Flavour Singlet $\mathcal{O}({\alpha }_s^2{m}_b^2/m_t^2)$ Corrections to the Partial Decay Rate $\Gamma (Z\to b\bar{b})$

Abstract

We analytically compute the flavour singlet $\mathcal{O}({\alpha }_s^2{m}_b^2/m_t^2)$ radiative corrections to the partial decay rate $\Gamma (Z\to b\bar{b})$. 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.Kühn for the flavour singlet massless corrections \cite{KniKue90} as well as our previous $\mathcal{O}({\alpha }_s^2{m}_b^2/M_Z^2)$ result \cite{CheKwi93}.

9 pages, 2 figures (eps-files will be ftp'ed on request)

References in corpus (2)

• Euclidean asymptotic expansions of Green functions of quantum fields (I) Expansions of products of singular functions
• Euclidean asymptotic expansions of Green functions of quantum fields (II) Combinatorics of the asymptotic operation

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• Small-threshold behaviour of two-loop self-energy diagrams: two-particle thresholds
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• Electroweak radiative corrections in Z boson decays