Bottom quark mass and alpha_s from the Upsilon system

TL;DR

Using QCD moment sum rules for the Upsilon system, the paper determines the bottom-quark mass and the strong coupling with two parallel analyses in the pole and MS-bar schemes. It employs Coulomb resummation to handle near-threshold dynamics, includes perturbative corrections up to two loops (with partial higher-order input via Padé approximants), and accounts for nonperturbative gluon-condensate effects in a controlled way. The extracted values are M_b ≈ 4.60 GeV, m_b(m_b) ≈ 4.13 GeV, and alpha_s(MZ) ≈ 0.119, with cross-checks showing reasonable scheme stability and a clear error budget dominated by unknown higher-order perturbative terms. The results are consistent with the current world average for alpha_s and cast doubt on earlier claims of a significantly lower alpha_s from low-energy determinations, while emphasizing the importance of scale-setting and higher-order calculations for precision.

Abstract

The mass of the bottom quark and the strong coupling constant alpha_s are determined from QCD moment sum rules for the Upsilon system. Two analyses are performed using both the pole mass M_b as well as the mass m_b in the $\MSb$ scheme. In the pole-mass scheme large perturbative corrections resulting from coulombic contributions have to be resummed. In the $\MSb$ scheme this can be avoided by an appropriate choice for the renormalization scale. For the bottom quark mass we obtain M_b = 4.60 +- 0.02 GeV and m_b(m_b) = 4.13 +- 0.06 GeV. Our combined result from both determinations for the strong coupling is alpha_s(M_Z) = 0.119 +- 0.008.

Figures (1)

• Figure 1: The $b$ quark pole mass as a function of $n$.