Determining the Proton's Gluonic Gravitational Form Factors

The proton is one of the main building blocks of all visible matter in the universe. Among its intrinsic properties are its electric charge, mass, and spin. These emerge from the complex dynamics of its fundamental constituents, quarks and gluons, described by the theory of quantum chromodynamics (QCD). Using electron scattering, its electric charge and spin, shared among the quark constituents, have been the topic of active investigation. An example is the novel precision measurement of the proton's electric charge radius. In contrast, little is known about the proton's inner mass density, dominated by the energy carried by the gluons, which are hard to access through electron scattering since gluons carry no electromagnetic charge. Here, we chose to probe this gluonic gravitational density using a small color dipole, the $J/\psi$ particle, through its threshold photoproduction. From our data, we determined, for the first time, the proton's gluonic gravitational form factors. We used a variety of models and determined, in all cases, a mass radius that is notably smaller than the electric charge radius. In some cases, the determined radius, although model dependent, is in excellent agreement with first-principle predictions from lattice QCD. This work paves the way for a deeper understanding of the salient role of gluons in providing gravitational mass to visible matter.