  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.
