### Research — Quantum chromodynamics and the strong nuclear force

As the fundamental theory of the strong nuclear force, quantum chromodynamics is responsible for quarks being confined into composite particles such as nucleons (protons and neutrons), through the quarks' interactions with gluons. The picture below illustrates where quarks and nucleons fit into the structure of matter, but you should not take it too literally: The mass of the proton is roughly 100 times the mass of the three quarks that the picture shows it being made out of. The vast majority of the mass of composite particles (and thus of the visible universe) comes from the energy of strong QCD interactions.

Lattice QCD dates back to the 1970s, although the first numerical lattice QCD computations were not performed until the 1980s. The field has advanced steadily since then, in parallel with the development of high-performance computing. Lattice QCD calculations are now able to predict the mass of the proton with percent-level accuracy, the culmination of decades of progress.

Predicting particle masses is only one of the many calculations that one can perform with lattice QCD, and in many ways it is one of the easiest. My own work in this field has focused on studying the strange quark content of nucleons [arXiv:1012.0562]. Although strange quarks are not among the "valence" quarks that determine the quantum numbers of the nucleons, the energy of the strong interaction allows pairs of strange quarks and antiquarks to be continually produced and annihilated through quantum processes. These "virtual" strange quark pairs account for a portion of the nucleon's mass, and affect its internal structure.

Determining the role of strange quark pairs in the nucleon may be crucial to understanding the nature of the dark matter that makes up the majority of the (visible and invisible) mass in the universe. Many models predict that the dark matter may couple more strongly to strange quarks than to the lighter (up and down) valence quarks. (It can couple even more strongly to heavier charm and bottom quarks, but there isn't enough energy in the nucleon to produce very many of those.) In order to predict how strongly the dark matter should couple to the nucleon as a whole (and thus to all the atoms and matter made out of nucleons), the strange quark content of the nucleon needs to be determined. Without this knowledge, it becomes more difficult to estimate which models of dark matter are still consistent with experimental constraints.

The fact that only strange quark pairs appear in the nucleon makes their contribution very difficult to evaluate on the lattice. In the mathematical shorthand of Feynman diagrams, strange quark pairs appear as closed loops that couple to the valence quarks of the nucleon only via gluon fields. In order to evaluate such "quark-line disconnected diagrams" exactly, the computation must be repeated with the strange quarks' closed loop beginning at every possible point in space and time (that is, every site on the lattice). This is not computationally feasible, so instead we are forced to develop methods to estimate the result. This still requires much more computing than does evaluating connected diagrams, and introduces a new source of statistical error.

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Last modified 6 September 2015