Researcher proposes quark-gluon plasma expansion model

Quark-gluon plasma is believed to have predominated in the primordial universe and can be recreated in the largest particle colliders in operation today.

By José Tadeu Arantes

Agência FAPESP – Quark-gluon plasma appears to be an exotic system, but according to the Big Bang model it predominated in the universe a fraction of a second after the initial instant. It became exotic, owing to the strong nuclear interaction, which confined quarks and gluons inside structures such as protons, neutrons and mesons.

The energy levels reached by the largest particle colliders in operation today – the Large Hadron Collider (LHC) at CERN on the Franco-Swiss border and the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory (BNL) in the United States – have enabled quark-gluon plasma to reappear, if only for the tiniest of instants.

Producing a state-of-the-art description of this system was the aim of a one-year project involving collaboration between a group led by Jorge Noronha, a professor at the University of São Paulo’s Physics Institute (IF-USP) in Brazil, and Ulrich Heinz, a professor at Ohio State University (OSU) in the United States. Entitled “A state-of-the-art description of the strongly coupled quark-gluon plasma using viscous relativistic hydrodynamics and the gauge/gravity duality”, the project was supported by FAPESP.

The original idea was to use relativistic hydrodynamics and the duality between string and field theories to understand more about the physics of quark-gluon plasma. “However, when we got down to work, something unexpected happened. For the first time, we found a model for this system’s expansion in spacetime and for its description as an ultra-relativistic fluid that expands almost at the speed of light,” Noronha told Agência FAPESP.

The discovery was reported in two articles, “New exact solution of the relativistic Boltzmann equation and its hydrodynamic limit” published by Physical Review Letters, and “Studying the validity of relativistic hydrodynamics with a new exact solution of the Boltzmann equation” published by Physical Review D.

“In light of the articles’ positive international repercussions, we decided to continue the research,” Noronha said. “The new project is longer, set to last two years.”

Relativistic hydrodynamics provided an effective description of the complicated microscopic dynamics of quark-gluon plasma. The Boltzmann equation is a mathematical model in the kinetic theory of gases. The authors adapted it to the relativistic context.

In its classical form, this equation was first put forward by Austrian physicist Ludwig Boltzmann in 1872 to describe the configuration of particles in a gas. Boltzmann was ahead of his time in conceiving of fluids as sets of molecules, atoms or ions, whose dynamics could be understood solely by analyzing collisional processes between particles.

“We applied the equation to an ultra-relativistic fluid that propagates at near-lightspeed both radially and longitudinally, and we were able to resolve it exactly using an ingenious mechanism known as the Weyl transform,” Noronha said.

“Basically this mechanism enabled us to transform the original problem, in which the plasma moves within flat spacetime, without curvature, into another rigorously equivalent problem in which the plasma remains static while spacetime expands and becomes curved.”

By using this highly novel approach, the researchers transformed a very hard problem of relativistic kinetic theory into a far easier problem of general relativity. “In the description of curved spacetime, the problem can be solved exactly,” Noronha explained. “Once we’d done that, we were able to go back and calculate precisely how the plasma expanded in the original flat space.”

Known matter

Noronha said the idea of transforming one problem into the other occurred to him because of his theoretical repertoire. “I work with applications of string theory [in the form of the AdS/CFT holographic duality], so general relativity concepts are always on my mind,” he said.

Quark-gluon plasma is created in an experimental context by colliding massive ions such as lead or gold nuclei at high energy. The nuclei are accelerated to 99.9% of the speed of light. When they collide, they explode into pure energy powerful enough to break apart protons and neutrons into their constituent quarks and gluons.

At the instant of its formation, this system is very small and very hot. Its temperature is in the range of 10¹² Kelvin. As a comparison, temperatures inside the Sun peak at approximately 10⁷ K. In other words, the plasma is 100,000 times hotter than the hottest region of the sun. This is the highest temperature ever obtained in a laboratory.

“It expands very fast in spacetime. And during this expansion it behaves like a fluid with the lowest possible viscosity, even less than a superfluid,” Noronha said.

The temperature falls very rapidly as it expands. Quarks and gluons regroup to form hadrons (protons, neutrons, mesons, etc.), which are measured by detectors. This quark-gluon plasma lasts a very short time, not much more than ten times the time taken by light to pass through a single proton.

According to Noronha, one of the reasons that researchers study quarks and gluons is that they account for 97% of the mass of all known matter.

“It’s become a cliché to say the Higgs boson is responsible for mass. But it isn’t quite the case. Over 70% of the Universe is dark energy, more than 20% is dark matter, and known matter comprises only about 4%. About 97% of known matter’s mass is due to quarks and gluons. So the Higgs boson is responsible for the remaining 3%,” he said.