Study of the energy distribution of hadrons produced through polarized or unpolarized top quarks can be considered as an indirect channel to search for the properties of this quark. According to the standard model of Particle Physics, top quark decays to the bottom quark and W-boson via the cascade decay mode and in the following the W-boson decays to the lepton pairs (or quark-antiquark pairs) and the bottom quark decays into an observable meson or baryon (a B-meson in most of the cases) through a hadronization process. Formerly, the energy spectrum of B-mesons produced through the polarized top quarks is studied by ignoring the polarization states of W-boson. In this paper, considering the different polarization states of W-boson, we will numerically study the angular distribution of the energy spectrum of B-mesons in a specific reference frame. Finally, we will compare this energy spectrum in two cases of polarized and unpolarized top quark.
In this work, we determine the non-perturbative fragmentation function (FF) of B-mesons (meson including a bottom quark flavor), phenomenologically, at next-to-leading order QCD perturbation theory using data from electron-positron annihilation. In this regard, we apply all current experimental data from OPAL, ALEPH, SLD2002 and DELPHI collaborations. We also apply the Hessian method to calculate the error in determination of FFs. As an application, using our extracted results we shall make our predictions for energy distribution of B-mesons produced through top quark decay. Study of the B-meson energy spectrum can be considered as a convenient channel to search for the properties of top quarks at CERN.
