Top Quark Decays into Heavy Quark Mesons

For top quark decays into heavy quark mesons $\Upsilon$ and $\bar{B}_c^*$ , a complete calculation to the leading order both in QCD coupling constant $\alpha_s$ and in $v$, the typical velocity of the heavy quarks inside the mesons, is performed. Relatons between the top quark mass and the decay branching ratios are studied. Comparion with the results which are obtained by using the quark frangmentation functions is also discussed. The branching ratios are consistent (within a factor of $2\sim 3 $) with that obtained using fragmentation functions at $m_t\sim 150$ GeV.