Complete Corrections of O(αα_s) to the Decay of the Z Boson into Bottom Quarks

TL;DR

This paper completes the non-universal O(αα_s) corrections to Γ(Z→bb) from top–W loop diagrams by computing the missing constant term and several subleading terms in the high Mt expansion. Employing a hard mass procedure, an automated diagrammatic workflow (EXP) with MATAD/MINCER, and a three-loop Z-boson polarization function, the authors derive analytic expansions in 1/Mt and 1/cΘ^2, along with gauge-parameter and mass-scheme checks. The results reveal that the constant term at next-to-leading order dominates over ln Mt^2, and numerical estimates for realistic inputs show a non-negligible mixed correction that must be included in precision Z-boson line-shape predictions. The work provides ready-to-implement expressions for both OS and MSbar schemes, enhancing the accuracy of electroweak fits involving Z→bb decays.

Abstract

For the vertex corrections to the partial decay rate $Γ(Z \to b\bar{b})$ involving the top quark only the leading terms of order $αα_s$ in the $1/M_t$ expansion are known. In this work we compute the missing next-to-leading corrections. Thus at $O(αα_s)$ the complete corrections to the decay of the Z boson into bottom quarks are at hand.

Figures (1)

• Figure 1: Diagrams contributing to $\delta\Gamma^W_b$ in ${\cal O}(\alpha)$. Thin lines correspond to bottom quarks, thick lines to top quarks, dotted lines to Goldstone bosons and inner wavy lines represent $W$ bosons.