General spin analysis from angular correlations in two-body decays

Abstract

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