Undergraduate Research at Jefferson Lab

Calculating Meson Loop Corrections to Nucleon Properties

Student: Ridge Liu

School: Rice University

Mentored By: Wally Melnitchouk

An asymmetry has been observed between the parton distribution functions (PDFs) of the antiup and antidown quarks and between those of the strange and antistrange quarks in a nucleon. One possible explanation for the asymmetries is the effect of meson loop diagrams on the 3-valence quark structure of the nucleon, which arises from the chiral (left- vs. right-handed) symmetry of the underlying Quantum Chromodynamics (QCD) theory. This effect is quantifiable through splitting functions which describe ways a photon probe can interact with a nucleon. The focus of this study is to calculate the effect of one-meson-loop diagrams on the self-energy of a nucleon and nucleon to meson + baryon splitting functions using dimensional regularization (DR), a method for regulating divergent integrals. We perform multiple checks on the calculation, including finding the leading nonanalytic behavior of the self-energy and splitting functions and comparing against published results. Here we present expressions for the self-energy and splitting functions calculated using DR. We also show the consistency of the calculations of the self-energy using DR with other regularization methods. In contrast to other regularization methods such as high-momentum cutoff, dimensional regularization has the advantage of being manifestly covariant, i.e. respecting Lorentz invariance. The expression for the splitting function will allow for quantifying the magnitude of the meson loop corrections to the PDFs, en route to explaining the aforementioned observed asymmetries.