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The Strangeness Content of the Nucleon

Principal Investigator: Andreas Schäfer, Institut für Theoretische Physik, Universität Regensburg (Germany)
HPC Platform: SuperMUC of LRZ
LRZ Project ID: pr84qe


Modern particle physics provides an extremely precise description of all observed phenomena, which implies that any yet unknown interaction can manifest itself only in minute effects. Consequently, in any search for it, e.g., at the Large Hadron Collider (LHC) at CERN, all standard physics effects must be known extremely precisely, in particular the structure of the colliding protons. Therefore, it is rather disquieting that the simple question “How much of the proton mass is due to quark-antiquark fluctuations?” is highly controversial, as answers differ by factors of two. As the proton energy and momentum is dominantly due to quantum fluctuations this is not a minor fluke but a severe problem, and this topic is addressed employing different methods: By analyzing medium-energy data with the help of chiral perturbation theory (ChPT) and dispersion relations, by parametrizing and fitting LHC high energy cross sections and by Lattice Quantum Chromodynamics (LQCD), using supercomputers like SuperMUC. Within LQCD it is important to compare results of different groups using different formalisms as significant extrapolation is required (in particular to an infinitely fine lattice of space-time points, which is called the continuum limit). If nevertheless the results of all groups agree there is hardly any space left for doubt.


LQCD calculations are highly technical and too complex to be explained in detail in a short report. The information of interest is contained in infinite dimensional integrals which one approximates numerically. This task is split into two distinct steps, namely the Markov Monte-Carlo generation of ensembles of representative quark-gluon fields in space time, and the evaluation of the quantities of interest on these ensembles. Both steps need supercomputing power and SuperMUC is perfectly suited. The result for the light quarks mass fraction in the proton is shown in Figure 1. Obviously, the improved precision reached by major efforts in LQCD as well as ChPT has accentuated a discrepancy rather than reducing it. One has to conclude that presently even the structure of the proton, the best known quark-gluon bound state, is not really understood. It is unclear what this implies for QCD in general.

The Strangeness Content of the NucleonFigure 1: Results of recent LQCD calculations for the proton mass contribution of the up and down quarks from different groups (RQCD: this work), using different formulations (some not including all systematics), in comparison to the result of a recent dispersive analysis (green).
Copyright: Institute for Theoretical Physics, Regensburg University

The most natural way to proceed is to perform a similar type of analysis for the strange quarks in the proton. This was the primary aim of the proposal, and, in fact, even more than the promised ensembles were successfully generated. However, the analysis requires also the renormalization factors, which were expected to come from another group within the international CLS effort.. Presently, these are being calculated by the Regensburg group such that results for the strange-antistrange quantum fluctuations in a proton should become available soon. If these turned out to be in conflict with a recent analysis by the ATLAS experiment at LHC, the puzzle would become even more fascinating.

Research Team:

G. Bali, V. Braun, P. Bruns, S. Collins, B. Gläßle, M. Göckeler, F. Hutzler, R. Rödl, J. Simeth, W. Söldner, A. Sternbeck

Scientific Contact:

Prof. Dr. Andreas Schäfer
Institut für Theoretische Physik, Universitaet Regensburg
D-93040 Regensburg/Germany
andreas.schaefer [@]

LRZ Project ID: pr84qe

January 2017