The Strange Quark Mass from QCD Sum Rules

Abstract

The strange quark mass is calculated from QCD sum rules for the divergence of the vector as well as axial-vector current in the next-next-to-leading logarithmic approximation. The determination for the divergence of the axial-vector current is found to be unreliable due to large uncertainties in the hadronic parametrisation of the two-point function. From the sum rule for the divergence of the vector current, we obtain a value of $m_s\equiv {\text{mb}}_s(1\text{gev})=189\pm 32\text{mev}$, where the error is dominated by the unknown perturbative $\mathcal{O}({\alpha }_s^3)$ correction. Assuming a continued geometric growth of the perturbation series, we find $m_s=178\pm 18\text{mev}$. Using both determinations of $m_s$, together with quark-mass ratios from chiral perturbation theory, we also give estimates of the light quark masses $m_u$ and $m_d$.

Comments: 31 pages, 5 figures as separate uu-file, (Small TeX-problem corrected) CERN--TH.7435/94, TUM-T31-78/94