Why are Quarks Confined?

Among the German supercomputer centers, the John von Neumann Institute for Computing (NIC) is special in two aspects. Firstly, it comprises two research laboratories, the Research Centre Jülich and DESY which provide – through NIC – computer resources both on general purpose supercomputers as well as on specialized massively parallel architectures (see chapter “Centers” and then “NIC” of this issue for a description of the machines). Secondly, NIC is the only national supercomputer center that maintains research groups. One is the Complex Systems Group, led by Peter Grassberger and the other is the Elementary Particle Physics Group led by the author.

The Elementary Particle Physics group concentrates on numerical simulations in Lattice Field Theory (LFT). The main target is Quantum Chromo Dynamics (QCD) as our theory of the strong interactions, a theory that makes rather strange predictions, however. It postulates that there are fundamental constituent particles, the quarks, which interact through the gluons; but, at the same time it states that we cannot observe these particles. Instead, we can only see the bound states of the constituent quarks, the Proton, the Neutron and other hadrons in which the quarks are permanently confined.

Thus information on the theory on the fundamental level can only be obtained indirectly. How can we do this? By assuming the existence of the quarks and gluons, we can give theoretical predictions for, say, proton scattering experiments. Probing a hadron at small distances, corresponding – because of the Heisenberg uncertainty principle – to high energies, the quarks and gluons behave as almost free particles and the coupling between them is small. In this regime perturbative techniques can be applied and a number of successful theoretical predictions could be made. However, the distances where perturbation works is at most 0.2 fm while the proton radius is already 1 fm. The reason for the failure of perturbation theory is that the coupling between the quarks and gluons grows with increasing distance, eventually becoming so strong that the perturbative series in the coupling breaks down. In addition, the masses of the lightest quarks are about 10 MeV, while the mass of the proton is 1 GeV, i.e. 100 times larger. Hence, we are dealing with an unique system of an enormous binding energy impossible to describe by perturbative techniques.

In 1974 Nobel laureate Kenneth Wilson suggested that our continuum of space-time should be replaced by a 4-dimensional grid of lattice points in order to study non-perturbative phenomena. In this way, the problem can be mathematically well formulated and the complicated equations describing the interaction of the elementary particles can be solved on a computer. In the end of the 1970s Michael Creutz, following this approach, performed the first “computer experiments” in which he showed that physical quantities can be evaluated using numerical simulation techniques. The success of these early simulations in simple models was followed by a world-wide activity leading to Lattice Field Theory as being now an integral part of theoretical high energy physics including even simulations of super symmetric theories.

At present, we do not know, whether QCD can explain many fundamental questions that arise in the strong interactions, e.g.: What is the non-perturbative mechanism that forces quarks to be confined and what is the strength of the coupling of the quarks? Why is the binding energy of hadrons so enormously large? What is the nature of the finite temperature QCD phase transition and what are the properties of the quark gluon plasma that existed shortly after the big bang? Can we understand within QCD that some physical processes are not invariant under time reversal? Can we determine the internal structure of hadrons? What is the mechanism of breaking the chiral symmetry of QCD i.e. the symmetry of exchanging left- and right-handed quarks?

Lattice Field Theory is the only method we have today to give answers to the above questions. It can provide quantitative information on the theory but can also give insight into the mechanisms of the underlying physics. Of course, the most promising theoretical model is QCD, but it is as yet far from being clarified whether it is indeed the correct one. It is very important to remark that a full QCD simulation using lattice techniques will provide unambiguous answers; either the numbers emerging from such a simulation agree with experiment and QCD is established as the theory of the strong interaction, or, they disagree in which case QCD would not be correct and we have to look for different and new models that are based on completely novel and as yet unknown physical mechanisms and particles.
What is a full simulation? In principle, in such a simulation all 6 quarks of QCD have to be taken into account. However, for most of the questions it would be completely sufficient to only incorporate the three lightest quarks, the up, down and strange quarks. Unfortunately, even such simulations are very demanding and require machines that reach Teraflops performance to run for at least one year. This would mean that the whole IBM Regatta system at NIC would have to be dedicated to resolve just one problem of QCD! This is clearly unrealistic and lattice physicists today still have to resort to approximations but also work on conceptual and algorithmic developments to ease the lack of sufficient computing resources.

Nevertheless, the progress in Lattice Field Theory and the development of computer architectures that today reach the multi-Teraflops regime led to many physical results that find more and more their way into the particle data booklet, the “bible” for high energy physicists. Examples are the value of the strong coupling, the quark masses, hadronic matrix elements, form factors, the glue ball spectrum and even a random number generator. Another field where lattice results are essential is matter under extreme condition, i.e. in heavy ion collisions or neutron stars. Here, the lattice provides quantitative information about, e.g., the critical temperature, the pressure and the particle spectrum. Thus, lattice results play already now a significant and important role in the interpretation of experimental data (see Figure 1 for a comparison of lattice results and experimental data).

Figure 1: A comparison of experimental data and lattice results for various quantities as given by the Particle Data Group. Shown is the relative deviation between experiment and non-perturbative lattice QCD computations. We show the value of the coupling constant as, several decay constants of mesons (the kaon (K), the pion p, the D- and the B-meson). In addition, the masses of the charm and the bottom quark masses are displayed

The physics projects discussed above could not be tackled without using high-end, powerful supercomputers. An important role is played by massively parallel supercomputers, in particular the APE (Array Processor Experiment) and the QCDOC (QCD On Chip) machines. The newest version of APE will be apeNEXT. We show in Figure 2 the main elements of the machine. It is a SPMD machine and runs asynchronously giving new challenges to the APE collaboration. The final installations will achieve 2-3Tflops for a stand alone system with price/performance ratio of 0.5Euro/Mflop (peak). These parameters will then meet the requirements formulated by an ECFA panel for the performance needs of Lattice Field Theory in the next years and the German Lattice Forum (LatFor) requirements which evaluates a need of 25 Tflops for the physics program of the German Lattice Community.

Figure 2: The design parts of the apeNEXT machine

• Karl Jansen
John von Neumann Institute for Computing (NIC)

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