1S and MSbar Bottom Quark Masses from Upsilon Sum Rules

TL;DR

This paper accurately determines the bottom quark 1S and ar MS masses using sum rules based on eta meson properties, improving precision over previous pole mass methods by employing the 1S scheme.

Contribution

It introduces the use of the 1S mass scheme for bottom quarks in sum rule analyses, reducing uncertainties and correlations compared to the pole mass scheme.

Findings

Bottom quark 1S mass: 4.71 b1 0.03 GeV

ar MS mass: 4.20 b1 0.06 GeV

Improved perturbative series and reduced uncertainties

Abstract

The bottom quark 1S mass, $M_b^{1S}$, is determined using sum rules which relate the masses and the electronic decay widths of the $\Upsilon$ mesons to moments of the vacuum polarization function. The 1S mass is defined as half the perturbative mass of a fictitious ${}^3S_1$ bottom-antibottom quark bound state, and is free of the ambiguity of order $\Lambda_{QCD}$ which plagues the pole mass definition. Compared to an earlier analysis by the same author, which had been carried out in the pole mass scheme, the 1S mass scheme leads to a much better behaved perturbative series of the moments, smaller uncertainties in the mass extraction and to a reduced correlation of the mass and the strong coupling. We arrive at $M_b^{1S}=4.71\pm 0.03$ GeV taking $\alpha_s(M_Z)=0.118\pm 0.004$ as an input. From that we determine the $\bar{MS}$ mass as $\bar m_b(\bar m_b) = 4.20 \pm 0.06$ GeV. The error in $\bar m_b(\bar m_b)$ can be reduced if the three-loop corrections to the relation of pole and $\bar{MS}$ mass are known and if the error in the strong coupling is decreased.