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Proton gravitational structure and mass decomposition on the light front

Sreeraj Nair1,2,3,*, Chandan Mondal1,2,3,†, Siqi Xu1,2,3,‡, Xingbo Zhao1,2,3,4,§, and James P. Vary5,∥ (BLFQ Collaboration)

  • *Contact author: sreeraj@impcas.ac.cn
  • †Contact author: mondal@impcas.ac.cn
  • ‡Contact author: xsq234@impcas.ac.cn
  • §Contact author: xbzhao@impcas.ac.cn
  • ∥Contact author: jvary@iastate.edu
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Phys. Rev. D 112, 114001 – Published 1 December, 2025

DOI: https://doi.org/10.1103/79fs-5ghd

Abstract

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 μ2=4  GeV2, 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.

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Phys. Rev. D 112, 114001– Published 1 December, 2025
  • Received 16 June 2025
  • Accepted 12 November 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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