## Investigating the puzzle of quark confinement using high-performance computing

### Dr. Mike Peardon, School of Mathematics, Trinity College Dublin

Understanding the structure of matter has always been at the heart of scientific research. All materials are built up from atoms whose nuclei carry almost all of their weight, and are surrounded by electrons whose dynamics describe their chemical properties. The heavy nucleus is in turn built up from protons and neutrons. At present, there is still a substantially unanswered problem; how do the proton and neutrons get their mass? High-energy particle accelerator experiments reveal that even the nucleons are not point-like particles, but are comprised of even smaller constituents. These particles are named the quark and the gluon. Murray Gell-Mann, one of the pioneers of the theoretical picture of sub-nuclear structure, gave the quark its name from a line in Joyce’s “Finnegan’s Wake”. This experimental picture is clouded however since no quark or gluon has ever been detected in isolation. The quarks and gluons and their interactions can be described in a mathematically beautiful and complete way by a quantum field theory called quantum chromodynamics (QCD), which is structurally similar to QED, the theory describing electromagnetism.

In spite of QCD’s many successes during the last thirty years in describing the strong nuclear forces, the problem of the proton’s mass remains puzzling. While it is actually hard to define or measure a mass for particles that can not be isolated, the theory suggests the quarks are very light and that a gluon, like its close relative the photon (the quantum of light) is massless. Paradoxically then, the proton is a heavy particle made up of nearly massless components. Einstein’s famous equation, E=mc2 suggests a way out. In the special theory of relativity, energy and mass were postulated to be entirely equivalent concepts, an idea that has been tested to great accuracy in many experiments. If the light quarks and gluons inside the proton carried large amounts of energy, their composite state would be massive. Unfortunately, this simple explanation sets up an immediate contradiction – if the quarks and gluons are very energetic, why don’t they merely fly apart, causing the proton to disintegrate? Ordinarily, if particles are to stick together, they must attract each other and this leads to a lowering of their total energy as they are brought into proximity. For example, the hydrogen atom consists of a proton and an electron and its mass is ever so slightly less than the sum of the masses of the proton and electron in isolation. The electron can be pulled away from the proton when the atom is ionised, which requires this energy difference to be put in to the system. In contrast, quarks and gluons inside the proton have more energy than the components ought to have in isolation. The explanation lies in a property called “confinement” that QCD must possess to be the correct description of quarks and gluons. QCD must simply forbid quarks and gluons from moving far away from one-another. How this theory provides the mechanism for confinement is still a highly active research area.

Researchers in the School of Mathematics of Trinity College, Dublin, working as part of the IITAC programme are using supercomputers to study QCD in detail in an attempt to uncover more information on the confinement mechanism. The research team is using a description of the theory called Lattice QCD to make direct predictions of the properties of composite particles. The interactions inherent in the theory are strong and non-linear, so traditional mathematical tools for studying quantum field theories break down as the confinement mechanism begins to operate. The group is collaborating directly with researchers in international experimental laboratories that are probing the sub-structure and properties of the theory with ever-increasing precision. These experiments are looking for exotic forms of matter in which the gluon fields are excited. These states include the “hybrid meson” and the whimsically named “glueball”. The glueball is of particular interest to the group, since it is a confined state consisting solely of gluons. The closest analogy in the theory of electromagnetism would be a heavy ball of pure light! The TCD team has developed extensive new methods to make predictions from QCD about the menagerie of short-lived particles with masses close to that of the proton that QCD predicts and that are being uncovered in new experimental searches. The lattice QCD method slices space and time into small cells and represents the fields of theory numerically, cell-by-cell. The Trinity group has pioneered new discretisation techniques that make a more refined slicing of the theory in the time-like direction. This refinement is exploited to measure the dynamics of the theory with much greater resolution, enabling more precise energy determinations than were possible using simpler lattice descriptions of QCD.

The strong interactions of QCD are then introduced by carefully modelling the random fluctuations of these fields inherent in quantum mechanics. This technique, called the Monte Carlo method, is widely used in computer simulations of many apparently very different systems across a broad spectrum of different academic disciplines. While the method allows for any property of the theory to be determined in principle, a practical problem remains since the calculations use enormous amounts of computer time. These calculations require a large number of processors to be harnessed in parallel to work in unison on the simulations. Due to this complexity, any means of getting answers to the required accuracy more quickly is then very important. The TCD group is interested in developing general computational algorithms for performing Monte Carlo calculations, and using these methods to look more closely into the dynamics of the confining force, the force that explains how quarks and gluons are bound inextricably inside protons and neutrons and how all matter gets almost all of its mass.