# The fully differential top decay distribution

## TL;DR

This paper derives a comprehensive four-dimensional decay distribution for top quark decays, enabling detailed analysis of decay parameters and potential improvements in measuring the $tbW$ interaction structure.

## Contribution

It provides the full differential decay distribution for top quark decay and discusses methods to measure its parameters, including the $tbW$ vertex components.

## Key findings

- Expressions for top decay amplitudes with general $tbW$ interactions
- Strategies for measuring decay parameters using distributions and asymmetries
- Potential for improved precision in $tbW$ vertex measurements

## Abstract

We write down the four-dimensional fully differential decay distribution for the top quark decay $t \to Wb \to \ell \nu b$. We discuss how its eight physical parameters can be measured, either with a global fit or with the use of selected one-dimensional distributions and asymmetries. We give expressions for the top decay amplitudes for a general $tbW$ interaction, and show how the untangled measurement of the two components of the fraction of longitudinal $W$ bosons - those with $b$ quark helicities of $1/2$ and $-1/2$, respectively - could improve the precision of a global fit to the $tbW$ vertex.