Non factorizable $O(\alpha\alpha_s)$ corrections to the process $Z\to b\bar{b}$

TL;DR

This paper computes complex two-loop quantum corrections to the Z boson decay into bottom quarks, including virtual top-quark effects and gluon emissions, using advanced large-mass expansion techniques.

Contribution

It provides the first detailed calculation of non-factorizable $O(\alphaeta_s)$ corrections to $Z o bar{b}$ involving the virtual top-quark, with all diagrams evaluated in a large top-mass expansion.

Findings

Derived closed-form expansion coefficients for large top-mass expansion.

Confirmed agreement with previous results up to $O(m_W^6/m_t^6)$.

Included gluon bremsstrahlung effects in the calculation.

Abstract

We evaluate non factorizable $O(\alpha\alpha_s)$ corrections to the process $Z\to b\bar{b}$ due to the virtual t-quark. All two-loop vertex diagrams with $W$'s and charged ghosts $\Phi$'s are included. They are evaluated in the large top-mass expansion up to the $10^{th}$ order. Gluon Bremsstrahlung is taken into account by integrating over the whole phase space. All calculations, including Bremsstrahlung, are done in dimensional regularization. The expansion coefficients of the large mass expansion are given in closed form. Their expansion in $y=m_Z^2/4m_W^2$ is in agreement with the coefficients up to $O(m_W^6/m_t^6)$ as given by Harlander et al.