Coulomb resummation for $b \bar b$ system near threshold and precision determination of $\al_s$ and $m_b$.

TL;DR

The paper presents a Coulomb-resummed sum-rule analysis of the $\Upsilon$ system to extract the bottom-quark pole mass $m_b$ and the strong coupling constant $\\alpha_s$, resolving inconsistencies among prior results. It compares direct and optimized nonrelativistic computations of the Coulomb Green function, advocating an effective Coulomb charge to minimize higher-order corrections. The optimized approach yields $m_b = 4.75 \pm 0.04$ GeV and $\\alpha_s(M_Z) = 0.118 \pm 0.006$, aligning with LEP data, while highlighting that neglecting pole contributions or using too low a normalization scale leads to biased results and underestimated uncertainties. The work stresses the crucial role of higher-order $\\alpha_s$ corrections and the need for a consistent treatment of next-to-leading-order effects in sum-rule analyses of near-threshold heavy-quark systems.

Abstract

We analyze sum rules for the $Υ$ system with resummation of threshold effects on the basis of the nonrelativistic Coulomb approximation. We find for the pole mass of the bottom quark $m_b=4.75\pm 0.04 GeV$ and for the strong coupling constant $\al_s(M_Z)=0.118\pm 0.006$. The origin of the contradiction between two recent estimates obtained within the same formal framework is clarified.