Nucleon Properties from First Principles
Dr. Stefan Krieg
Forschungszentrum Jülich, Institute for Advanced Simulation, Jülich Supercomputing Centre
Local Project ID:
HPC Platform used:
Hazel Hen of HLRS
Nucleons, the protons and neutrons, make up more than 99% of the mass of ordinary matter. Both particles were discovered early in the last century and are well known experimentally. While their masses have long been measured precisely, they only recently could be calculated from first principles (Durr, et al., 2008) (Borsanyi, et al., 2014). The reason lies in the complicated nature of the strong force that is responsible for the generation of the bulk of their masses. While other known fundamental interactions, such as the electric or magnetic forces, become weak when interacting particles are far away from one another and grow strong as they come closer, the opposite is true for the strong force.
It takes only about 1% of 1% of 1% of the energy stored in a proton’s mass (according to E=mc²) to ionize a Hydrogen atom, overcoming the electromagnetic force and sending its constituents, the electron and the proton, on their separate ways. Because the strong force between quarks (the elementary particles that “feel” the strong interaction) does not decrease as they are being pulled away from one another, we cannot repeat the same exercise as before: pulling two quarks apart, at some distance we have invested so much energy in our game of “quantum tugging war” that there is enough energy (again, according to E=mc²) to generate, out of the ever bubbling quantum vacuum, two new quarks close to the old ones; the rope (at this scale called ‘string’) has broken. Consequently, quarks are social animals and cannot be found alone in nature but only in composite particles, the so-called hadrons.
In the quantum world, the strong force comes in quanta called gluons and is theoretically described by a theory called Quantum Chromodynamics. Due to the strongly binding and non-linear nature of the strong force, numerical techniques are required to compute properties of hadrons, such as the nucleons.
While the proton’s mass was known long before it could be theoretically computed, this is not true for the proton’s charge radius. Historically, the radius was measured using two different experimental methods, which converged to deliver the same value. This changed recently when a new experiment, using a different approach, arrived at a significantly different result. Today, experimental determinations differ by over 5 standard deviations. On the upside, the precise value of the radius is thus a quantity for which a theoretical calculation can predict a value, rather than “postdict” what is already known. This is also true for other parameters, such as the so called scalar and tensor charges, which are relevant for searches of new physics beyond what is already encapsulated in the Standard Model of elementary particle physics.
However intriguing this sounds, the challenge in calculating these quantities is the amount of computational resources that are required. Only by using supercomputers, such as the ones made available to researchers through the Gauss Centre for Supercomputing (GCS), can we even attempt to compute these quantities with any precision. The present status of our calculations is illustrated in Figure 1 and Figure 2. The figures illustrate our present statistical precision and results from one of the new methods that were developed and tested using the resources provided by the GCS.
While there may still be some way to go before the simulations can weigh in on the proton radius puzzle, the results are encouraging and demonstrate that we are on the right path forward.
 Technically that would be a quark and an anti-quark making up a meson.
Dr. Stefan Krieg
Forschungszentrum Jülich GmbH
Institute for Advanced Simulation (IAS)
Jülich Supercomputing Centre (JSC)
Wilhelm-Johnen-Straße, D-52425 Jülich (Germany)
e-mail: s.krieg [@] fz-juelich.de
HLRS Project ID: HighPQCD