General spin analysis from angular correlations in two-body decays

Seong Youl Choi; Jae Hoon Jeong; Ji Ho Song

doi:10.1140/epjp/s13360-020-00132-1

EPJ

a
b
c
d
e
ap
st
h
plus
ds
pv
ti
qt
am
n

2024 Impact factor 2.9

EPJ PLUS - Condensed Matter and Complex Systems

Eur. Phys. J. Plus (2020) 135: 210
https://doi.org/10.1140/epjp/s13360-020-00132-1

Regular Article

General spin analysis from angular correlations in two-body decays

Seong Youl Choi^*, Jae Hoon Jeong and Ji Ho Song

Department of Physics and RIPC, Jeonbuk National University, Jeonju, 54896, Korea

^* e-mail: choisy7@gmail.com

Received: 9 March 2019
Accepted: 22 November 2019
Published online: 3 February 2020

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.