Resummed pole mass, static potential, and Upsilon(1S) spectrum

Abstract

Employing the heavy quark pole mass and static potential that were obtained from resummation of the renormalon-caused large order behavior to all orders, and matching the resummed static potential to the long distance Cornell potential we obtain a new estimate of the bottom quark mass % $m_b^{\bar{\text % MS}}=4.20$ GeV at $\alpha_s(M_z)=0.118$ from $\Upsilon$(1S) system. We point out that the pure perturbative QCD approach to $\Upsilon$(1S) spectrum should have a sizable systematic error of about 100 MeV, due to the absence of the long distance confining potential, and that the incorporation of the latter is essential for accurate determination of the ground state energy. We also recalculate the nonperturbative Leutwyler-Voloshin effect using a resummed octet potential matched to a confining linear potential, and obtain a result that is substantially smaller than the estimates based on Coulombic potentials. The hyperfine splitting is estimated to be $50 \pm 8$ MeV at $\alpha_s(M_z)=0.118$.