Ab initio determination of light hadron masses

S. Dürr,1 Z. Fodor,1,2,3 J. Frison,4 C. Hoelbling,2,3,4 R. Hoffmann,2 S. D. Katz,2,3 S. Krieg,2 T. Kurth,2 L. Lellouch,4 T. Lippert,2,5 K. K. Szabo,2 G. Vulvert4

Science 322 (2008) 1224

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1 John von Neumann–Institut für Computing, Deutsches Elektronen-Synchrotron Zeuthen, D-15738 Zeuthen and Forschungszentrum Jülich, D-52425 Jülich, Germany.
2 Bergische Universität Wuppertal, Gaussstrasse 20, D-42119 Wuppertal, Germany.
3 Institute for Theoretical Physics, Eötvös University, H-1117 Budapest, Hungary.
4 Centre de Physique Théorique (UMR 6207 du CNRS et des Universités d'Aix-Marseille I, d'Aix-Marseille II et du Sud Toulon-Var, affiliée à la FRUMAM), Case 907, Campus de Luminy, F-13288, Marseille Cedex 9, France.
5 Jülich Supercomputing Centre, FZ Jülich, D-52425 Jülich, Germany.

More than 99% of the mass of the visible universe is made up of protons and neutrons. Both particles are much heavier than their quark and gluon constituents, and the Standard Model of particle physics should explain this difference. We present a full ab initio calculation of the masses of protons, neutrons, and other light hadrons, using lattice quantum chromodynamics. Pion masses down to 190 mega–electron volts are used to extrapolate to the physical point, with lattice sizes of approximately four times the inverse pion mass. Three lattice spacings are used for a continuum extrapolation. Our results completely agree with experimental observations and represent a quantitative confirmation of this aspect of the Standard Model with fully controlled uncertainties.

The light hadron spectrum of QCD. Horizontal lines and bands are the experimental values with their decay widths. Our results are shown by solid circles. Vertical error bars represent our combined statistical (SEM) and systematic error estimates. The pion, kaon and cascade have no error bars, because they are used to set the light quark mass, the strange quark mass and the overall scale, respectively.

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