Journal of High Energy Physics

, 2019:57 | Cite as

Up- and down-quark masses from QCD sum rules

  • C. A. DominguezEmail author
  • A. Mes
  • K. Schilcher
Open Access
Regular Article - Theoretical Physics


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.


QCD Phenomenology 


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Supplementary material

ESM1 Up-down-quark_masses_sum_rules_calculations.nb (NB 530 kb)


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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Centre for Theoretical and Mathematical Physics and Department of PhysicsUniversity of Cape TownRondeboschSouth Africa
  2. 2.Institut für PhysikJohannes Gutenberg-UniversitätMainzGermany

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