Use of $\Lambda_{b}$ Polarimetry in Top Quark Spin-Correlation Functions

Due to the absence of hadronization effects and the large top mass, top quark decay will be uniquely sensitive to fundamental electroweak physics at the Tevatron, at the LHC, and at a future linear collider. A complete measurement of the four helicity amplitudes in top decay is possible by the combined use of Lambda_b and W polarimetry in stage-two spin-correlation functions (S2SC). In this paper, the most general Lorentz-invariant decay density matrix is obtained for the decay sequence (t --> W b) where (b --> l nu c) and (W --> l nu), and likewise for the CP-conjugate mode. These density matrices are expressed in terms of b-polarimetry helicity parameters which enable a unique determination of the relative phases among the helicity amplitudes. Thereby, S2SC distributions and single-sided distributions are expressed in terms of these parameters. The four b-polarimetry helicity parameters involving the A(-1,-1/2) amplitude are considered in detail. Lambda_b polarimetry signatures will not be suppressed in top quark analyses when the final neutrino's angles-and-energy variables are used for (b --> l nu c).