Three-Loop Polarization Function and $\mathcal{O}({\alpha }_s^2)$ Corrections to the Production of Heavy Quarks

Abstract

The three-loop vacuum polarization function $\Pi (q^2)$ induced by a massive quark is calculated. A comprehensive description of the method is presented. From the imaginary part the $\mathcal{O}({\alpha }_s^2)$ result for the production of heavy quarks $R(s)=σ(e^+e^-\to \mbox{hadrons})/σ(e^+e^-\to μ^+μ^-)$ can be extracted. Explicit formulae separated into the different colour factors are given.

28 pages, latex, 29 figures, the complete postscript file of this preprint, including figures, is available via anonymous ftp at ftp://www-ttp.physik.uni-karlsruhe.de/ttp96-13/ttp96-13.ps or via www at http://www-ttp.physik.uni-karlsruhe.de/cgi-bin/preprints/

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