Di An: Exploring the nucleon electromagnetic form factors with non-perturbative methods

Abstract

The thesis studies the nucleon electromagnetic form factors at low energies, which is crucial for understanding the internal structure of nucleons and their excited states. Yet the non-perturbative nature of Quantum Chromodynamics (QCD) poses significant challenges on the theory side. 

It's been known that the effective field theory of QCD—chiral perturbation theory (ChPT)— cannot describe the nucleon elastic form factors well since it does not contain the vector mesons explicitly. To tackle the challenge, this thesis introduces a model-independent formalism that integrates ChPT with non-perturbative dispersion theory, termed Dispersively Modified Chiral Perturbation Theory. The new formalism can incorporate the ρ meson model independently while still maintaining the chiral power counting. This novel approach allows for the investigation of both the Q2 dependence and quark mass dependence of nucleon form factors, ensuring consistency with chiral symmetry while remaining systematically improvable. It is also demonstrated in the thesis that the new formalism outperforms the plain ChPT when comparing both to lattice QCD calculations.

The nucleon transition form factors (TFFs) are also poorly understood at low energies due to the meson cloud effects. In the thesis, a dispersive approach is proposed to explore the transition form factors of the nucleon to its excited state N*(1520) with JP=3/2—. It is the first time a model-independent calculation is made for N*(1520). The results show good agreement with the existing data on TFFs in the space-like region. Based on the dispersive formalism, predictions for the time-like TFFs are made for future experiments. This work advances the model-independent understanding of nucleon structure and the strong force at low energies.