====== TTP01-19 The Cross Section of e^+ e^- Annihilation into Hadrons of Order alpha_s^4 n_f^2 in Perturbative QCD ======
 
 
   <hidden TTP01-19  The Cross Section of e^+ e^- Annihilation into Hadrons of Order alpha_s^4 n_f^2 in Perturbative QCD > We present  the first genuine QCD five-loop calculation
 of the vacuum  polarization functions: analytical  
 terms of order alpha_s^4 n_f^2 to the
 absorptive parts of vector and scalar correlators.  
 These corrections  form  an important   gauge-invariant 
 subset of the full  O(alpha_s^4) correction to
 $e^+ e^- annihilation  into hadrons and the Higgs decay rate
 into hadrons respectively. They discriminate between different
 widely used estimates of  the full result. 
 </hidden>
|**P.A. Baikov, K.G. Chetyrkin and J.H. K\"uhn**  | 
|**  Phys. Rev. Lett.  88 012001-012004 2002  **  |
| {{preprints:2001:ttp01-19.pdf|PDF}} {{preprints:2001:ttp01-19.ps|PostScript}} [[http://arxiv.org/abs/hep-ph/0108197|arXiv]]   |
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