RHIC data reveal intriguing dip in momentum fluctuations in high-density nuclear matter

Scientists using the STAR detector to study particle collisions at the Relativistic Heavy Ion Collider (RHIC) have found an intriguing dip in their data in a relatively unexplored region of the nuclear phase diagram—a map of how nuclear matter behaves under various conditions of temperature and density. The dip appears in data tracking collision-by-collision variations in the momenta of particles emerging from collisions between gold nuclei at RHIC, near RHIC’s lowest collision energies. These collisions create the highest-density nuclear matter and may indicate that something interesting is happening in that dense region of the phase diagram. The findings are described in a paper just published in Physical Review Letters.

RHIC, which operated as a U.S. Department of Energy (DOE) Office of Science user facility for nuclear physics research at DOE’s Brookhaven National Laboratory from 2000 to 2026, was designed to create exotic forms of matter, including the quark-gluon plasma that existed in the very early universe and matter that approaches the density of neutron stars. A dip in the momentum fluctuations—which are closely tied to the temperature of the matter—may be a sign that the way nuclei transform into these exotic substances changes character at RHIC’s lower energies.

Exploring whether such a change in transition behavior exists—and, if so, where a hypothesized “critical point” demarcating this change is located on the nuclear phase diagram—has been a long-sought goal of physicists conducting research at RHIC.

“The type of matter we are trying to study is a recreation, or a mini version, of the Big Bang,” said Rutik Manikandhan, a STAR Collaboration member from the University of Houston and a leader on the new analysis. “The existence of a critical point would tell us about all the phases of matter that could have existed when the universe began. It would sharpen our understanding of the quark-gluon plasma, how it condensed into the protons and neutrons that make up visible matter, and how matter behaves inside neutron stars.”

Mapping matter, one collision energy at a time

RHIC has been central to the exploration of nuclear matter by colliding the nuclei of heavy atoms such as gold at nearly the speed of light.

The most energetic collisions completely melt the boundaries of the protons and neutrons that make up the nuclei, freeing the quarks and gluons inside to form the quark-gluon plasma. Lower-energy collisions do something different: They leave the protons and neutrons intact but squeeze them to extraordinary density, approaching the conditions inside a neutron star.

By scanning across collision energies, physicists can chart different regions of the nuclear phase diagram—much as an earlier generation of scientists mapped out the gaseous, solid and liquid phases of water.

The new STAR analysis covers collision energies from 3 to 7.7 billion electron volts (GeV), exploring the lowest energies RHIC could produce and the densest matter it could create. To see the full picture, the team compared these low-energy collision data with previously published STAR data reaching up to 200 GeV.

Throughout, they studied only particles emerging at right angles to the colliding beams and near the middle of the collision debris. This ensured they were looking at particles measured consistently across all energies and more than two decades of RHIC operations.

The STAR scientists measured how much each particle’s momentum deviated from the average, then compared those deviations from collision to collision. Because particles that come from hotter matter carry more momentum on average, this comparison tracks how much the temperature of the fireball changes from one collision to the next.

“This momentum correlation measurement gives us an experimental window into temperature fluctuations,” said Chunjian Zhang, a junior faculty member at Fudan University and a co-leader of the STAR analysis. “We can use it as a proxy to look for temperature fluctuations.”

As reported in the paper, the momentum fluctuations fall steeply as collision energy rises from 3 GeV. They reach a minimum around 5.2–7.7 GeV and then climb again at higher energy. The departure from a smooth trend has a significance of about 5 sigma—the scientific standard for declaring such a deviation statistically significant.

The dip could therefore indicate that temperature fluctuations are being suppressed in the region of the phase diagram probed by these low collision energies.

Critical suppression

Suppression is what the critical-point scenario predicts. How much a system’s temperature varies depends on its heat capacity—how much heat it must absorb before its temperature budges. A large heat capacity means a steady temperature and small fluctuations.

Near a critical point, theory predicts that heat capacity should grow dramatically. Matter there can soak up energy while barely warming, so temperature fluctuations should be suppressed—producing the kind of dip STAR observed.

Beyond the critical point, at still higher densities, physicists expect something different again: a first-order phase transition. That’s an abrupt phase change like those familiar in everyday life. Add heat to a glass of ice water and the temperature stays at 32 degrees Fahrenheit (zero degrees Celsius) until every last piece of ice has melted; the energy goes into changing the water from solid to liquid rather than raising the temperature.

“This is called latent heat, because heat is still going into the system, but it’s being used to transform the phase of matter rather than to raise the temperature,” Manikandhan said.

At RHIC’s highest, quark-gluon-plasma-creating energies, by contrast, the nuclear matter transition is known to be a smooth crossover, with no sharp boundary at all. It’s more like butter softening slowly in a warm pan, gradually changing from nuclei made of protons and neutrons to free-flowing quarks and gluons.

Somewhere between those two behaviors, if a critical point exists, the character of the transition must change. Locating that changeover is the goal.

Not settled yet

While the dip in momentum and temperature fluctuations is consistent with other possible hints of critical-point behavior seen in different STAR measurements at low energies, the STAR team is careful to say that the new data are not proof that such a critical point exists.

“No single observable settles the question of finding the critical point, and other explanations for this new STAR result still remain open,” Manikandhan said.

For example, a recent theory paper has provided a non-critical-point explanation for the new STAR data.

The STAR team deliberately compared its data with predictions from another model physicists normally use to describe these collisions, known as “A Multi-Phase Transport” (AMPT). That model, which does not have critical-point behavior built in, fails to reproduce the dip feature observed by STAR. That does not establish that a critical point is responsible for the dip. But it does mean that something is happening that the AMPT picture does not capture.

The STAR team looks forward to additional input from theorists to provide further insight into what its data show.

“Different measurements are sensitive to different aspects of the same physics, and each one carries its own alternative explanations,” Zhang said. “What’s compelling is when independent measurements start pointing in the same direction.”

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