Non-Singlet Corrections of O(\alpha_s^2 G_F M_t^2) to \Gamma(Z\to b\bar{b})

TL;DR

This paper calculates non-singlet quantum corrections at two-loop order to the Z boson decay rate into bottom quarks, focusing on the effects of the top quark mass in the loop diagrams.

Contribution

It provides the first detailed analysis of non-singlet diagrams at O(\alpha_s^2 G_F M_t^2), extending previous heavy-top approximations.

Findings

Non-singlet corrections significantly affect the decay rate.

Heavy-top approximation remains valid at this order.

Results improve precision of theoretical predictions for Z decay.

Abstract

The partial decay rate of the $Z$ boson into bottom quarks constitutes an important decay channel. This is mainly due to the virtual presence of the top quark in the loop diagrams giving rise to correction factors which are quadratic in the top quark mass. At one- and two-loop order it turned out that the leading term in the heavy-top expansion leads to very good approximations to the exact result. In this work the non-singlet diagrams at O(\alpha_s^2 G_F M_t^2) are considered.