Determining the gluonic gravitational form factors of the proton

B. Duran, Z.-E. Meziani (), S. Joosten, M. K. Jones, S. Prasad, C. Peng, W. Armstrong, H. Atac, E. Chudakov, H. Bhatt, D. Bhetuwal, M. Boer, A. Camsonne, J.-P. Chen, M. M. Dalton, N. Deokar, M. Diefenthaler, John Dunne, L. El Fassi, E. Fuchey, Huasheng Gao, D. Gaskell, O. Hansen, F. Hauenstein, D. Higinbotham, S. Jia, A. Karki, C. Keppel, Peter King, H. S. Ko, X. Li, R. Li, D. Mack, S. Malace, M. McCaughan, R. E. McClellan, R. Michaels, D. Meekins, Michael Paolone, L. Pentchev, E. Pooser, A. Puckett, R. Radloff, M. Rehfuss, P. E. Reimer, S. Riordan, B. Sawatzky, A. Smith, N. Sparveris, H. Szumila-Vance, S. Wood, J. Xie, Z. Ye, C. Yero and Z. Zhao
Additional contact information
B. Duran: Argonne National Laboratory
Z.-E. Meziani: Argonne National Laboratory
S. Joosten: Argonne National Laboratory
M. K. Jones: Thomas Jefferson National Accelerator Facility
S. Prasad: Argonne National Laboratory
C. Peng: Argonne National Laboratory
W. Armstrong: Argonne National Laboratory
H. Atac: Temple University
E. Chudakov: Thomas Jefferson National Accelerator Facility
H. Bhatt: Mississippi State University
D. Bhetuwal: Mississippi State University
M. Boer: Virginia Polytechnic Institute & State University
A. Camsonne: Thomas Jefferson National Accelerator Facility
J.-P. Chen: Thomas Jefferson National Accelerator Facility
M. M. Dalton: Thomas Jefferson National Accelerator Facility
N. Deokar: Temple University
M. Diefenthaler: Thomas Jefferson National Accelerator Facility
L. El Fassi: Mississippi State University
E. Fuchey: University of Connecticut
D. Gaskell: Thomas Jefferson National Accelerator Facility
O. Hansen: Thomas Jefferson National Accelerator Facility
F. Hauenstein: Old Dominion University
D. Higinbotham: Thomas Jefferson National Accelerator Facility
S. Jia: Temple University
A. Karki: Mississippi State University
C. Keppel: Thomas Jefferson National Accelerator Facility
H. S. Ko: Université Paris-Saclay
X. Li: Duke University
R. Li: Temple University
D. Mack: Thomas Jefferson National Accelerator Facility
S. Malace: Thomas Jefferson National Accelerator Facility
M. McCaughan: Thomas Jefferson National Accelerator Facility
R. E. McClellan: Pensacola State College
R. Michaels: Thomas Jefferson National Accelerator Facility
D. Meekins: Thomas Jefferson National Accelerator Facility
Michael Paolone: Temple University
L. Pentchev: Thomas Jefferson National Accelerator Facility
E. Pooser: Thomas Jefferson National Accelerator Facility
A. Puckett: University of Connecticut
R. Radloff: Ohio University
M. Rehfuss: Temple University
P. E. Reimer: Argonne National Laboratory
S. Riordan: Argonne National Laboratory
B. Sawatzky: Thomas Jefferson National Accelerator Facility
A. Smith: Duke University
N. Sparveris: Temple University
H. Szumila-Vance: Thomas Jefferson National Accelerator Facility
S. Wood: Thomas Jefferson National Accelerator Facility
J. Xie: Argonne National Laboratory
Z. Ye: Argonne National Laboratory
C. Yero: Old Dominion University
Z. Zhao: Duke University

Nature, 2023, vol. 615, issue 7954, 813-816

Abstract: Abstract 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 chromodynamics3–5. 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 proton7,8 from our measurement. We used a variety of models9–11 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.

Date: 2023
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DOI: 10.1038/s41586-023-05730-4

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