Fully analytical O(\alpha_s) results for on-shell and off-shell polarized W-boson decays into massive quark pairs

TL;DR

This paper presents exact analytical calculations at order alpha_s for polarized W-boson decay functions into massive quark pairs, with applications to top quark and Higgs decay processes, highlighting mass and off-shell effects.

Contribution

It provides the first complete analytical O(α_s) results for polarized decay structure functions of W bosons into massive quarks, including off-shell and mass effects in cascade decays.

Findings

Significant deviations from massless approximations near thresholds.

Analytical expressions for polarized decay functions at O(α_s).

Detailed analysis of off-shell and mass effects in Higgs and top decays.

Abstract

We provide analytical $O(\alpha_s)$ results for the three polarized decay structure functions $H_{++},\,H_{00}$ and $H_{--}$ that describe the decay of a polarized $W$ boson into massive quark--antiquark pairs. As an application we consider the decay $t\to b+W^+$ involving the helicity fractions $\rho_{mm}$ of the $W^+$ boson followed by the polarized decay $\hbox{$W^+(\uparrow)$}\to q_1\bar{q}_2$ described by the polarized decay structure functions $H_{mm}$. We thereby determine the $O(\alpha_s)$ polar angle decay distribution of the cascade decay process $t\to b+W^+(\to q_1\bar{q}_2)$. As a second example we analyze quark mass and off-shell effects in the cascade decays $H\to W^{-}+W^{\ast +}(\to q_1\bar{q}_2)$ and $H\to Z+Z^{\ast}(\to q\bar{q})$. For the decays $H\to W^{-}+W^{\ast +}(\to c\bar b)$ and $H\to Z+Z^{\ast}(\to b\bar{b})$ we find substantial deviations from the mass-zero approximation in particular in the vicinity of the threshold region.