====== TTP98-13 Next-to-next-to-leading order vacuum polarization function  of heavy quark near threshold and sum rules for  $b \bar b$ system. ======
 
 
   <hidden TTP98-13  Next-to-next-to-leading order vacuum polarization function  of heavy quark near threshold and sum rules for  $b \bar b$ system. > A correlator of the vector current of a heavy quark
 is computed analytically near threshold 
 in the next-to-next-to-leading order in perturbative and relativistic 
 expansion that 
 includes $\al_s^2$, $\al_sv$ and $v^2$ corrections
 in the coupling constant and velocity of the heavy quark
 to the  nonrelativistic Coulomb approximation.
 Based on this result, the numerical values of the $b$-quark pole mass
 and the strong coupling constant are determined 
 from the analysis of sum rules for
 the $\Upsilon$ system.
 </hidden>
|**A.A.Penin and A.A.Pivovarov**  | 
|** Phys. Lett. B435 413-419 1998  **  |
| {{preprints:1998:ttp98-13.pdf|PDF}} {{preprints:1998:ttp98-13.ps|PostScript}} [[http://arxiv.org/abs/hep-ph/9803363|arXiv]]   |
| |