Quantum fluctuations help solve decade-old puzzle

Elliptic flow distribution pattern of particle jets in quark-gluon plasma was reproduced by computer simulation.

By José Tadeu Arantes  |  Agência FAPESP – A high-energy nuclear physics puzzle that scientists have been trying to solve for ten years has just been cracked by computer simulation. The problem relates to the distribution pattern of particle jets produced in collisions of heavy nuclei inside the largest particle accelerators operating in the world today, the Large Hadron Collider (LHC) in Europe and the Relativistic Heavy Ion Collider (RHIC) in the United States.

An article describing the result was recently published in Physical Review Letters. 

Jorge Noronha, a professor at the University of São Paulo’s Physics Institute (IF-USP) in Brazil, took part in the study as part of his research project on "Relativistic heavy-ion collision dynamics – macroscopic approaches derived from microscopic physics", supported by FAPESP.

“We discovered that quantum fluctuations in the initial conditions of the fluid are the necessary ingredient to explain the elliptic pattern displayed by the angular distribution of the particles created in collisions,” Noronha told Agência FAPESP.

The fluid mentioned by Noronha is quark-gluon plasma (QGP), which filled the universe during a tiny instant of time after the Big Bang according to the standard model of particle physics. Scientists have used the two huge colliders to recreate QGP by smashing together atomic nuclei at ultrarelativistic velocities (very close to the speed of light).

The temperature produced by these collisions is so high that the quarks and gluons confined within the protons and neutrons that make up atomic nuclei are temporarily released and can move about freely for an instant, forming QGP.

QGP is a very small medium, only slightly larger than the diameter of a proton, which is approximately 10-15 m (1 femtometer or one quadrillionth of a meter). QGP behaves like a quasi-perfect fluid that offers particles practically no resistance to movement.

“There are two especially important ‘experimental signatures’ of QGP. One is the so-called ‘elliptic flow of hadrons’. This has to do with the angular distribution of the particles generated by collisions. Once the system has formed, and the quarks and gluons recombine to form hadrons – protons, neutrons, and mesons – the detectors record the angles at which these reconfigured particles hit them. What we’ve found is that there are preferential angles that in aggregate define various patterns. The elliptic pattern predominates,” Noronha said.

“The second signature is called ‘jet quenching’. When a jet of quarks or gluons travels within the plasma at close to the speed of light, it is braked by the medium and loses energy. For more than ten years, particle physicists have tried in vain to understand how this energy loss leads to the angular distribution observed. We’ve now succeeded. We combine jet physics and hydrodynamics to describe the real situation of a jet moving in a medium that is itself expanding at quasi-light speed.”

Particle distribution patterns

Elliptic flow is not the only possible pattern. Angular distribution can also be triangular or quadrangular, for example. Studies of QGP therefore decompose possible distributions using a specific mathematical sequence called a Fourier series to determine the number of particles in a given pattern. Elliptic flow predominates, but until now no one could explain why.

The puzzle was solved by introducing quantum fluctuations into the model.

“The atomic nuclei that are smashed together in the collider are made up of protons and neutrons. But the protons and neutrons aren’t immobile within each nucleus: they move about within a small volume. So the distribution of energy in the nucleus, which provides the initial conditions for the problem, isn’t uniform. It fluctuates continuously. That gives you an idea of what we mean by quantum fluctuations,” Noronha said.

Heisenberg’s uncertainty principle, one of the pillars of quantum physics, should be mentioned at this point. According to the uncertainty principle, a particle’s position and speed cannot be precisely determined at the same time. The more accurately its speed is measured, the less accurately its position can be known, and vice versa. The concept of quantum fluctuation is intimately associated with the uncertainty principle.

Moreover, quarks and gluons are always moving even while confined within protons and neutrons, and particle-antiparticle pairs are continuously being produced and annihilated. Roughly speaking, according to the standard model, a proton contains three quarks. However, this is just a snapshot of something highly dynamic. It would be more appropriate to think of a proton as a choppy sea of energy in which quarks and antiquarks are incessantly created and destroyed.

“Actually, the proton is a very complicated reality, and we’re only starting to understand it. People have proposed several different models to describe it,” Noronha said.

In sum, QGP is a very high-energy system similar to the primordial universe, and it fluctuates as it is traversed by jets of particles at velocities close to the speed of light. The jets lose energy as they travel. Experimental detection of the resulting particles shows that their angular distribution is predominantly configured in an elliptic pattern.

“By introducing quantum fluctuations into the initial conditions used in computer simulations, we were able for the first time to produce a result compatible with the experimentally observed pattern,” Noronha said.

“This calculation involved several layers of theory. We had to consider the system’s initial energy density, how the system evolves from each initial condition as it expands at quasi-light speed, and how each jet of quarks or gluons loses energy in the plasma. Because of fluctuation, you have to simulate each event separately, considering various initial energy densities, which means running hundreds of simulations. After all that, you have to calculate the statistical distribution of the various simulations to arrive at something close to real behavior.”

The simulations were performed on computers hosted by Columbia University in the US, Goethe University Frankfurt in Germany, and the University of São Paulo in Brazil. The results proved consistent with the experimental data.

“As well as calculating elliptic flow, we also calculated for the first time the triangular flow of high-energy particles. This flow is different from zero only when quantum fluctuations are included,” Noronha said.

The article “Event-by-Event Hydrodynamics + Jet Energy Loss: A Solution to the R_AA⊗ v₂Puzzle” (doi: http://dx.doi.org/10.1103/PhysRevLett.116.252301) can be read at: http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.116.252301.