  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
$X_2\to Y X_1$ with polarized $X_2$ 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 $X_2$ rest frame and those in a laboratory frame
with $X_2$ 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 $e^-e^+\to Z\to \tau^-\tau^+$ followed by $\tau^-\to
\rho^-\nu_\tau\to (\pi^-\pi^0)\nu_\tau$ and the sequential process $e^-e^+\to
t\bar{t}$ followed by $t\to W^+ b \to (\ell^+\nu_\ell)b$, and one non-standard
decay process of a new vectorlike heavy top quark, $T\to Z t$, followed by
$Z\to \ell^-\ell^+$. All the useful formulas directly applicable to any
combinations of spins and any types of couplings in the two-body decay $X_2\to
Y X_1$ followed by suitable $Y$ two-body decays processes are collected and
described in detail.
