A familiar particle - newly explored: insights into the inner life of the proton

The proton is one of three building blocks of the atom. Together with neutrons and electrons it forms the matter we know. Since the 1960s, we have known that a proton consists of three quarks. However, researchers now have a much more differentiated picture of the familiar particle. A small team at the Max Planck Institute for Physics (MPP) used the ORIGINS Data Science Lab (ODSL) to reanalyse data from the ZEUS experiment with novel statistical methods. Like this they obtained much more precise analysis results.

The infographic presents the chaos of all the different elementary particles - quarks and gluons – inside a proton. Image: D. Dominguez/CERN

Roughly speaking, a proton is formed by three quarks: two up quarks and one down quark. However, its internal structure is actually more complex than that. When protons are studied at very high energies, the resolution improves and reveals additional constituents. In addition to the three valence quarks, which determine its essential properties, the proton consists of a sea of many more quarks and antiquarks as well as gluons. The latter are the exchange particles of the strong force which holds together the valence quarks.

Why is it so important to study the proton? Because of its complex structure, the particle cannot be fully described in theoretical models. However, such models are important for making predictions, for example about collisions in the Large Hadron Collider (LHC). There, colliding proton bundles are used to search for unusual events and new particles in the decays.

Ever-changing momenta

MPP Director and ORIGINS scientist Allen Caldwell, who initiated the research, highlights a second aspect: "The structure of the proton depends on the strong force, about which little is known so far and which we cannot get to grips with using the current tools of theoretical particle physics. A more detailed understanding of proton's inner workings could help."

An important parameter for theoretical calculations is the average momentum of the individual components - and how much it fluctuates. "The momentum in a fast, high-energy proton is expected to be statistically equally distributed," says Allen Caldwell. "The gluons carry one half, the quarks and antiquarks the other. However, this state is not constant - if you look at the proton at a particular moment, for example, it's possible that the two up quarks are responsible for the total momentum."

New statistics for old data

For their current study, the research team used "old" data from the earlier ZEUS experiment at the HERA accelerator in Hamburg. Electrons and protons were made to collide there from 1991 to 2007.

“We evaluated particular collisions where the quark that participated in the interaction with the electron carried a large portion of the proton momentum. This data was previously unused in part because the data was not available in the format commonly used for proton structure studies," explains ORIGINS scientist Francesca Capel, who began this work as an ODSL-postdoc and now heads an astroparticle physics research group at MPP. The newly developed code uses a modern computer language, Julia, and the Bayesian approach to statistical analysis.

The research work did not yield any fundamentally new findings. However, the scientists succeeded in determining the average value for the momentum of the up-valence quarks with high accuracy. They were also able to determine the amount of time that these quarks are responsible for approximately all of the proton's momentum. In summary, the study is in line with the expectation that at high energies the momentum distribution in the proton is balanced, that is, half lies with the quarks and half with the gluons. The researchers plan to continue exploring the proton structure. The data from additional experiments beyond the ZEUS data would also be suitable for this purpose.

MPP press release

Ritu Aggarwal, Michiel Botje, Allen Caldwell, Francesca Capel, and Oliver Schulz (2023), Constraints on the up-quark valence distribution in the proton, Physical Review Letters

Prof. Allen Caldwell
Max Planck Institute for Physics / ORIGINS Excellence Cluster
email: caldwell(at)

Dr. Francesca Capel
Max Planck Institute for Physics / ORIGINS Excellence Cluster
email: capel(at)