Flavour Singlet ${\cal O}(\alpha_s^2 m_b^2/m_t^2)$ Corrections to the Partial Decay Rate $\Gamma(Z\rightarrow b\bar{b})$

Abstract

We analytically compute the flavour singlet ${\cal O}(\alpha_s^2 m_b^2/m_t^2)$ radiative corrections to the partial decay rate $\Gamma(Z\rightarrow b\bar{b})$. These corrections arise from anomalous ``double traingle'' diagrams containing a single $\gamma_5$ matrix inside each of two closed fermion loops. They represent the next-to-leading term of the asymptotic expansion in the inverse large top mass. As a byproduct of the calculcation we confirm the results of B.Kniehl and J.H.K\"uhn for the flavour singlet massless corrections \cite{KniKue90} as well as our previous ${\cal O}(\alpha_s^2 m_b^2/M_Z^2)$ result \cite{CheKwi93}.