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 $R(s)=\sigma (e^{+}{e}^{-}\to \text{mbox}hadrons)/\sigma (e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-})$ can be extracted. Explicit formulae separated into the different colour factors are given.

Comments: 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/