Angular analysis of polarized top quark decay into B-mesons in two different helicity systems

TL;DR

This paper calculates next-to-leading order radiative corrections to the angular distribution of B-hadrons from polarized top quark decays in two helicity systems, aiding top polarization studies and understanding of hadronization.

Contribution

It introduces a comparison of polarized top decay energy spectra in two different helicity coordinate systems at NLO, enhancing analysis of top polarization and fragmentation functions.

Findings

Predicted B-hadron energy spectra in polarized top decays.

Compared angular distributions in two helicity systems.

Provided insights into top polarization measurement methods.

Abstract

We calculate the ${\cal O}(\alpha_s)$ radiative corrections to the spin dependent differential decay rates of the process $t\rightarrow b+W^+$. These are needed to study the angular distribution of the energy of hadrons produced in polarized top quark decays at next-to-leading order (NLO). In our previous work, we studied the angular distribution of the scaled-energy of bottom-flavored hadrons (B) from polarized top quark decays, using a specific helicity coordinate system where the top quark spin was measured relative to the bottom momentum (system~1). Here, we study the angular distribution of the energy spectrum of B-hadron in a different helicity system, where the top spin is specified relative to the W-momentum (system~2). These energy distributions are governed by the polarized and unpolarized rate functions which are related to the density matrix elements of the decay $t\rightarrow W^++b$. Through this paper, we present our predictions of the B-hadron spectrum in the polarized and unpolarized top decay and shall compare the polarized results in two different helicity systems. These predictions can be used to determine the polarization states of top quarks and also provide direct access to the B-hadron fragmentation functions (FFs) and allow us to deepen our knowledge of the hadroniazation process.