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The Alternate View
John G. Cramer

SOLVING THE RHIC PUZZLE

I do not usually write about my own scientific work, but I’m going to make an exception for this column and tell you about a physics puzzle and how we solved it. Back in 1991, almost a decade before the facility actually went into operation, I wrote a column ("RHIC: Big Bangs in the Lab", Analog, June 1991) about the Relativistic Heavy Ion Collider (RHIC), a large accelerator project that was then in the early stages of construction. The column was written a few months after I joined what is now called the STAR Collaboration, a group of physicists (now numbering 577) who ultimately built a large "time-projection chamber" detector for tracking and making measurements on the charged particles produced in RHIC collisions.

The RHIC facility is actually two ring-accelerators that accelerate heavy nuclei in opposite directions to nearly the speed of light and then bring them into collision, creating an ultra-hot "fireball" from nuclear systems meeting head-on. RHIC was designed to create a quark-gluon plasma, a new state of matter that has not yet been studied. Standard cosmology says that this was the state of the universe in the first few microseconds after the Big Bang, at the time when the cosmos cooled to a plasma of quarks and gluons, but was not yet cool enough to make the transition to a "soup" of nucleons and mesons, followed by electrons and nuclei, then atoms and photons, etc. The quark-gluon plasma represents new and unexplored territory in the domain of nuclear and particle physics. Exploring this quark-matter territory could simply provide a confirmation of our present ideas about matter under extreme conditions, or it could reveal new and unanticipated wonders. If the history of accelerator physics is any guide, one can expect surprises when a new accelerator facility opens up unexplored territory, and indeed there have been surprises (and puzzles) coming from RHIC.

The RHIC facility was completed in 1999. However, the initial attempt to produce collisions with RHIC in the summer of 1999 was unsuccessful. It was ultimately discovered that the machine had been damaged by wrong-headed pressure tests before operation began and that expensive repairs were needed. The RHIC collisions and measurements finally began in 2000. There have now been five years of running, and a great deal of data has been collected at the two large RHIC experiments, PHENIX and STAR, and also at the two smaller experiments, BRAHMS and PHOBOS. The data has produced much excitement and much progress has been made, but up to now, the data has been telling a confusing story.

To understand the confusion, we have to talk a bit about the conditions in a quark-gluon plasma. First consider what happens when a gas of hydrogen atoms is heated until the orbiting electrons come loose. In the gas, electrons are bound by electrical forces to protons that form the nuclei of hydrogen atoms. When the energy gets high enough, the electrons are detached from the protons. When this happens, the gas becomes a plasma, with a "fluid" of charged electrons sloshing back and forth against the more massive "fluid" formed by the protons.

By analogy, at the much higher temperatures available at RHIC we should be able to do the same thing with nuclei. Each proton and neutron in a nucleus can be considered as a "bag" containing three quarks held together by the strong force, which is moderated by massless particles called gluons. If we subject the system to enough heat and pressure, the quarks should be surrounded by gluons, pulled in all directions by color forces, and should become relatively free particles, no longer constrained to stay in their bags in groups of three. At RHIC, where gold nuclei are brought into collision at energies of up to 200 GeV per nucleon, theoretical lattice-gauge calculations indicate that a plasma made of quarks and gluons should be produced.

The problem with verifying that a RHIC collision produced a quark-gluon plasma is that such a QGP state would be present early in the collision for a very brief time, after which the system expands and cools to become a collection of baryons (3 quarks) and mesons (quark-antiquark pairs) going their separate ways. With the STAR detector, we must measure this "debris" of baryons and mesons from a collision and attempt to deduce what happened in the early stages of the collision.

Even if we are constrained to view only the aftermath of a RHIC collision, the prospects for finding that a QGP was present are not hopeless. There are several characteristic signals of a QGP that can be looked for. First, it should have a very high initial pressure. This should accelerate the particles coming from the collision more in some directions than others, and should produce a characteristic "elliptic flow" pattern in particles emerging from the collision. And indeed, such an elliptic flow pattern was one of the first signals observed in RHIC collisions.

Another characteristic of a QGP is that it manifests the strong force at its strongest, without the shielding and cancellation that occurs when quarks form mesons and baryons. Therefore, the very energetic particles that are created early in a collision and that must pass through a QGP on their way out should interact strongly with it and should have a high probability of losing energy or disappearing completely before they escape. And indeed, such disappearance of the most energetic mesons and baryons is another signal that has been observed to be present in RHIC collisions.

If we stopped there, we might say that two independent signals are telling us that a quark-gluon plasma has been created in RHIC collisions. However, there is a severe problem. The size, shape, and time evolution of the fireball emitting pi mesons (i.e., "pions," particles made of a quark-antiquark pair) can be measured using a technique called "Hanbury-Brown Twiss interferometry" or HBT. It is used on pairs of pions from the collision, looking for an enhanced probability of such pairs that are close in momentum.

Since a quark-gluon plasma has many more particles and quantum numbers than an equivalent fireball made of baryons and mesons, it has more ways of squirreling away energy and should be slower to release that energy. Therefore, if a QGP lies at the heart of a RHIC collision, the resulting fireball should grow larger in size and should expand and emit particles longer than a fireball that never made a QGP. Therefore, the pre-RHIC theoretical expectation was that when HBT interferometry was done on RHIC collisions, one would see a very large source (10-20 femtometers or fm) that emits pions for a long time (3-10 fm/c).

However, the actual measurements seem to say otherwise. The measured source sizes are about the same size as those from lead-lead collisions measured on other accelerators operating 10 to 100 time lower in energy. The source size at RHIC shows no dramatic growth. Further, it appears that the pions are emitted explosively, in a time so short that it can’t be measured (less than 1 fm/c). Instead of bringing the nuclear liquid to a gentle boil and observing the "steam" of a quark-gluon plasma, the whole boiler seems to be exploding in our faces! This mysterious behavior is now called the "RHIC HBT Puzzle." It has proved to be a serious barrier for those who would like to announce that the quark-gluon plasma has been discovered at RHIC.

I am an experimental physicist who was one of the founding members of the STAR Collaboration. I have been one of the leaders of the STAR HBT interferometry work at RHIC. But I sometimes also do theoretical studies, and perhaps 1/4 of the roughly 200 papers I have published over the years are in theory rather than experiment. And I had an idea about what might be missing from the theories that predict large sources and long emission durations at RHIC. I suspected that the problem was that those theories were not using quantum mechanics to describe the pions from the fireball, and in particular were not including the possibility that these particles could be deflected or absorbed on the way out of the fireball. Fortunately, one of my theorist colleagues at the University of Washington, Gerald A. Miller, is a master at performing just the kind of calculations needed, and I was able to interest him in joining me, along with a graduate student and a visitor, to form a group that tried this approach.

Our work took about two years. We formulated a relativistic quantum mechanical description of the problem, wrote a computer program that could predict HBT source sizes, emission durations, and pion momentum distributions, and then hooked this program to a "search code," a program that would systematically vary the variables used in the program to fit data measured by the STAR detector for collisions of gold nuclei at the highest RHIC energy. When we looked at the data-fitting results, we found a surprise.

We had begun the work with the assumption that the important missing ingredient in the previous theories was that they ignored the absorption and loss of pions on the way out of the fireball medium. We had also included a "potential well" that describes the deflection and energy change of the particles, but we didn’t consider it to be very important. But when the fitting began, we found that good fits could only be obtained if we started the pions at the bottom of a very deep potential well and made them use most of their kinetic energy to climb out and escape. The well needed was so deep that it roughly equaled the mass-energy of the particles. This could be interpreted as saying that the pions were losing most of their mass in the fireball medium.

That numerical result triggered a flash of insight. In vacuum, a pion has a mass of 140 MeV, but in the hot dense medium of a quark gluon plasma, the standard model predicts a "chiral symmetry" phase transition that makes the particles lose most of their mass for two reasons: Surrounded by external color forces, the size of the pion grows, reducing the internal motion that accounts for most of its mass. Further, the quarks lose the "dressing" of virtual particles they had in vacuum, and they become essentially massless. Therefore, pions in a region where chiral symmetry has been at least partially restored should lose most of their mass. They would have to do work against a deep potential well to regain their mass when they emerge into the vacuum. Our fitting results were pointing to chiral symmetry.

And so we built the characteristics of chiral symmetry into our program and re-did the fits. The results were spectacular. All the data could be fitted with reasonable values of the fitting variables. And the calculations showed that the apparent small source size and short emission duration of the analysis had been illusions produced by the deep well from which the particles were emitted and by their absorption on the way out of the fireball. The actual source was larger and emitted longer.

According to most theoretical descriptions of hot dense media, a quark-gluon plasma and chiral symmetry restoration should happen at about the same temperature and pressure. The deep potential well that emerges from our results provides evidence that a chiral phase transition has occurred in the collision. By implication, therefore, it supports the picture that RHIC collisions are producing a quark-gluon plasma. Our results have converted a problem for the QGP interpretation into another piece of evidence in support of it.

In other words, we have solved the RHIC HBT Puzzle. The problem was that previous theoretical treatments were leaving out quantum mechanics, were leaving out the loss of pions in the medium, and were leaving out the deep potential well from which the pions must emerge. When those elements are added, all the pieces click into place and the puzzle is solved. Our paper describing this work has just been accepted for publication in the journal Physical Review Letters.

AV Columns Online: Electronic reprints of over 120 "The Alternate View" columns by John G. Cramer, previously published in Analog, are available online at: http://www.npl.washington.edu/av. The paper referenced below can be obtained at: http://www.arxiv.org.

Reference:

Solving the RHIC HBT Puzzle

John G. Cramer, Gerald A. Miller, Jackson M. S. Wu, and Jin-Hee Yoon, "Quantum Opacity, the RHIC HBT Puzzle, and the Chiral Phase Transition", Physical Review Letters (accepted for publication), electronic preprint nucl-th/0411031.