ELEMENTARY PARTICLE PHYSICS

All visible matter around us is made from nuclei, each consisting of protons and neutrons. One of the triumphs of 20th century particle physics is the realisation that protons and neutrons are made from even smaller building blocks, the so-called quarks, which are now regarded as the fundamental constituents of matter. Particles such as the proton and neutron (collectively referred to as baryons) are considered bound states of three quarks. The theory of Quantum Chromodynamics (QCD) describes with very high accuracy the forces that act between these elementary building blocks. However, it remains a great challenge to provide a quantitative description of particles such as the proton and nuclear matter in terms of the underlying interaction between quarks. In this project scientists study bound states of two baryons (so-called dibaryons) as prototypes of more complex systems such as light nuclei. The formulation of QCD on a space-time grid is employed, which makes the theory amenable to a numerical treatment. More specifically, the focus is on the so-called H dibaryon, whose existence has been predicted 40 years ago. These studies show that such a state may actually exist.

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The familiar protons and neutrons consist of different combinations of “up” (u) and “down” (d) quarks. There is, however, a very rich and complex spectrum of similar particles (collectively referred to as hadrons) involving also heavier variants of quarks, such as the “strange” (s), “charm” (c) or “bottom” (b) quarks. One particular example is the Λ-baryon with quark content uds. In the same way that protons and neutrons form the known nuclei that are listed in the chart of nuclides, it is conceivable that nuclei exist in which one (or more) nucleons are replaced by a Λ-baryon. The first such hypernucleus has indeed been discovered in 1952, and a great effort has since been invested to investigate and understand these systems in detail. In 1977, the theorist Bob Jaffe argued that a bound state consisting of two Λ-baryons – the so-called H dibaryon – may exist. Since his findings were obtained using a simple theoretical model, it is important to establish whether the underlying theory of QCD predicts the existence of such a state. This is the main focus of our project.

The question of the existence of the H dibaryon is all the more challenging, since experimental searches have remained largely inconclusive. Studying the H dibaryon also offers the opportunity to understand, in terms of the underlying fundamental theory of QCD, the interaction between hadrons, which is ultimately responsible for the formation of nuclear matter.

To study the H dibaryon we employ Lattice QCD, i.e. the formulation of the theory on a four-dimensional, Euclidean space-time grid. In this way the strongly coupled theory of QCD is amenable to a numerical treatment based on Monte Carlo integration. Lattice QCD has been used successfully to determine the masses of low-lying hadrons from the exponential fall-off rate of correlation functions. However, when applied to the H dibaryon, one is faced with a major challenge: The correlation function describing a multi-hadron state such as the H dibaryon shows a very unfavourable signal-to-noise ratio. This implies that huge statistics are required to resolve the energy levels reliably. This is all the more important since the binding energy (i.e. the energy difference between the H dibaryon and a pair of Λ-baryons) is of the order of a few MeV and thus quite small.

Our initial study was performed for QCD with a mass-degenerate doublet of dynamical up and down quarks. In a first step we have studied the energy spectrum in a situation where the strange quark is mass-degenerate with the up and down quarks. In order to achieve high statistics at moderate numerical cost, we have employed the technique of “all-mode-averaging”. In addition, we have used a method known as “distillation” to construct correlator matrices for the H dibaryon, which allow for a reliable and efficient determination of the energy levels of the ground state and the first few excitations. Another numerical challenge is the effort associated with performing the large number of necessary contractions to form the various entries in the correlator matrix.

The requirement to perform a high-statistics calculation, comprising up to 100000 individual samples per ensemble, together with the numerically demanding tasks associated with the construction of the correlator matrices implies that the use of a powerful supercomputer is indispensable. The JUQUEEN HPC system at JSC is ideally suited for running the highly parallelised and optimised code that we have developed.