$T$-odd correlations in polarized top quark decays in the sequential decay $t(\uparrow) \to X_b+W^+(\to \ell^+ + \nu_\ell)$ and in the quasi three-body decay $t(\uparrow) \to X_b+ \ell^+ + \nu_\ell$

TL;DR

This paper investigates $T$-odd correlations in polarized top quark decays, identifying structure functions and calculating electroweak loop contributions to understand potential CP-violation signals.

Contribution

It identifies $T$-odd structure functions in top decays and computes electroweak loop effects on these functions, highlighting absorptive contributions absent in QCD.

Findings

Identified two $T$-odd structure functions in sequential decay

Calculated electroweak one-loop triangle diagram contributions

Quantified the impact of Im $g_R$ on $T$-odd observables

Abstract

We identify the $T$-odd structure functions that appear in the description of polarized top quark decays in the sequential decay $t(\uparrow) \to X_b+W^+(\to \ell^+ + \nu_\ell)$ (two structure functions) and the quasi-three-body decay $t(\uparrow) \to X_b+ \ell^+ + \nu_\ell$ (one structure function). A convenient measure of the magnitude of the $T$-odd structure functions is the contribution of the imaginary part Im $g_R$ of the right-chiral tensor coupling $g_R$ to the $T$-odd structure functions which we work out. Contrary to the case of QCD the NLO electroweak corrections to polarized top quark decays admit of absorptive one-loop vertex contributions. We analytically calculate the imaginary parts of the relevant four electroweak one-loop triangle vertex diagrams and determine their contributions to the $T$-odd helicity structure functions that appear in the description of polarized top quark decays.