Why We Need Lattice QCD: Exploring the Heart of Nuclear Matter

by Christian Kummer

Hello, my name is Christian. As part of my PhD work with the AQTIVATE fellowship, I study lattice QCD—a fascinating approach to understanding the fundamental forces of nature. In this blog article I want to talk about the lattice, what it means and why we do things this way.

Figure 1: Lattice QCD can be used to study and visualize vacuum fluctuations. From The University of Adelaide, Copyright by Derek Leinweber.

But let’s start slightly off topic at quantum electrodynamics (QED), a quantum field theory which was developed in the late 40’s and early 50’s of the last century. QED generalizes the principles of quantum mechanics, offering a far more powerful framework. This theory describes the behavior of electrically charged particles and photons, which transmit forces between the charged particles. In fact, this theory is so powerful that it has led to the often-called best prediction in all of science: The magnetic moment of the electron has been predicted, and verified, with an accuracy of ten digits. To put this into perspective, that is the same as measuring the circumference of the earth with a precision of a centimeter.

Since QED was such a success, physicists have been adapting many ideas into quantum chromodynamics (QCD) to describe the behavior of nuclear matter, i.e. quarks and gluons, the particles which make up protons, neutrons and many exotic particles. However, there is a big difference between QED and QCD: QED can be studied perturbatively, which is something physicists are good at. Perturbatively means using small, manageable corrections to approximate solutions. In QCD however, this approach is not possible. This has to do with the fact that it is impossible to observe a free quark or gluon, they are always bound inside other particles (in contrast with electrons, which can be free particles and allow QED to work so well). This limitation makes it challenging to calculate nuclear matter properties efficiently.

However, there is a solution to this problem. One can use QCD non-perturbatively. This means using a numerical method to account for all interactions across a discretized space-time grid. In practice there are some restrictions of course. It is impossible to plug in every possible location, so we just choose some discrete points, inside a tiny spacetime volume. We arrange these points on a symmetric grid called a lattice, where each point is equidistant from its neighbors. It usually has a total side length of a few femtometer, which is 10-15 meters, about the size of a proton. On this grid we place the quarks and gluons and calculate the interactions between neighboring particles.

On the lattice, we simulate particles like protons and calculate properties such as mass, spin, and momentum distribution. My research focuses on the average momentum fraction of quarks in the proton—a key insight into its structure. Lattice QCD allows us to study quarks and gluons with high precision, matching experimental data for known properties and predicting quantities that cannot be directly measured, like generalized parton distributions.

In summary, lattice QCD is a powerful tool for exploring nuclear matter, bridging theory and experiment. I’m excited to contribute to this field and uncover the fundamental workings of the universe.