====== TTP93-08 Complete QCD Corrections of Order $\alpha_s^2$ to the Z Decay Rate ======
 
 
<hidden TTP93-08  Complete QCD Corrections of Order $\alpha_s^2$ to the Z Decay Rate > The axial part of the Z decay rate  into hadrons ($\G^A_Z$) gets
 extra singlet contributions due to the huge  splitting between top
 and bottom quark masses.  By treating the axial neutral current in
 the large top-mass limit we partially re-derive in a systematic manner
 the known results on the contribution of the $\as^2$ order anomalous
 "double triangle" diagrams to  $\G^A_Z$ and resolve an ambiguity
 concerning the scale at which  the strong coupling constant
 $\alpha_s$ is to be taken in these diagrams.
 We evaluate and sum  all
 leading log  and next to leading log QCD corrections of orders
 $\as^{1+n}(\ln(M_Z/4m^2_t))^n$ and $\as^{2+n}(\ln(M_Z/4m^2_t))^n$
 respectively.
 
 We examine the sensitivity of our results  to a change of
 the renormalization scales  to estimate the size of yet unknown
 corrections of order $\alpha_s^3$ to $\G^A_Z$.  The analysis implies
 that the corrections  might change the magnitude of the singlet
 term by up to 30\%   while they hardly might be of noticeable
 numerical significance in comparison with the total contribution from
 non-singlet  terms.
 </hidden>
|**K.G.Chetyrkin, J.H.K\"uhn**  | 
|** Phys. Lett. B308 127--136 1993  **  |
| {{preprints:1993:ttp93-08.pdf|PDF}} {{preprints:1993:ttp93-08.ps|PostScript}}   |
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