Determining the gluonic gravitational form factors of the proton

The proton is one of the main building blocks of all visible matter in the Universe¹. Among its intrinsic properties are its electric charge, mass and spin². These properties emerge from the complex dynamics of its fundamental constituents-quarks and gluons-described by the theory of quantum chromodynamics^3-5. The electric charge and spin of protons, which are shared among the quarks, have been investigated previously using electron scattering². An example is the highly precise measurement of the electric charge radius of the proton⁶. By contrast, little is known about the inner mass density of the proton, which is dominated by the energy carried by gluons. Gluons are hard to access using electron scattering because they do not carry an electromagnetic charge. Here we investigated the gravitational density of gluons using a small colour dipole, through the threshold photoproduction of the J/ψ particle. We determined the gluonic gravitational form factors of the proton^7,8 from our measurement. We used a variety of models^9-11 and determined, in all cases, a mass radius that is notably smaller than the electric charge radius. In some, but not all cases, depending on the model, the determined radius agrees well with first-principle predictions from lattice quantum chromodynamics¹². This work paves the way for a deeper understanding of the salient role of gluons in providing gravitational mass to visible matter.