Physicists Measure Pressure Distribution inside Proton

The proton, one of the components of atomic nuclei, is composed of fundamental particles called quarks and gluons. A team of physicists at the Department of Energy’s Thomas Jefferson National Accelerator Facility has found an extremely high outward-directed pressure from the center of the proton, and a much lower inward-directed pressure near the proton’s periphery. They have also found that quarks are subjected to a pressure of 10³⁵ pascals near the proton’s center, which is approximately ten times greater than the pressure in the heart of neutron stars, the most densely packed known objects in the Universe.

The first measurement of a subatomic particle’s mechanical property reveals the distribution of pressure inside the proton. Image credit: Thomas Jefferson National Accelerator Facility.

“The distribution of pressure inside the proton is dictated by the strong force, the force that binds three quarks together to make a proton. Our results also shed light on the distribution of the strong force inside the proton,” said Dr. Volker Burkert, lead author of the study.

“We are providing a way of visualizing the magnitude and distribution of the strong force inside the proton. This opens up an entirely new direction in nuclear and particle physics that can be explored in the future.”

Once thought impossible to obtain, this measurement is the result of a clever pairing of two theoretical frameworks with existing data.

First, there are the generalized parton distributions; they allow physicists to produce a 3D image of the proton’s structure as probed by the electromagnetic force.

The second are the gravitational form factors of the proton. These form factors describe what the mechanical structure of the proton would be if researchers could probe the proton via the gravitational force.

American physicist Dr. Heinz Pagels, who developed the concept of gravitational form factors in 1966, famously observed in a paper detailing them that there was ‘very little hope of learning anything about the detailed mechanical structure of a particle, because of the extreme weakness of the gravitational interaction.’

Recent theoretical work, however, has connected generalized parton distributions to the gravitational form factors, allowing the results from electromagnetic probes of protons to substitute for gravitational probes.

“This is the beauty of it. You have this map that you think you will never get. But here we are, filling it in with this electromagnetic probe,” said co-author Dr. Latifa Elouadrhiri.

The electromagnetic probe consists of beams of electrons produced by the Continuous Electron Beam Accelerator Facility, a DOE Office of Science User Facility.

These electrons are directed into the nuclei of atoms, where they interact electromagnetically with the quarks inside protons via a process called deeply virtual Compton scattering.

In this process, an electron enters a proton and exchanges a virtual photon with a quark, transferring energy to the quark and proton. A short time later, the proton releases this energy by emitting another photon and continues on intact. The process is analogous to the calculations Dr. Pagels performed for how it would be possible to probe the proton gravitationally via a hypothetical beam of gravitons.

Dr. Burkert, Dr. Elouadrhiri and their colleague, Dr. Francois-Xavier Girod, were able to exploit a similarity between the well-known electromagnetic and hypothetical gravitational studies to get their result.

“There’s a photon coming in and a photon coming out. And the pair of photons both are spin-1. That gives us the same information as exchanging one graviton particle with spin-2,” Dr. Girod said.

“So now, one can basically do the same thing that we have done in electromagnetic processes — but relative to the gravitational form factors, which represent the mechanical structure of the proton.”

The findings appear in the journal Nature.

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V.D. Burkert et al. 2018. The pressure distribution inside the proton. Nature 557: 396-399; doi: 10.1038/s41586-018-0060-z