Final-state interactions ine+e−→tt¯→bl+νb¯W−near the top quark threshold

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Abstract
We calculate final-state interaction corrections to the energy-angular distribution of l+ in semileptonic top quark decay, where the parent top quark is produced via e+e−→tt¯ near threshold. These are the corrections due to gluon exchange between t and b¯(t¯ and b) and between b and b¯. Combining with other previously known corrections, we explicitly write down the l+ energy-angular distribution including the full O(αs)=O(β) corrections near the tt¯ threshold. Numerical analyses of the final-state interaction corrections are given. We find that they deform the l+ distribution typically at the 10% level. We also find that all qualitative features of the numerical results can be understood from intuitive pictures. The mechanisms of various effects of the final-state interactions are elucidated. Finally we define an observable which is proper to the decay process of the top quark (dependent only on dΓt→bl+ν/dEldΩl of a free polarized top quark) near the tt¯ threshold. Such a quantity will be useful in extracting the decay properties of the top quark using the highly polarized top quark samples.
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