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The modularity property of the helicity formalism is used to provideamplitude expressions and stage-two spin-correlation functions which can easilybe used in direct experimental searches for electro-weak symmetries anddynamics in the decay processes $t \to W^+ b$, $\bar t \to W^- \bar b$. Theformalism 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 mostgeneral 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 termsof eight helicity parameters and, equivalently, in terms of the structures ofthe $J_{\bar b t}$ current. The parameters are physically defined in terms ofpartial-width-intensities for polarized-final-states in \newline $t\to W^{+}b$decay. The full angular distribution for the reactions $q \bar q$ and $g g \tot \bar t \to (W^+ b) (W^- \bar b) \to ...$ can be used to measure theseparameters. Since this adds on spin-correlation information from the next stageof decays in the decay sequence, such an energy-angular distribution is calleda stage-two spin-correlation (S2SC) function.Comment: Minor clarifications. Expressions for r_{+-}, rho_{+-}, and \xi for (  L + S-P) coupling corrected. 36 pages LaTex + Tables + 14 Fig

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

General tests for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>t</mml:mi><mml:mo>→</mml:mo><mml:mrow><mml:msup><mml:mrow><mml:mi>W</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow><mml:mi>b</mml:mi></mml:math>couplings at hadron colliders

General tests fort→W+bcouplings at hadron colliders