Global analysis of fragmentation functions and their application to polarized top quark decays considering new {\it BABAR} and {\it Belle} experimental data

Recently, the {\it Belle} and {\it BABAR} Collaborations published the single-inclusive electron-positron annihilation data at the center of mass energies ($\sqrt{s}$) of $10.52$ GeV and $10.54$ GeV, respectively. These new data offer one the possibility to determine the nonperturbative initial conditions of fragmentation functions much more accurately. In our previous work \cite{Soleymaninia:2013cxa}, we extracted the fragmentation functions for $\pi^\pm$ and $K^\pm$ particles at next-to-leading order (NLO) including these new data, for the first time. These new data are in the regions of larger scaled-energy $z$ and lower $\sqrt{s}$. Our main purpose is to show that adding these new data in our analysis how much improve the fragmentation functions of $\pi^\pm$ and $K^\pm$ at NLO. We hope this analysis can obvious the effects of these recent data on FFs for whom is studying the behavior of light meson FFs. We also apply, for the first time, the extracted fragmentation functions to make our predictions for the scaled-energy distributions of $\pi^\pm$ and $K^\pm$ inclusively produced in polarized top quark decays at NLO.