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

TL;DR

This paper provides detailed next-to-leading order calculations of the hadron energy spectrum in polarized top quark decays, incorporating effects of quark and hadron masses, gluon fragmentation, and using realistic fragmentation functions.

Contribution

It introduces analytical NLO corrections for top decay processes with nonzero b-quark mass and applies a comprehensive scheme to predict hadron energy distributions.

Findings

Analytical expressions for decay widths with nonzero b-quark mass.

Inclusion of gluon fragmentation and hadron mass effects.

Predictions consistent with experimental fragmentation data.

Abstract

We present the analytical expressions for the next-to-leading order corrections to the partial decay width $t(\uparrow) \rightarrow bW^+$, followed by $b\rightarrow H_bX$, for nonzero b-quark mass ($m_b\neq 0$) 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 $e^+e^-$ annihilation data from CERN LEP1 and SLAC SLC by relying on their universality and scaling violations.