  We analyse the semileptonic decay of a polarised top-quark with a large
velocity based on the perturbative QCD factorisation framework. Thanks to the
factorisation and the spin decomposition, the production part and the decay
part can be factorised and the spin dependence is introduced in the decay part.
The decay part is converted to the top-jet function which describes the
distribution of jet observables and the spin is translated to the helicity of
the boosted top. Using this top-jet function, the energy profile of b-jet is
investigated and it is turned out that the sub-jet energy for the
helicity-minus top is accumulated faster than that for the helicity-plus top.
This behaviour for the boosted top can be understood with the negative
spin-analysing-power of b-quark in the polarised-top decay.
