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Determining the spin of any new particle and measuring its couplings to otherparticles and/or itself are crucial in reconstructing the structure of anyquantum field theory containing the particle. A general helicity formalism isemployed 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 dynamicalproperties of three involved particles and for determining their spinsaltogether. We perform a general and comprehensive analytic analysis with ourspecial focus on grasping fully how to connect the decay helicity amplitudesand decay distributions in the $X_2$ rest frame and those in a laboratory framewith $X_2$ moving with a non-zero velocity through Wick helicity rotation onhelicity states and amplitudes. This theoretical framework is demonstrated in adetailed illustrative manner with the Standard Model (SM) processes, thesequential 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 $e^-e^+\tot\bar{t}$ followed by $t\to W^+ b \to (\ell^+\nu_\ell)b$, and one non-standarddecay 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 anycombinations of spins and any types of couplings in the two-body decay $X_2\toY X_1$ followed by suitable $Y$ two-body decays processes are collected anddescribed in detail.

General Spin Analysis from Angular Correlations in Two-Body Decays