Up- and down-quark masses from QCD sum rules
C. Dominguez (Centre for Theoretical and Mathematical Physics and Department of Physics, University of Cape Town, Rondebosch, 7700, South Africa); A. Mes (Centre for Theoretical and Mathematical Physics and Department of Physics, University of Cape Town, Rondebosch, 7700, South Africa); K. Schilcher (Centre for Theoretical and Mathematical Physics and Department of Physics, University of Cape Town, Rondebosch, 7700, South Africa, Institut für Physik, Johannes Gutenberg-Universität, Staudingerweg 7, Mainz, D-55099, Germany)
The QCD up- and down-quark masses are determined from an optimized QCD Finite Energy Sum Rule (FESR) involving the correlator of axial-vector current divergences. In the QCD sector this correlator is known to five loop order in perturbative QCD (PQCD), together with non-perturbative corrections from the quark and gluon condensates. This FESR is designed to reduce considerably the systematic uncertainties arising from the hadronic spectral function. The determination is done in the framework of both fixed order and contour improved perturbation theory. Results from the latter, involving far less systematic uncertainties, are: $$ {\overline{m}}_u\left(2\ \mathrm{GeV}\right)=\left(2.6\pm 0.4\right) $$ MeV, $$ {\overline{m}}_d\left(2\ \mathrm{GeV}\right)=\left(5.3\pm 0.4\right) $$ MeV, and the sum $$ {\overline{m}}_{ud}\equiv \left({\overline{m}}_u+{\overline{m}}_d\right)/2 $$ , is $$ {\overline{m}}_{ud}\left(2\ \mathrm{GeV}\right)=\left(3.9\pm 0.3\right) $$ MeV.
