General tests fort→W+bcouplings at hadron colliders

The modularity property of the helicity formalism is used to provide amplitude expressions and stage-two spin-correlation functions which can easily be used in direct experimental searches for electroweak symmetries and dynamics in the decay processes $t\to W^{+}b$ and $\overline{t}\to W^{-}\overline{b}.$ The formalism is used to describe the decay sequences $t\to W^{+}b\to {(l}^{+}\nu )b$ and $t\to W^{+}b\to {(j}_{\overline{d}}{j}_u)b.\mathrm{}$ Helicity amplitudes for $t\to W^{+}b$ are obtained for the most general $J_{\overline{b}t}$ current. Thereby, the most general Lorentz-invariant decay density matrix for $t\to W^{+}b\to {(l}^{+}\nu )b$ or for $t\to W^{+}b\to {(j}_{\overline{d}}{j}_u)b$ is expressed in terms of eight helicity parameters and, equivalently, in terms of the structures of the $J_{\overline{b}t}$ current. The parameters are physically defined in terms of partial-width intensities for polarized final states in $t\to W^{+}b$ decay. The full angular distribution for the reactions $q\overline{q}$ and $\mathrm{gg}\to t\overline{t}\to {(W}^{+}{b\left)\right(W}^{-}\overline{b})\to \cdots$ can be used to measure these parameters. Since this adds on spin-correlation information from the next stage of decays in the decay sequence, such an energy-angular distribution is called a stage-two spin-correlation function.