====== TTP03-40 $M(\eta_b)$ and $\alpha_s$ from Nonrelativistic Renormalization Group ======
 
 
   <hidden TTP03-40  $M(\eta_b)$ and $\alpha_s$ from Nonrelativistic Renormalization Group > We sum up the next-to-leading logarithmic corrections to the heavy-quarkonium
 hyperfine splitting using the nonrelativistic renormalization group. 
 On the basis of this result, we predict the mass of the $\eta_b$ meson to be 
 $M(\eta_b)=9421 \pm 10\,{(\rm th)} \,{}^{+9}_{-8}\,(\delta\alpha_s)~{\rm MeV}$.
 The experimental measurement of  $M(\eta_b)$ with a few MeV error would be 
 sufficient to determine $\alpha_s(M_Z)$ with an accuracy of $\pm 0.003$.  
 The use of the nonrelativistic renormalization group is mandatory to reproduce
 the experimental value of the hyperfine splitting in charmonium.
 </hidden>
|**Bernd A. Kniehl, Alexander A. Penin, Antonio Pineda, Vladimir A. Smirnov, Matthias Steinhauser**  | 
|**  Phys.Rev.Lett.  92 242001 2004  **  |
| {{preprints:2003:ttp03-40.pdf|PDF}} {{preprints:2003:ttp03-40.ps|PostScript}} [[http://arxiv.org/abs/hep-ph/0312086|arXiv]]   |
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