More Signs of Phase-change 'Turbulence' in Nuclear Matter

STAR Collaboration unveils most precise data yet in search for a 'critical point' in nuclear phase transitions

September 29, 2025

UPTON, N.Y. — Members of the STAR Collaboration, a group of physicists collecting and analyzing data from particle collisions at the Relativistic Heavy Ion Collider (RHIC), have published a new high-precision analysis of data on the number of protons produced in gold-ion smashups over a range of energies. The results, published in Physical Review Letters, suggest one part of a key signature of a so-called “critical point.” That’s a unique point on the “map” of nuclear phases that marks a change in the way quarks and gluons, the building blocks of protons and neutrons, transform from one phase of matter to another.

Discovering the critical point has been a central goal of research at RHIC, a U.S. Department of Energy (DOE) Office of Science user facility for nuclear physics research at DOE’s Brookhaven National Laboratory. Like centuries-old efforts to map out the solid, liquid, and gaseous phases of substances like water, it’s considered essential for fully understanding and describing the quark-gluon plasma. This unique form of nuclear matter is generated by RHIC’s most energetic nuclear collisions, which effectively “melt” the protons and neutrons that make up the colliding gold ions, briefly liberating their innermost building blocks to form a nearly perfect fluid state that once filled our early universe.

The new results bolster STAR’s confidence in earlier tantalizing hints of a critical point — a transition in how this melting occurs, depending on the temperature and density of the nuclear matter. But the scientists are not ready to declare discovery until another portion of the key signature reveals itself — possibly in still-to-be-analyzed STAR data.

“Since the last findings, STAR undertook a huge collection of datasets using many new and upgraded detector components that have allowed us to track more particles over wider areas within the detector than ever before,” said Ashish Pandav, a STAR collaborator from DOE’s Lawrence Berkeley National Laboratory and among those leading the analysis effort. “In addition, RHIC’s accelerator team implemented innovative techniques to increase collision rates even at low energy.”

With these detector and accelerator improvements, the STAR team has collected an unprecedented volume of high-precision data at a range of collision energies. “These measurements are letting us observe very subtle deviations or subtle patterns in the data,” Pandav said.

Xiaofeng Luo, a STAR collaborator from Central China Normal University and one of the leaders of the analysis, noted, “Finding the critical point would put a landmark on the nuclear phase diagram. It would mark a fundamental milestone in our understanding of how matter behaves under extreme conditions — from the birth of the universe to the cores of neutron stars.” 

Subtle signs, high-order analysis

To find evidence of a critical point, the scientists are searching for signs of fluctuations in the number of protons emerging from collisions event by event. Like the turbulence airline passengers experience as a plane enters a cloud, such fluctuations are expected as the conditions created in the collisions approach the critical point.

But the signs of fluctuations in the nuclear environment aren’t as obvious as drinks and snacks bouncing off seat-back trays on a plane. To “see” them, the scientists must look beyond simple counts of protons produced in collisions to “higher order” statistical analyses that describe aspects of how those counts are distributed. These higher statistical orders include, for example, the spread of the values, whether they are skewed one way or another relative to the central value, and how sharp or broad the peaks and the tails are when the data points are plotted on a graph.

“The higher the order, the more subtle the properties of the shape of the distribution, and the higher the precision you need to be able to see those properties,” said Mikhail Stephanov, a nuclear theorist at the University of Illinois Chicago who made predictions for what the STAR scientists should observe.

The experiments are measuring these fluctuation properties at different collision energies, Stephanov noted. In matter without a critical point, he explained that these higher order values are expected to stay flat or change in only one direction, going up or down, for example, as the collision energy is lowered. But if there is a critical point, Stephanov’s theoretical calculations predict that the peak/tail sharpness value — more formally known as “kurtosis” — should first fall, then turn and rise above its baseline, and then turn downward again.

“These changes in direction mean that there is some particular energy at which something happens that does not happen at other points,” he said. “It’s as if a plane — whether climbing, descending, or cruising — hits turbulence. Instead of the usual steady acceleration, passengers feel sudden shifts in the direction of the acceleration. It is a clear signal that the plane is passing a point where something significant is happening in the atmosphere.”

Like the boundary between distinct weather systems that can trigger such turbulence, the critical point can be thought of as a “front” between two distinct ways by which nuclear matter melts into quarks and gluons.

A partial signature

In the airplane analogy, passengers would be unlikely to notice the change in the higher-order statistical analysis of the turbulence.

“It’s too subtle,” Stephanov noted. “You need a special instrument to detect that change.”

But the STAR detector is a truly sensitive instrument. In its latest proton production data, it now has the strongest indications to date of at least some of the predicted kurtosis changes.

When compared with baseline expectations if there were no critical point, “We see a clear and prominent minimum in the data for kurtosis at a RHIC gold-ion collision energy around 20 billion electron volts (GeV),” STAR’s Pandav said. As the collision energy goes down further, the kurtosis values go up again and return to being squarely within the baseline range at 7.7 GeV.

That dip and subsequent rise with respect to various baseline calculations derived by theorists could represent one half of the expected signature of a critical point. “Depending on the baseline value used, that’s at a level of two to five sigma — a statistically significant range,” Pandav said.

But what happens below that 7.7 GeV energy level? STAR has one additional data point already published from fixed-target collisions at 3 GeV. The proton kurtosis value at that energy appears to fall slightly below its value at 7.7 GeV, but still within the range of baseline values.

“There is still a big gap between 7.7 and 3 GeV,” Stephanov said. Does the kurtosis value rise above its baseline and then turn back down as the theory-based signature predicts?

STAR will be able to answer at least part of that question with additional data from additional fixed-target low-energy collisions already in hand. “That’s going to come up very soon in the future; it’s on the to-do list for STAR,” said ShinIchi Esumi, a STAR collaborator from the University of Tsukuba and another leader of the analysis.

Bedangadas Mohanty of the National Institute of Science Education and Research, who played a leading role in shaping the Beam Energy Scan program at RHIC, said, “These results reflect more than 15 years of sustained global effort to precisely map the nuclear phase diagram.”

The STAR team is also looking forward to further refinements in the theory describing the predicted signatures for the critical point.

“So far, the signatures are what one would expect from a critical point, at least the part of them that we can see, but we still need a much better understanding of how a critical point produces such signatures,” Stephanov said. “And, as a theorist, I’d say there is still work to be done to better quantify the expected signatures.

“Eventually,” he noted, “we’d like to translate the signatures we see into properties of the nuclear phase diagram — the ‘map’ of how the phases of nuclear matter change with varying temperature and baryon density. But first we have to make sure we are convinced that the critical point is there.”

The effort that culminated in this STAR Collaboration analysis was supported by a group of scientists from institutions around the world who held regular meetings twice a week across time zones to review and examine the results. These achievements were made possible with the sustained dedication and support of the entire STAR Collaboration. The expert operation of RHIC by staff in Brookhaven Lab’s Collider-Accelerator Department was critical to providing the high-quality data used in this study.

The study was supported by the DOE Office of Science, the U.S. National Science Foundation, and a wide range of international funding agencies listed in the paper. RHIC operations are funded by the DOE Office of Science. Data analysis was performed using computing resources at the Scientific Computing and Data Facilities (SCDF) at Brookhaven Lab, the National Energy Research Scientific Computing Center (NERSC) at Lawrence Berkeley National Laboratory, and via the Open Science Grid consortium.

Brookhaven National Laboratory is supported by the Office of Science of the U.S. Department of Energy. The Office of Science is the single largest supporter of basic research in the physical sciences in the United States and is working to address some of the most pressing challenges of our time. For more information, visit science.energy.gov.

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