Breaking down the entire spectrum of spin correlations of a pair of particles involving fermions and gauge bosons

We discuss a formalism for the spin correlations and polarizations in two-particle systems with spins half-half, half-one and one-one, and provide the connections between the polarizations and correlations with the joint angular distributions of decay products identifying the asymmetries for them. We demonstrate the formalism in the processes $e^-e^+\to t\bar{t}$, $gb \to tW^-$ and $e^-e^+\to ZZ$ in the standard model as examples. We investigate the effect of some anomalous couplings on the polarizations and spin correlations in the processes $e^-e^+\to t\bar{t}$, $gb \to tW^-$ and $u\bar{d}\to ZW^+$ at parton level and compare their strengths. The spin correlations have the potential to provide a significant improvement over the polarizations in probing the anomalous couplings.