The fully differential top decay distribution

We write down the four-dimensional fully differential decay distribution for the top quark decay $t\to Wb\to \mathrm{\ell }\nu b$. 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 $1\mathrm{/}2$ and $-1\mathrm{/}2$, respectively - could improve the precision of a global fit to the $tbW$ vertex.