The Valence Quark Structure of the Nucleon

The nucleon is a composite object, formed from a sea of quarks, anti-quarks and gluons being continuously created and annihilated. Among this complexity, however, there are three valence quarks that give the nucleon its baryon and flavor numbers. Here we investigate the dynamical structure of valence quarks inside the nucleon. The primary tool used will be patron distribution functions (PDFs), which give the distribution of momentum fraction, x, of the quarks and gluons inside the nucleon. By examining the PDFs of the valence quarks from phenomenological fits, we derive a new model-independent relation of PDF peaks and connect it to quantum chromodynamics (QCD) evolution. This new relation can be used as a constraint in future extractions of PDFs. Next, we outline a model we created, the residual field model, to give a mean-field description of the valence quarks inside the nucleon, which will act as a baseline to study short-range quark–quark interactions. The model treats valence quarks as effective fermions of fixed number inside a valence subsystem, while the rest of the nucleon (gluons, sea quarks/anti-quarks, a pion cloud, etc.) exists in a residual subsystem. The valence PDFs are then calculated within the effective light-front diagrammatic approach with the introduction of non-perturbative light-front valence-quark and residual wave functions. Good quantitative agreement is found with existing phenomenologically derived down valence PDFs. While qualitatively we replicate the up-valence distribution, a systematic underestimation at large x leads us to conclude that the addition of hard gluon exchanges is needed to accurately describe the large x region. We then outline how to use perturbative QCD to describe those hard interactions and incorporate them into the model.