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Field theory as a fundamental theory of particle physics

Fundamental theory of particle physics is described by field theory. Then, can we say that particle physics is completed once we provide the Lagrangian for the field theory? The answer is no. We still have to solve the theory and compute quantities characterizing reactions of particles in order to verify the theory by comparing the results with experiments.

Since field theory is a non-linear system with infinite degrees of freedom, it is a very hard work to solve it. There are some cases in which a theory is solved due to its symmetry. There are other cases in which an interesting phenomenon is sufficiently well approximated by an expansion with respect to a small parameter included in a theory (perturbative expansion) and we are satisfied with this approximation. However, solving the field theory is, in general, an extremely difficult problem. It is no exaggeration to say that most of the work for particle and nuclear theorists is to struggle with such unsolved problems.

"Solving" field theory from first principles

One thing we can do in such a situation is to `solve' field theory by making maximal use of numerical calculations. Specifically, by putting field theory on a lattice and by performing computer simulations, we can derive results from field theory without relying on perturbative expansions. Since we cannot treat infinite degrees of freedom on computers, we need to make several approximations. One also needs to learn special techniques for numerical calculations. These efforts are worth while however, since they enable us to solve field theory from first principles (from Lagrangian), which many other theoretical physicists simply give up.

Among the variety of field theories, quantum chromodynamics is the most vigorously investigated in the KEK theory group. The quantum chromodynamics(QCD) is the fundamental theory describing the interaction among quarks and gluons (strong interaction). In QCD the coupling constant becomes so large at low energy that we cannot apply the perturbative expansion to the phenomena that actually occur in measuring devices for particle physics experiments. For example, a wide variety of reactions occur in the measuring devices for B-Factory experiments. We need to solve QCD in order to obtain theoretical predictions for reactions involving quarks. At present the lattice simulation is the only way to solve QCD non-perturbatively.

Supercomputer

We need to perform enormous amount of calculation to simulate lattice QCD. It can easily reach the amount tractable by the fastest supercomputer in the world. For this reason we carry out our computation on the KEK supercomputer system (see the photo below), which has the world's leading performance.

Lattice gauge theory

In addition to the use of such commercial supercomputers, we are also involved in a project on constructing supercomputers dedicated for lattice QCD simulation. This project is proceeding in cooperation with RIKEN in Japan, and Columbia University and Brookhaven National Laboratory in USA. From 1997 to 1998, we have constructed QCDSP (QCD with DSP), which is a supercomputer specialized for lattice QCD calculations. This is a parallel processing system made of ten to twenty thousand inexpensive high-end digital signal processor (DSP), and it is 1TFlops class special supercomputer realized by developing and producing integrated circuit only for communication and memory management. It enabled us to deal with chiral symmetry on the lattice for the first time. Chiral symmetry is the characteristic property of hadron physics, and it plays an important role when we try to describe the properties of hadrons such as mass and decays in lattice QCD.

Based on this success, we started to develop a new special supercomputer, QCDOC (QCD on a chip) which has twenty times better performance than that of QCDSP supercomputer. Designing is finished in 2004, and the construction of three QCDOC supercomputers with 10TFlops is completed in March, 2005. (Each supercomputer is made of two hundred mother boards. The photo on the right shows the mother boards (left) and thirty-two daughter cards (right) to be placed on the mother boards.) This became possible by reducing the node computer composed of seven integrated circuit on QCDSP to one integrated circuit and by speeding it up. It is expected that these new supercomputers enable more strict numerical calculations in lattice QCD and further development of hadron physics.

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