Determining the spin of any new particle and measuring its couplings to other particles and/or itself are crucial in reconstructing the structure of any quantum field theory containing the particle. A general helicity formalism is employed to describe the polarization of the particle Y in a two-body decay X2 → Y X1 with polarized X2 for the purpose of diagnosing the dynamical properties of three involved particles and for determining their spins altogether. We perform a general and comprehensive analytic analysis with our special focus on grasping fully how to connect the decay helicity amplitudes and decay distributions in the X2 rest frame and those in a laboratory frame with X2 moving with a non-zero velocity through Wick helicity rotation on helicity states and amplitudes. This theoretical framework is demonstrated in a detailed illustrative manner with the Standard Model (SM) processes, the sequential process e − e + → Z → τ − τ + followed by τ − → ρ − ντ → (π − π 0 )ντ and the sequential process e − e + → tt followed by t → W + b → (ℓ + ν ℓ )b-, and one non-standard decay process of a new vectorlike heavy top quark, T → Zt, followed by Z → ℓ − ℓ + . All the useful formulas directly applicable to any combinations of spins and any types of couplings in the two-body decay X2 → Y X1 followed by suitable Y two-body decays processes are collected and described in detail.On the high energy frontier, equipped with the Large Hadron Collider (LHC) [5], we are now probing the electroweak (EW) scale (v = 246 GeV) and beyond intensively and extensively after having established the SM by the decisive discovery of a Higgs boson [6,7] followed by very precise measurements of its mass and couplings [8,9] and model-independent determinations of its spinless nature [10][11][12][13][14][15]. The true theory for the origin and stability of the EW scale [16][17][18][19] beyond the SM is highly expected to be revealed with a huge amount of accumulated data.One generic prediction in most of new models is the presence of new particles partnered with some or all of the SM particles. For instance, every SM particle in low-energy supersymmetry (SUSY) [20-25] has a * choisy7@gmail.com † jeong229@jbnu.ac.kr ‡ sonjiho0@nate.com 1 Generally, azimuthal-angle correlations can be included in the analysis as well, but they involve quantum interference among the states with different helicities and require by far more complicated kinematic reconstructions [28]. For the sake of simple and straightforward kinematical analyses, we do not consider them here, postponing the analysis involving azimuthal-angle correlations as our later project.2 In principle any multi-body decay modes of the particle Y can be considered for extracting the information on Y polarization.As a consequence, the decay helicity amplitudes in the LAB for the two-body decay are related to those in the X 2 RF through two Wick helicity rotations on the Y and X 1 states as