Hadron energy spectrum in polarized top-quark decays considering the effects of hadron and bottom quark masses

We present the analytical expressions for the next-to-leading order corrections to the partial decay width t(↑) → bW⁺, followed by b @→ H_bX, for nonzero b-quark mass (m_b ≠ 0) in the fixed-flavor-number scheme (FFNs). To make the predictions for the energy distribution of outgoing hadrons H_b, as a function of the normalized H_b-energy fraction x_H, we apply the general-mass variable-flavor-number scheme (GM-VFNs) in a specific helicity coordinate system where the polarization of top quark is evaluated relative to the b-quark momentum. We also study the effects of gluon fragmentation and finite hadron mass on the hadron energy spectrum so that hadron masses are responsible for the low x_H threshold. In order to describe both the b-quark and the gluon hadronizations in top decays we apply realistic and nonperturbative fragmentation functions extracted through a global fit to the e⁺e^- annihilation data from CERN LEP1 and SLAC SLC by relying on their universality and scaling violations. (orig.)