Vertex Functions of QCD on the Lattice

Protons and neutrons, which build the nuclei of atoms, are members of a large family of particles which interact via the so-called strong nuclear force. These particles are collectively known as hadrons. They are not elementary but made from smaller constituents, the quarks and gluons. Quantum Chromodynamics (QCD) is the theory which describes how quarks and gluons interact and form hadrons. While QCD has been experimentally verified on numerous occasions, there are some of its aspects which are not yet fully understood.This project`saimistogaina deeper understanding of hadrons by studying the basic building blocks of QCD, the so-called vertex functions. The QCD vertex functions are not physical observables, they cannot be measured directly by any experiment. Despite being unobservable, these objects areof crucialimportance forunderstanding thefundamental aspects of the theory, and they also serve as intermediate steps in some calculations of measurable quantities. We intend to investigate these vertices by employing the so-called lattice Quantum Field Theory, which has been and is applied with great success to QCD, however, it is computationally very demanding. Most of the vertex functions which we plan to analyze have already been studied on the lattice. However, many of these results are of improvable quality, either because they are by now out-dated or they do not provide all the necessary information for follow-up computations.Dueto severalreasons, includinga better insight intotheroleofvertexfunctionsfor hadron physics, the availability of significantly improved algorithms,andtheincreased computerperformance,wewill beabletoproduceresults which are considerablysuperior inmany ways whencomparedtoprevious investigations. Suchrefined calculationsarevaluable both,in themselvesand asa reference pointandguideforvarious other approaches to QCD. Additionally, we will also study some vertex functions which have never before been investigated on the lattice due to technical difficulties, and which might offer information into yet undiscovered exotic states of matter, the so-called glueballs.

The main purpose of this project was to contribute to a better understanding of the forces and matter structures which govern the formation of nuclei (cores) of atoms. Many features of the atomic nucleus and its constituents have by now been well understood and successfully described with complicated mathematical models. However, there are still certain experimental facts related to these matters, which we have not been able to fully explain with our current theories. As an example, it is not yet clear why the particles which make up the atomic nuclei, the so-called quarks, only seem to exist as bound states, i. e. no nucleus has ever been successfully broken down into its constituent quark parts. Having a fundamental understanding of the mechanisms behind such experimental observations can help mankind gain a better control of the sub-nuclear world, with possibly profound consequences for our technological development. In this project we attempted to shed some light on these matters, by investigating a certain mathematical model called lattice quantum chromodynamics (QCD), which purportedly describes the strong nuclear forces. The main idea was to use large-scale computer simulations to study the basic building blocks of QCD, in hope of gaining some insight into whether or not this theory can truly explain the relevant known features of nuclear and sub-nuclear interactions. As these kinds of investigations are highly involved, it is still early to say what kind of impact our results and conclusions will have on future studies in this field. However, we are convinced that this project contributes in a positive way to the overall effort of studying and understanding QCD and its implications. In particular, we were able to identify certain practices used by many lattice QCD researchers, which can potentially lead to quantitative results with questionable accuracy. Some of our conclusions should thus help the future investigators to get a better control over their results, meaning that they should be able to give much better estimates if the data theyve produced is biased in some way. Moreover, our simulations seem to confirm a certain long-standing hypothesis about one of the fundamental QCD building blocks, the so-called three-gluon vertex. In the future, this confirmed feature of the three-gluon interaction may end up being the key to uncovering some of the mysteries of QCD and the strong nuclear force itself. We feel that this makes our project a worthwhile effort.