The inner density structure of the proton being determined by the energy of gluons is a concept that arises from Quantum Chromodynamics (QCD), the theory describing the strong nuclear force and the behavior of quarks and gluons within hadrons like protons. While there isn't a direct experimental "proof" of this concept, it is based on theoretical understanding and indirect evidence.
In QCD, gluons are the fundamental particles that mediate the strong force between quarks, which are the building blocks of protons. The strong force is responsible for holding quarks together inside hadrons. Gluons themselves carry energy, and their energy distribution within the proton affects its inner structure.
One way to study the internal structure of protons is through deep inelastic scattering experiments. In these experiments, high-energy particles are fired at protons, and by measuring the scattered particles, scientists can gain insight into the internal composition of the proton. These experiments have provided evidence for the existence of partons, which are the constituents of the proton carrying its momentum.
Partons, including quarks and gluons, are characterized by their momentum distributions, or parton distribution functions (PDFs). These PDFs provide information about the probability of finding a quark or a gluon carrying a specific fraction of the proton's total momentum.
The behavior of gluons and their energy distribution within the proton can be inferred from measurements of PDFs and from calculations using theoretical models such as lattice QCD simulations and perturbative QCD. These calculations consider the strong interaction between quarks and gluons and provide insight into the internal dynamics of the proton.
While there isn't a direct experimental proof that the inner density of the proton is solely determined by the energy of gluons, the theoretical framework of QCD, combined with experimental evidence from deep inelastic scattering experiments and calculations based on QCD, supports the idea that gluons play a significant role in shaping the proton's inner structure. Further experimental and theoretical studies continue to refine our understanding of the proton's inner workings.