====== TTP96-17 THREE-LOOP HEAVY QUARK VACUUM POLARIZATION ======
 
 
<hidden TTP96-17  THREE-LOOP HEAVY QUARK VACUUM POLARIZATION > The real and imaginary part of the vacuum polarization function
 $\Pi(q^2)$ induced by a massive quark is calculated in perturbative
 QCD up to order $\alpha_s^2$.
 We combine the information from small and large momentum
 region and from the threshold using conformal mapping
 and Pad\'e approximation. This leads us to formulae for
 $\Pi(q^2)$ valid for arbitrary $m^2/q^2$. Taking subsequently
 the imaginary part we get the ${\cal O}(\alpha_s^2)$ to
 $R  \equiv \sigma(e^+ e^- \to \mbox{hadrons})/
            \sigma(e^+ e^- \to \mu^+ \mu^-)$.
 This extends the calculation by
 K\"all\'en and Sabry from two to three loops.
 </hidden>
|**K.G. Chetyrkin, J.H. Kuehn, M. Steinhauser**  | 
|** Elementary Particle Theory, QCD and QED in Higher Orders, Nucl. Phys. B</B> (Proc.Suppl.)<B>51C 66-70 1996  **  |
| {{preprints:1996:ttp96-17.pdf|PDF}} {{preprints:1996:ttp96-17.ps|PostScript}}   |
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