====== TTP97-33 Non-Abelian Dipole Radiation and the Heavy Quark Expansion ======
 
 
   <hidden TTP97-33  Non-Abelian Dipole Radiation and the Heavy Quark Expansion > Dipole radiation in QCD is derived to the second order in
 $\alpha_s$. A power-like evolution of the spin-singlet heavy quark
 operators is obtained to the same accuracy. We give an ${\cal
 O}(\alpha_s^2)$ relation between the short-distance low-scale running
 heavy quark mass and the $\overline{\rm MS}$ mass.  We discuss the
 properties of an effective QCD coupling $\alpha_s^{(d)}(E)$ which
 governs the dipole radiation. We argue that this coupling is
 advantageous for describing heavy quark physics.
 </hidden>
|**Andrzej Czarnecki, Kirill Melnikov, and Nikolai Uraltsev**  | 
|** Phys. Rev. Lett. 80 3189 1998  **  |
| {{preprints:1997:ttp97-33.pdf|PDF}} {{preprints:1997:ttp97-33.ps|PostScript}} [[http://arxiv.org/abs/hep-ph/9708372|arXiv]]   |
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