Oak Ridge and Argonne supercomputers explore interactions between quarks and gluons

Lattice QCD calculations of strongly interacting particles enable increasingly precise determinations of the parameters of particle physics. Image courtesy E. Lunghi of Indiana University, J. Laiho of the University of Glasgow, and R. Van de Water of Brookhaven National Laboratory.

Schoolchildren learn that atoms, the building blocks of matter, are composed of such particles as protons, neutrons, and electrons. Scientists know that protons and neutrons contain even smaller particles called quarks and gluons. Nearly all the visible matter in the universe is made up of these subatomic particles. While the behavior of protons and neutrons is well understood, less is known about the interactions of quarks and gluons.

Scientists do recognize, however, that quarks and gluons interact in fascinating ways. For example, the force between two quarks increases as they move apart. Quarks are classified into six categories—up, down, charm, strange, bottom, and top—depending on their properties. Gluons, for their part, can capture energy from quarks and function as glue to bind quarks. Groups of gluons can also bind, forming glueballs. Scientists have identified another unique property of gluons, which they describe as color. Quarks can absorb and give off gluons, and when they do so, they are said to change color. Scientists believe quarks seek to maintain a state of color balance, and the process of absorbing and shedding gluons helps quarks achieve that balance.

The scientific community recognizes four fundamental forces of nature—electromagnetism, gravity, the strong force (which holds an atom’s nucleus together), and the weak force (responsible for quarks’ ability to change color)—that are thought to be related. The study of the strong interaction in terms of quarks and gluons is called quantum chromodynamics, or QCD.

A team of scientists collaborating under the leadership of Paul Mackenzie of Fermi National Accelerator Laboratory has been awarded a total of 80 million processor hours at the Oak Ridge Leadership Computing Facility (OLCF) and the Argonne Leadership Computing Facility (ALCF) for QCD research to help develop a unified theory of how the four forces interact. Physicists believe that more fundamental interactions must unite the presently observed forces. Supercomputing aids in the search for this new physics by making possible the comparison of current theories with experiment so anomalies can be sought.

“Leadership class computing makes it possible for researchers to generate such precise calculations that someday theoretical uncertainty may no longer limit scientists’ understanding of high-energy and nuclear physics,” said Mackenzie.

The Executive Committee of the U.S. Lattice Quantum Chromodynamics Collaboration includes Richard Brower (Boston University), Norman Christ (Columbia University), Frithjof Karsch (Brookhaven National Laboratory), Julius Kuti (University of California–San Diego), John Negele (Massachusetts Institute of Technology), David Richards (Jefferson Laboratory), Stephen Sharpe (University of Washington), and Robert Sugar (University of California—Santa Barbara).

A four-dimensional lattice model

Because quarks and gluons interact differently than do protons and neutrons, researchers are employing a distinct methodology for their study. Elementary particles follow a continuous path through space and time by hopping on a four-dimensional lattice model in a process called discretization. The team uses supercomputers to perform calculations to relate experimentally observed properties of these strongly interacting particles to QCD.

The highly advanced computational power of the Cray XT4/XT5 (at the OLCF) and IBM Blue Gene/P (at the ALCF) supercomputers enables the research team to produce and validate high-precision lattice QCD calculations that are essential to the analysis of recently completed experiments in high-energy and nuclear physics and other studies currently in progress. Simulations are used to relate the fundamental theoretical equations governing quarks and gluons to predictions of physical phenomena made in laboratories.

Using Monte Carlo techniques to predict the random motions of particles, the simulations generate a map of the locations of up, down, and strange quarks on a fine-grained lattice. The up and down quarks have masses sufficient to enable researchers to extrapolate physical properties.

Employing fundamentals from the Standard Model of subatomic physics, team members are exploring quark properties and dynamics. They are trying to determine the mass spectrum and coupling of strongly interacting particles and the electromagnetic properties of particles made up of interacting quarks (baryons and mesons) to create an understanding of a nucleon’s internal structure.

The team is studying three distinct quark actions—clover, domain wall, and improved staggered—and validating calculations that cannot be checked through direct comparison with experiment. It does the latter by performing the calculations with more than one method of equation discretization or by transferring continuous models and equations into discrete counterparts.

The researchers have completed domain-wall configuration ensembles of lattice spacings of 0.114 and 0.086 femtometers on lattices of sizes 243×64 and 323×64, respectively; in expressions such as 243×64, 24 is the number of lattice sites in the 3 spatial directions and 64 is the extent of the lattice in time. These are the largest domain-wall lattices ever attempted and will allow calculations with smaller lattice spacings and therefore smaller discretization errors than ever before achieved with domain-wall fermions. For the staggered quarks, the team has completed a set of runs with lattice spacings of 0.06 and 0.045 femtometers. These are the largest, most computationally challenging staggered ensembles generated to date.

These ensembles are currently being analyzed in studies of the decays and mixings of particles containing heavy quarks to enable major improvements in determining a number of elements in the quark mixing matrix. The calculations are enabling precise tests of the Standard Model, aiding in a deeper understanding of fundamental physics.

Improved versions are being created for both the domain-wall and staggered methods for formulating the continuum equations for fermions on a discrete lattice. A new method has been developed for domain-wall fermions (the Aux Det method), which will permit calculations with smaller quark masses. (Previous calculations were done with quark masses that were larger than those in real life because calculations with heavier quark masses require smaller computing resources.) An improved discretization method has also been developed for staggered fermions (HISQ fermions) that substantially reduces discretization errors.

Using the resources of two supercomputing facilities has dramatically advanced research in this field and in other strongly coupled field theories of importance to the study of high-energy and nuclear physics. The work was funded by the National Science Foundation and the Department of Energy through its Office of High Energy Physics, Office of Nuclear Physics, and Office of Advanced Scientific Computing.—by Kathryn Jandeska

Kathryn Jandeska is a senior writer/editor at Argonne National Laboratory.