Locating the proton mass

8 May 2023
The spectrometers that have been used to detect the decay products of the elastically photoproduced J/ψ. Credit: Jefferson Lab

Researchers at Jefferson lab in the US have gained a deeper understanding of the role of gluons in providing mass to visible matter. Based on measurements of the photoproduction of J/ψ particles, the findings suggest that the proton’s structure has three distinct regions, with an inner core driven by gluonic interactions making up most of its mass.

Although the charge and spin of the proton have been extensively studied for decades, relatively little is known about its mass distribution. This is because gluons, which despite being massless provide a sizeable contribution to the proton’s mass, are neutral and thus cannot be studied directly using electromagnetic probes. The Jefferson team instead used the gluonic gravitational form factors (GFFs). Similar to electromagnetic form factors, which provide information about a hadron’s charge and magnetisation distributions, the GFFs (technically the matrix elements of the proton’s energy–momentum tensor) encode mechanical properties of the proton such as its mass, density, pressure and shear distributions.

To access the GFFs, the team measured the threshold cross section of exclusive J/ψ photoproduction at different energies by forcing photons with energies between 9.1 and 10.6 GeV to interact with a liquid hydrogen target. Gluons dominate the production of J/ψ at small momentum transfer since J/ψ mesons share no valence quarks with the proton. Due to the J/ψ’s vector quantum numbers, this process can occur at certain energies by gluons in scalar (dilaton-like) and tensor (graviton-like) states. The researchers fed their cross-section results into QCD models describing the gluonic GFFs and extracted the parameters defining the GFFs, enabling them to deduce one mass radius and one scalar radius.

We need a new generation of high-precision J/ψ experiments to get a better picture

Zein-Eddine Meziani

The analysis revealed a scalar proton radius of 1 fm, which is substantially larger than both the charge radius (around 0.85 fm) and the proton mass radius (0.75 fm). This led the team to propose that the proton structure consists of three distinct regions: an inner core that makes up most of the mass radius and is dominated by the tensor gluonic field structure, followed by the charge radius resulting from the relativistic motion of quarks, all enveloped in a larger confining scalar gluon density.

“Given that the proton’s scalar gluon radius is the largest we need to understand how this converts to our understanding of the gluonic structure of nuclei. For example, what would be the scalar radius of 4He compared to its charge radius?” says study leader Zein-Eddine Meziani of Argonne. The team plans to extend its studies to include the J/ψ muon final state decay, doubling the statistics of the current measurement, and to extract the gluon pressure distribution. “It is hard to say much right now, but this is a field in its infancy and the direct role of gluons in nuclei is not well understood,” adds Meziani. “We need a new generation of high-precision J/ψ experiments to get a better picture.”

Further reading

B Duran et al. 2023 Nature 615, 813


  • Strong interactions | Conference HADRON 2023 5—9 June 2023 | Genova, Italy
  • Strong interactions | Conference QCD 2023 10—14 July 2023 | Montpellier, France
  • Strong interactions | Workshop CHARM 2023 21 July 2023 | Siegen, Germany
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