Elusive low-energy constant determined from fundamental theory

With the help of innovative large-scale simulations on various supercomputers, physicists at Johannes Gutenberg University Mainz (JGU) have succeeded in gaining new insights into previously elusive aspects of the physics of strong interaction: Associate Professor Dr. Georg von Hippel and Dr. Konstantin Ottnad from the Institute of Nuclear Physics and the PRISMA⁺ Cluster of Excellence have calculated the interaction of the pion with the Higgs field with unprecedented precision based on quantum chromodynamics. Their findings were recently published in the renowned scientific journal Physical Review Letters.

Large-scale simulations as the only option

The physics of strong interactions describes the properties of atomic nuclei and the nucleons they consist of. The interactions are based on the properties of quarks and gluons, which in turn are described by quantum chromodynamics (QCD), the fundamental theory of strong interactions.
One of the challenges in studying strong interactions is that the properties of these particles cannot be easily calculated directly from QCD. Instead, numerical methods, in particular lattice QCD, are used. In lattice QCD, quarks, gluons, and their interactions are simulated on a discrete grid—or lattice—of space and time. Although this method has enabled considerable progress, it also has its own difficulties: on the one hand, the effects of this description of space and time on the calculations must be well understood; on the other hand, the simulations require computing power that can only be provided by supercomputers.

At low energies, however, strong interactions can often be better explained within the framework known as “chiral perturbation theory.” The building blocks of this framework are light mesons, such as the pion, which act as “interaction carriers” and mediate the strong interaction between nucleons. This theory is based on the principles of QCD and encompasses all properties of the underlying quarks and gluons. However, it describes the resulting physics in a different way. “You can understand this with an analogy from everyday life,” explains von Hippel. “We all know that water consists of H₂O molecules, but when we have it in front of us in the sink, it is much more practical to describe it as a liquid with a certain density, surface tension, and viscosity, which ultimately, of course, all result from the properties of the H₂O molecules.”

In order to correctly reproduce the properties of QCD, chiral perturbation theory depends on a series of so-called low-energy constants. These describe the strength of the various interactions between mesons and with external fields such as the electromagnetic field. "Some of these low-energy constants cannot be determined from experimental data and must be calculated using QCD. We have now determined one such low-energy constant precisely for the first time. It can be understood as the strength of the interaction of the pion with the Higgs field," says von Hippel.

Large-scale simulations of lattice QCD on supercomputers are the only way to calculate the low-energy constants from QCD. Thanks to specially developed algorithms, von Hippel and Ottnad were able to achieve lattice results with more than ten times the accuracy of previous calculations. “We were able to determine a previously largely unknown value with controlled accuracy from the lattice simulations,” says von Hippel. Von Hippel and Ottnad performed the calculations on supercomputers at the Gauss Centre for Supercomputing e. V. at the Leibniz Supercomputing Centre and the Jülich Supercomputer Centre, as well as on the Mainz high-performance computing clusters Clover, MOGON NHR, MOGON II, and HIMster-2.

Radius of the pion calculated with unprecedented precision

However, von Hippel and Ottnad did not only use their calculations to determine the low-energy constants of chiral perturbation theory. For an accompanying paper recently published in the journal Physical Review D, they also used their approach to calculate contributions to the radius of the pion with unprecedented precision. “Our work shows that quantities that were previously considered unattainable are now accessible to modern lattice QCD simulations,” summarizes von Hippel. “Our results are a first step into a new phase of lattice calculations. In the future, we want to determine other physical quantities such as the radii of kaons or the moments of quarks.”