Charm and Bottom Quark Masses from Perturbative QCD

Abstract

Using a new result for the first moment of the hadronic production cross section at order ${\cal O}(α_s^3)$, and new data on the $J/ψ$ and $ψ'$ resonances for the charm quark, we determine the \msb masses of the charm and bottom quarks to be $\bar{m}_c(\bar{m}_c) = 1.295 \pm 0.015$ GeV and $\bar{m}_b(\bar{m}_b) = 4.205 \pm 0.058$ GeV. We assume that the continuum contribution to the sum rules is adequately described by pQCD. While we observe a large reduction of the perturbative error, the shifts induced by the theoretical input are very small. The main change in the central value of $m_c$ is related to the experimental data. On the other hand, the value of $m_b$ is not changed by our calculation to the assumed precision.

Figures (2)

• Figure 1: Singlet diagrams with a three-gluon cut.
• Figure 2: Definition of the numerical constants $N_i$ from the $\epsilon$ expansion of vacuum integrals.