The proton is a positively charged (+) subatomic particle located in the atomic nucleus. It plays a central role in both atomic physics and high-energy particle physics. Within the framework of modern theoretical physics, the structure of the proton, its internal dynamics, and experimental measurement methods remain key areas of ongoing research.

^{A representative illustration of the proton. (Generated by artificial intelligence.)}

Definition and General Properties

The proton is a baryon with a positive electric charge of +1e, a spin of ½, and a mass of approximately 938.272 MeV/c². Free protons are rarely found in nature; they are typically present as components of atomic nuclei. Alongside neutrons, protons form the atomic nucleus and are among the fundamental particles that determine an atom’s chemical properties. Within quantum field theory, the proton is described through quark-gluon dynamics. According to the Standard Model, the proton consists of two up quarks and one down quark (valence quarks), bound together by gluons.

Internal Structure and Dynamics of the Proton

The proton is not composed solely of three valence quarks; it also contains virtual quark-antiquark pairs (known as sea quarks) that are continuously generated and annihilated through gluon interactions. The motion of quarks and gluons accounts for a significant portion of the proton’s mass. Although the intrinsic mass of individual quarks is small, the energy density in gluon fields and the binding energy among quarks contribute to over 98% of the proton’s total mass.

For many years, it was assumed that the proton’s spin arose solely from its valence quarks. However, deep inelastic scattering experiments have revealed that the quarks' spin accounts for only about 30% of the total. This observation led to what is known as the "proton spin crisis." Contemporary models suggest that the spins of gluons and the orbital angular momenta of quarks also contribute to the total spin. Isolating and measuring these components remains a significant experimental challenge.

Proton Radius: Experimental Approaches and Scientific Debate

The radius of the proton, as inferred from its charge distribution, has been measured using different experimental techniques, yielding conflicting results. Electron-proton scattering experiments have estimated the proton radius to be approximately 0.88 femtometers (fm), whereas spectroscopic analyses of muonic hydrogen have yielded values around 0.84 fm. This discrepancy is attributed to the nature of the measurement techniques and the specifics of lepton-proton interactions. The differing results have led to what is known as the "proton radius puzzle," which has spurred a range of new experimental initiatives.

Electron-Proton Scattering Experiments

Scattering experiments designed to probe the proton’s electromagnetic structure provide insights into the spatial distribution of quarks and electromagnetic form factors. Electron-proton scattering has been a critical tool for testing the proton’s charge and magnetic moment distributions. However, variations in theoretical models and data analysis methods used in these experiments can result in divergent interpretations.

Lepton-Nucleus Interactions and Muonic Systems

In recent years, measurements involving muonic hydrogen—systems in which a muon replaces the electron—have indicated a smaller proton radius. These findings have led to the development of theories suggesting that different types of leptons (such as electrons and muons) might interact differently with the same nucleus. Such experiments are valuable not only for probing the details of electroweak interactions but also for exploring potential extensions to the Standard Model.