General Tests for t ---> W+ b couplings 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 electro-weak symmetries and dynamics in the decay processes $t \to W^+ b$, $\bar t \to W^- \bar b$. The formalism is used to describe the decay sequences $t\to W^{+}b\to (l^{+}\nu)b$, and $t\to W^{+}b\to (j_{\bar d}j_u)b$. Helicity amplitudes for $t \to W^+ b$ are obtained for the most general $J_{\bar b t}$ current. Thereby, the most general Lorentz-invariant decay-density-matrix for $t\to W^{+}b\to (l^{+}\nu)b$, or for $t\to W^{+}b\to (j_{\bar d}j_u)b$, is expressed in terms of eight helicity parameters and, equivalently, in terms of the structures of the $J_{\bar b t}$ current. The parameters are physically defined in terms of partial-width-intensities for polarized-final-states in \newline $t\to W^{+}b$ decay. The full angular distribution for the reactions $q \bar q$ and $g g \to t \bar t \to (W^+ b) (W^- \bar b) \to ...$ 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 (S2SC) function.