Bottom Quark Fragmentation in Top Quark Decay

We study the fragmentation of the b quark in top decay in NLO QCD, within the framework of perturbative fragmentation, which allows one to resum large logarithms $\sim \log (m_t^2\mathrm{/}{m}_b^2)$. We show the b-energy distribution, which we compare with the exact $\mathcal{O}({\alpha }_S)$ result for a massive b quark. We use data from $e^{+}{e}^{-}$ machines in order to describe the b-quark hadronization and make predictions for the energy spectrum of b-flavoured hadrons in top decay. We also investigate the effect of NLL soft-gluon resummation in the initial condition of the perturbative fragmentation function on parton- and hadron-level energy distributions.