Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

1S and MSbar Bottom Quark Masses from Upsilon Sum Rules

A. H. Hoang

TL;DR

Using Υ sum rules in NRQCD, the paper adopts the 1S short-distance bottom-quark mass to avoid pole-mass ambiguities and computes NNLO moments to fit experimental data. The analysis yields M_b^{1S} = 4.71 ± 0.03 GeV (with α_s(M_Z) = 0.118 ± 0.004) and, via the upsilon expansion, ar m_b(ar m_b) = 4.20 ± 0.06 GeV, with the latter limited by unknown three-loop corrections and α_s precision. The work also discusses low-scale running and PS/LS mass schemes as cross-checks, finding compatible results and arguing that the 1S scheme provides the most natural, perturbatively stable framework for non-relativistic bottomonium. Overall, the study demonstrates reduced perturbative uncertainties and weaker correlations with α_s in the 1S scheme, outlining clear paths to tighter MSbar precision with future higher-order calculations.

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 $Υ$ 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 $Λ_{QCD}$ 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 $α_s(M_Z)=0.118\pm 0.004$ 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.

1S and MSbar Bottom Quark Masses from Upsilon Sum Rules

TL;DR

Using Υ sum rules in NRQCD, the paper adopts the 1S short-distance bottom-quark mass to avoid pole-mass ambiguities and computes NNLO moments to fit experimental data. The analysis yields M_b^{1S} = 4.71 ± 0.03 GeV (with α_s(M_Z) = 0.118 ± 0.004) and, via the upsilon expansion, ar m_b(ar m_b) = 4.20 ± 0.06 GeV, with the latter limited by unknown three-loop corrections and α_s precision. The work also discusses low-scale running and PS/LS mass schemes as cross-checks, finding compatible results and arguing that the 1S scheme provides the most natural, perturbatively stable framework for non-relativistic bottomonium. Overall, the study demonstrates reduced perturbative uncertainties and weaker correlations with α_s in the 1S scheme, outlining clear paths to tighter MSbar precision with future higher-order calculations.

Abstract

The bottom quark 1S mass, , is determined using sum rules which relate the masses and the electronic decay widths of the mesons to moments of the vacuum polarization function. The 1S mass is defined as half the perturbative mass of a fictitious bottom-antibottom quark bound state, and is free of the ambiguity of order 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 GeV taking as an input. From that we determine the mass as GeV. The error in can be reduced if the three-loop corrections to the relation of pole and mass are known and if the error in the strong coupling is decreased.

Paper Structure

This paper contains 7 sections, 26 equations, 2 figures, 5 tables.

Table of Contents

  1. Introduction
  2. The $1S$ Bottom Quark Mass
  3. The $\Upsilon$ Sum Rules
  4. Numerical Results
  5. Determination of the $\overline{\hbox{MS}}$ Mass and the Upsilon Expansion
  6. The Low Scale Running and the Potential Subtracted Bottom Quark Masses
  7. Conclusions

Figures (2)

  • Figure 1: Result for the allowed region in the $M_b^{1S}$-$\alpha_s$ plane for the unconstrained fit based on the theoretical moments at NNLO (a) and NLO (b). The dots represent points of minimal $\chi^2$ for a large number of random choices within the ranges (\ref{['parameterranges']}) and the sets (\ref{['nsets']}). Experimental errors are not displayed. The two-loop running has been employed for the strong coupling.
  • Figure 2: Result for the allowed $M_b^{1S}$ values for a given value of $\alpha_s$ at NNLO (a) and NLO (b). The dots represent points of minimal $\chi^2$ for a large number of random choices within the ranges (\ref{['parameterranges']}) and the sets (\ref{['nsets']}), and randomly chosen values for the strong coupling $\alpha_s(2.5~\hbox{GeV})$. Experimental errors at the $95\%$ CL level are displayed as vertical lines. It is illustrated how the allowed range for $M_b^{1S}$ is obtained if $0.114\le\alpha_s(M_z)\le 0.122$ is taken as an input. The two-loop running has been employed for the strong coupling.