive pictures. The natures that \bar{b} is emitted preferrably in the parent \bar{t}'s spin direction and that there is attractive force between \bar{b} and \bar{t} generate: shift of |p_t|-distribution, forward-backward asymmetry of t, modification of the top-quark polarization vector, and energy-angle-correlated deformation of l^+ distributions.