Can we determine the exact size of the nucleon?: A comprehensive study of different radii

The concept of nucleon radii plays a central role in our understanding of the internal structure of protons and neutrons, providing critical insights into the non-perturbative regime of quantum chromodynamics (QCD). While the charge radius is often interpreted as the “size” of the nucleon, this interpretation is an oversimplification that overlooks the multifaceted nature of nucleon structure. This paper provides a comprehensive overview of the different nucleon radii, including the charge and magnetic radii, the axial radius, and the emerging concepts of mechanical and mass radii. We discuss the definitions as well as the experimental, theoretical and phenomenological determinations of these radii, highlighting their distinct physical origins and implications. By synthesizing recent experimental results and theoretical advancements, we emphasize that each radius reflects a specific aspect of the nucleon's internal structure, such as its electric charge distribution, magnetic properties, weak interactions, or internal mechanical stress. In particular, we address the common but misleading interpretation of the proton radius as a simple measure of its size, underscoring the nuanced and context-dependent nature of nucleon radii. Through this exploration, we aim to clarify the roles of these radii in characterizing nucleon structure and to identify open questions that remain to be addressed. This work contributes to a deeper understanding of the nucleon and its significance in the broader context of particle and nuclear physics.