Physicists calculate the proton pressure distribution for the first time

Neutron stars are among the densest objects in the universe and support pressures so strong that a teaspoonful of star material equals about 15 times the weight of the moon. Yet, it turns out that protons – the fundamental particles that make up most of the visible material in the universe – are subject to even higher pressures.

For the first time, MIT physicists have calculated the pressure distribution of a proton and found that the particle contained a highly pressurized core which, at its most intense point, generates higher pressures than those found at the same time. inside a neutron star.

This nucleus moves away from the center of the proton, while the surrounding region settles. (Imagine a baseball trying to lie inside a collapsing football.) The opposing pressures act to stabilize the proton's overall structure.

The results of physicists, published today in Letters of physical examination, are the first time scientists calculate the pressure distribution of a proton taking into account the contributions of quarks and gluons, the fundamental and subatomic constituents of the proton.

"Pressure is a fundamental aspect of the proton on which we know very little at the present time," says lead author Phiala Shanahan, an assistant professor of physics at MIT. "We have now found that quarks and gluons in the center of the proton generate significant external pressure and that beyond the edges, there is a confining pressure. With this result, we are moving towards a complete picture of the proton structure. "

Shanahan conducted the study with co-author William Detmold, an associate professor of physics at MIT. Both are researchers at the Nuclear Science Laboratory.

Remarkable quarks

In May 2018, physicists from the US Department of Energy's Thomas Jefferson National Accelerator Facility announced that they had measured the proton pressure distribution for the first time, using a beam of electrons that they had shot at a hydrogen target. The electrons interacted with the quarks inside the protons of the target. Physicists then determined the distribution of pressure throughout the proton, depending on how the electrons dispersed from the target. Their results showed a center of high pressure in the proton which, at its maximum pressure point, measured about³⁵ pascals, or 10 times the pressure inside a neutron star.

However, Shanahan says that their image of the proton pressure was incomplete.

"They found a pretty remarkable result," says Shanahan. "But this result was subject to a number of important assumptions that were necessary because of our incomplete understanding."

Specifically, the researchers based their pressure estimates on the interactions of the quarks of a proton, but not on its gluons. Protons consist of quarks and gluons, which constantly interact dynamically and fluctuating within the proton. The Jefferson Lab team was unable to determine the quark contributions with its detector, which, according to Shanahan, leaves out a large part of the proton pressure contribution.

"Over the last 60 years, we have gained a fairly good understanding of the role of quarks in the proton structure," she says. "But the structure of the gluon is much, much more difficult to understand because it is notoriously difficult to measure or calculate."

A gluon shift

Instead of measuring the pressure of a proton using particle accelerators, Shanahan and Detmold sought to include the role of gluons by using supercomputers to calculate the interactions between quarks and gluons that contribute to pressure. of a proton.

"Inside a proton, a bubbling quantum vacuum of quark and antiquarks pairs, as well as gluons, appears and disappears," says Shanahan. "Our calculations include all these dynamic fluctuations."

To do this, the team used a physics technique known as lattice QCD, for quantum chromodynamics, which is a set of equations describing the strong force, one of the three fundamental forces of the standard model of particle physics. (The other two are the weak force and the electromagnetic force.) The strong force is what binds quarks and gluons to form a proton.

Network QCD calculations use a four-dimensional grid, or network, of points to represent the three dimensions of space and one of time. The researchers calculated the pressure inside the proton using the equations of quantum chromodynamics defined on the lattice.

"It's extremely demanding in terms of calculation. So we use the world's most powerful supercomputers to do these calculations, "says Shanahan.

The team spent about 18 months performing various quark and gluon configurations in several supercomputers, then determining the average pressure at each point in the center of the proton, right up to its edge.

Compared to the Jefferson Lab results, Shanahan and Detmold found that by including the gluon contribution, the pressure distribution in the proton had changed considerably.

"We have examined gluon's contribution to pressure distribution for the first time, and we can really see that, compared to previous results, the peak has become stronger and the pressure distribution extends further away from the proton center, "said Shanahan. .

In other words, it appears that the highest pressure in the proton is about 10³⁵ pascals, 10 times that of a neutron star, reported by Jefferson Lab researchers. The surrounding low-pressure region extends further than previously expected.

Confirming these new calculations will require much more powerful detectors, such as the Electron-Ion collider, a proposed accelerator that physicists are looking to use to probe the internal structures of protons and neutrons, in more detail than ever, including gluons. .

"We are in the early days of quantitatively understanding the role of gluons in a proton," says Shanahan. "By combining the experimentally measured quark contribution, with our new calculation of the gluon part, we get the first complete image of the proton pressure, a prediction that can be tested by the new collider over the next 10 years."

This research was funded, in part, by the National Science Foundation and the US Department of Energy.