Importance of Tests for the Complete Lorentz Structure of the t --> W+ b vertex at Hadron Colliders

The most general Lorentz-invariant decay-density-matrix for $t\to W^{+}b\to (l^{+}\nu)b$,orfor$t\to W^{+}b\to (j_{\bar d}j_u)b$, is expressed in terms of eight helicity parameters. The parameters are physically defined in terms of partial-width-intensities for polarized-final-states in $t\to W^{+}b$ decay. The parameters are the partial width, the $b$ quark’s chirality parameter $\xi$, the $W^{+}$ polarimetry parameter $\sigma$, a “pre-SSB” test parameter $\zeta$, and four $W_L$-$W_T$ interference parameters $\eta$, ${\eta }^{{}^{\mathrm{\prime }}}$, $\omega$, ${\omega }^{{}^{\mathrm{\prime }}}$ which test for ${\tilde{T}}_{FS}$ violation. They can be used to test for non-CKM-type CP violation, anomalous ${\mathrm{\Gamma }}_{L,T}$'s, top weak magnetism, weak electricity, and second-class currents. By stage-two spin-correlation techniques, percent level statistical uncertainites are typical for measurements at the Tevatron, and several mill level uncertainites are typical at the LHC.