# The Quantum Mechanical Structure of Protons and Other Hadrons

**Principal Investigator:** Andreas Schäfer, Institut für Theoretische Physik, Universität Regensburg (Germany)

**HPC Platform:** JUQUEEN of JSC and SuperMUC of LRZ

Particle Physics tells us that all phenomena observed in the physical world are caused by just four types of interaction. These are gravitation and the electro-magnetic, weak, and strong interactions. Additional interactions may be discovered in future, but if so, they will (necessarily) be far too weak to play any role for our everyday lives.

While the nature of the strong interaction (normally called Quantum Chromodynamics QCD), which binds quarks and gluons to bound states called hadrons, is completely understood its consequences are not. The reason is that the strong interaction is not only incredibly strong (e.g. its characteristic energy density is 100,000 t/(mm)^3) but also completely dominated by quantum effects (e.g. the mass of its constituents contribute only roughly 1 percent to the proton mass, the rest is caused by quantum fluctuations).

Because our intuition is trained by classical physics, genuine quantum effects are often very difficult to understand except in mathematical language. One of the few exceptions are so-called Generalized Parton Distributions (GPDs) which allow for a probabilistic interpretation, just as classical physics.

GPDs are in the focus of extremely demanding worldwide experimental efforts. These experiments can be complemented by (equally demanding) numerical simulations in what is called Lattice QCD. Here “Lattice” refers to the fact that space-time is replaced by a lattice of points, the density of which is extrapolated to infinity. (The quantities easiest measurable on the lattice are those most difficult to obtain from experiment.)

Results as those shown in the figure required extremely high statistics as well as the control of potentially large systematic uncertainties. The primary requirement was sheer compute power and thus the usage of optimal hardware architecture. Such lattice simulations consist of two steps (production and analysis) with different hardware requirements which, therefore, were performed on two HPC systems, namely JUQUEEN and SuperMUC.

Copyright: Institut für Theoretische Physik, Universität Regensburg

Even without any technical discussion, the nature of the results can be understood: Angular momentum in QCD can be described by probability distributions, just as in classical mechanics (the fundamental reason being that isotropy of space is a symmetry of both theories). In the figure, non-vanishing transverse orbital angular momentum results in transverse shifts. The figures illustrate the correlation of spin and orbital angular momentum inside of a proton.

**Scientific Contact:**

Prof. Dr. Andreas Schäfer

Institut für Theoretische Physik, Universitaet Regensburg

D-93040 Regensburg/Germany

andreas.schaefer [@] physik.uni-r.de

*October 2016*