Proton gravitational structure and mass decomposition on the light front

Gravitational form factors (GFFs) of hadrons encode essential information about the internal distributions of mass, spin, pressure, and shear among their quark and gluon constituents. We compute the quark and gluon GFFs of the proton using a fully relativistic, nonperturbative framework based on a light-front quantized Hamiltonian with quantum chromodynamics (QCD) input. This allows us to quantify the impact of a dynamical gluon on the proton’s mechanical properties, such as pressure and shear distributions. Our predictions agree well with recent lattice QCD results and experimental extractions. We also determine the proton’s mass and mechanical radii and address the long-standing puzzle of its mass decomposition. At the scale <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msup> <a:mi>μ</a:mi> <a:mn>2</a:mn> </a:msup> <a:mo>=</a:mo> <a:mn>4</a:mn> <a:mtext> </a:mtext> <a:mtext> </a:mtext> <a:msup> <a:mi>GeV</a:mi> <a:mn>2</a:mn> </a:msup> </a:math> , we find that quark energy, gluon field energy, the quark condensate, and the QCD trace anomaly contribute 31.5%, 34.7%, 11.3%, and 22.5%, respectively, which are consistent with lattice QCD findings.