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The QGP Critical Point

by John G. Cramer

Alternate View Column AV-227

RHIC, STAR, critical point, quark-gluon plasma, QGP, Big Bang, hadron gas, phase transition, proton freezout

Published in the November-December-2023 issue of Analog Science Fiction & Fact Magazine;
This column was written and submitted 07/06/2023 and is copyrighted ©2023 by John G. Cramer.
All rights reserved. No part may be reproduced in any form without
the explicit permission of the author.

In 1822, the French physicist Baron Charles Cagniard de la Tour (1777-1859) was studying the sound made by a flint ball rolling within a sealed gun barrel that was filled with a test gas or liquid. He noticed that the sound changed dramatically at a certain temperature, as he varied temperature and pressure. Thus, he discovered the critical point, above which gas and liquid phases of the medium have exactly the same density and become indistinguishable, i.e., transition to a super-critical fluid. Cagniard's first results showed that CO2 could be liquefied at temperature 31°C and pressure of 73 atmospheres, but not at a slightly higher temperature, even under pressures as high as 3,000 atmospheres. For water, he found the critical point to be 374°C at 218 atmospheres.

As it turns out, the thermodynamic concept of a critical point has applications well beyond the realm of atoms and molecules. In particular, in the early stages of the Big Bang, our very hot and dense universe was filled with a super-critical fluid made of quarks and gluons, which we call a quark-gluon plasma (QGP). As the universe expanded and the QGP dropped in temperature and pressure, it reached a critical point at which the quarks and gluons ceased to be free particles, sticking together in bound groups of three quarks under the influence of the strong force, and the QGP made a transition to a very hot medium of baryons, i.e., protons, neutrons, heavier short-lived massive particles, and some light nuclei. Ultimately this medium transitioned to a proton-dominated plasma, which in turn transitioned to an electrically-neutral gas of hydrogen atoms, and stars and galaxies began to form.

Since the 1990s experimental physicists working at accelerators have studied very high-energy collisions of heavy nuclei, attempting to find evidence of the QGP and its critical point. This has proved difficult, because many theorist-proposed "signals" of the transition from hot baryons to QGP have failed. Now, however, recent work by the STAR Collaboration at the Relativistic Heavy-Ion Collider (RHIC) facility at Brookhaven National Laboratory (BNL) shows promise of success.

Let me here interject a personal account of this area of research. In 1990 I had just finished a 5-year stint as Director of the University of Washington's Nuclear Physics Laboratory. During that period we had succeeded in constructing (on time and under budget) a new $10 million superconducting linear accelerator that boosted the ion beams of our laboratory's tandem Van de Graaff accelerator into a new energy regime. However, my own nuclear physics research program had withered under the many directorship distractions, and I was looking for something new for my research.

As it happened, at just the right time I was invited to the Lawrence Berkeley National Laboratory (LBNL), where a new experimental collaboration was forming that would use the projected RHIC facility then being constructed at BNL. RHIC was scheduled to begin operation in 1999. After consideration, I decided to leave low-energy nuclear physics and make the great leap into this new research field, which is called ultra-relativistic heavy ion physics. I described the RHIC project then in the works in AV-46, which appeared in the June-1991 Analog.

What would we study at RHIC?  Richard Feynman once described experimental nuclear physics like this: "If you are given a pocket watch and want to know how it works, the sensible thing is to carefully take it apart and examine the pieces. However, in nuclear physics the "watch" is a nucleus, and the only way we have of trying to understand how it works is to shoot ‘bullets' (i.e., particles) at it and observed the parts that fly out." In ultra-relativistic heavy ion physics, we are doing something even more peculiar, in that we are colliding one watch with another one and trying to understand the hot ball of flying parts that has otherwise not existed since the early stages of the Big Bang.

Over the first eight years years, our new collaboration constructed at LBNL a large detector called a time-projection chamber (or TPC) and air-freighted it to BNL in an Air Force C-17. The TPC starts as a large hollow cylinder surrounded by magnetic coils, a magnetic solenoid. Inside this solenoid is a gas-filled cylindrical volume threaded by twin parallel electric fields that pull positively charged ions made in the gas to the two ends of the cylinder. There the drifting ions encounter charged wires, producing discharge avalanches that are recorded by detector electronics. Combining the locations of the discharges with the drift time of the ions allows simultaneous 3-D reconstruction of thousands of ion tracks made by charged particles (mostly pi mesons, with a sprinkling of heavier particles) produced in the head-on collision of gold nuclei accelerated by RHIC. The tracks curve in the magnetic field of the solenoid, providing their momentum. The amount of track ionization allows determination of particle type (pions, kaons, protons, deuterons, tritons, …).

Our new detector and collaboration needed a name, so an early LBNL collaboration meeting staged a "name the detector" competition.  I submitted the name "Solenoidal Tracker At RHIC" or STAR, and, to my surprise, I won the contest. (My prize was a pass to a high-end bathhouse in Berkeley, which I never used.) Thus, the STAR Collaboration and the STAR Detector got their names.

In the 1990s in preparation for the planned 1999 startup of RHIC and first operation of the STAR detector, I formed an experimental group at the University of Washington, arranged for Department of Energy funding, and we participated in experiments NA35 and NA49 at CERN. At that time, CERN's Super Proton Synchrotron (SPS), now the LHC's injector, accelerated protons for most of the year, but for the month before Christmas it accelerated bare lead-208 (and lighter) nuclei to 200 GeV/nucleon, producing the highest-energy lead beams then available anywhere in the world. In our experiments, we studied the collisions of accelerated lead nuclei with fixed targets, using other versions of TPCs.

RHIC was scheduled to begin operation in 1999, and our group spent that Summer at Brookhaven, waiting for Au+Au collisions. However, a serious vacuum-system mis-design delayed the start of RHIC. In 2000 the STAR detector was ready, and we began taking data as soon as RHIC could provide colliding beams. The spectacular "starburst" images produced by STAR, showing RHIC collisions with thousands of charged particles emerging from a single event, made the covers of most science magazines that year.

For the next 15 years (until 2015 when the Department of Energy stopped our group funding because I had retired from UW teaching) I worked in the STAR Collaboration. My research focus was Hanbury-Brown-Twiss (HBT) correlations between the charged pi mesons made in the RHIC collisions. These HBT correlations allowed us to deduce the size and detailed geometry of the collision fireball.

We had naïvely expected that a QGP transition would produce dramatic changes in the fireball geometry. However, we observed nothing so dramatic and obvious in our STAR HBT work. I wrote about this in AV-128, published in the July-August-2005 Analog. This lack of a definitive QGP signal was also true of other aspects of RHIC collisions studied by STAR and other experiments. There were hints, but a "smoking-gun" QGP signal proved to be much more elusive and complicated than expected.

Most theories proposed in the 1990s before RHIC went into operation modeled the collision volume as a "particle cascade" in a super-hot gas. A few theorist nonconformists suggested instead using relativistic hydrodynamics, modeling the region as a liquid. When our STAR results began to emerge, the hot-gas cascade theories failed, while the relativistic hydrodynamic predictions matched many aspects of the data. The implication was that the QGP, and the early universe itself, were liquid in behavior. However, detailed characteristics of this QGP liquid remained very elusive. This prompted RHIC to undertake an "energy scan", operating the collider in a succession of 9 energy steps, stepping down to 7.7 GeV/nucleon from the maximum collision energy of 200 GeV/nucleon.

Now, about eight years since I retired from the STAR Collaboration, they have produced what looks like the smoking gun of the QGP transition, a determination of the QGP critical point. The signal used, suggested by theorists in 2020, requires some explanation. As the critical point is approached the two media, QGP liquid and hot hadronic gas, have differing mass densities, and the proximity of the critical point should magnify density fluctuations. On the hadronic-gas side, there is the possibility of the formation, not only of neutrons and protons, but also of more complex nuclei, particularly the hydrogen isotopes deuterium and tritium. Density fluctuations should increase the probability that light nuclei should form.

These nuclei are easily identified and distinguished in the STAR detector because heavier ion tracks have more ionization. The STAR group focused on tritium productions in the Au+Au collisions. In particular, they used the dimensionless ratio R=N(t)*N(p)/N(d)2, where N(x) is the number of particles of type x produced in a given collision. R indicates the strength of tritium production. Therefore, an increased R signals enhanced density fluctuations at a particular collision energy.

They found that in most collisions studied R is about 0.42 and is well predicted by theoretical models that do not include density fluctuations. However, for the most central collisions at the energies of 19.6 and 27.0 GeV/nucleon, R has a value of about 0.48, a 14% rise. No such enhancement is observed for more peripheral collisions at the same energies.

The observed enhancement in R has a combined statistical significance of about 4.1 s (standard deviations). By physics convention, a statistical significance of over 6 s is required to take an observed effect as "definite", so the observed enhancement is to be taken as a "strong indication" rather than as an "observed result". Nevertheless, it represents a strong indication that the QGP critical point has been found in central Au+Au collisions at around 24 Gev/nucleon.

This, of course, is not the end of the story. There are presently no useful theoretical predictions of the QGP critical point. Theoretical studies with a realistic equation of state are badly needed to confirm that the enhancement in R is due to large baryon density fluctuations near the critical point. The STAR Collaboration also needs to improve the statistics of their observation and to look in their data for similar enhancements in other light nuclei, e.g., 3He and 4He. Further, this special region of interest around 24 GeV/nucleon needs additional experimental investigation to look for other signals indicating that the collisions are at the QGP critical point.

Watch this column for further results. 

John G. Cramer's 2016 nonfiction book describing his transactional interpretation of quantum mechanics, The Quantum Handshake - Entanglement, Nonlocality, and Transactions, (Springer, January-2016) is available online as a hardcover or eBook at: or .

SF Novels:  John's 1st hard SF novel Twistor is available online at:   His 2nd and 3rd novels, Einstein's Bridge and its new sequel Fermi's Question, are now available as eBooks from Baen Books at: and .

Alternate View Columns Online: Electronic reprints of 227 or more of "The Alternate View" columns written by John G. Cramer and previously published in Analog are currently available online at: .


Enhancement of Tritium Production:

M. I. Abdulhamid, et al. (STAR Collaboration), “Beam Energy Dependence of Triton Production and Yield Ratio (Nt×Np/N2d) in Au+Au Collisions at RHIC,” Phys. Rev. Lett. 130, 202301 (2023); arXiv:2209.08058 [nucl-ex].

E. Shuryak and J. M. Torres-Rincon, “Light-nuclei production and search for the QCD critical point,” European Physical Journal A 56, 241 (2020); arXiv:2005.14216 [nucl-th].

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