A new calculation will help physicists interpret experimental data from particle collisions at the RHIC and LHC to better understand the interactions of quarks and gluons.
A group of theorists has used some of the world’s most powerful supercomputers to produce a major advance in nuclear physics.
The team has developed a calculation of the heavy quark diffusion coefficient. This number describes how quickly a melted soup of quarks and gluons transfers its momentum to heavy quarks. The answer: very fast.
As described in the paper, ‘Heavy Quark Diffusion from 2 + 1 Flavor Lattice QCD with 320 MeV Pion Mass,’ the momentum transfer from the ‘freed up’ quarks and gluons to the heavier quarks occur at the limit of what quantum mechanics will allow.
These quarks and gluons have so many short-range, strong interactions with the heavier quarks that they pull the particles along with their flow.
The calculation will help explain experimental results that show heavy quarks getting caught up in the flow of matter generated in heavy ion collisions at the Relativistic Heavy Ion Collider (RHIC) at Brookhaven and the Large Hadron Collider (LHC) at Europe’s CERN laboratory.
The new study also demonstrates that this matter – the quark-gluon plasma (QGP) – is nearly perfect liquid. Its viscosity is so low that it also approaches the quantum limit.
“Initially, seeing heavy quarks flow with the QGP at RHIC and the LHC was very surprising,” said Peter Petreczky, co-leader of the work and member of the nuclear theory group at the U.S. Department of Energy’s Brookhaven National Laboratory.
“It would be like seeing a heavy rock get dragged along with the water in a stream. Usually, the water flows, but the rock stays.”
The calculation explains why this surprising image makes sense when thinking about the low viscosity of the QGP.
The low viscosity was a major motivator for the calculation
The low viscosity of matter generated in RHIC’s collisions of gold ions was a major motivator for the new calculation, explained Petreczky.
The collisions melt the boundaries of individual protons and neutrons to set the inner quarks and gluons free. The resulting QGP flowed with little resistance, showing that there are many strong interactions between the quarks and gluons in the hot quark soup.
“The low viscosity implies that the ‘mean free path’ between the ‘melted’ quarks and gluons in the hot, dense QGP is extremely small,” said Swagato Mukherjee co-leader of the work and member of the nuclear theory group at the U.S. Department of Energy’s Brookhaven National Laboratory.
The mean free path is the distance a particle can travel before interacting with another particle.
“If you think about trying to walk through a crowd, it’s the typical distance you can get before you bump into someone or have to change your course,” he said.
The quarks and gluons are able to interact strongly and frequently with a short mean free path.
The collisions dissipate and distribute the energy of the fast-moving particles. The strongly interacting QGP exhibits collective behaviour, including nearly frictionless flow.
“It’s much more difficult to change the momentum of a heavy quark because it’s like a train—hard to stop,” Mukherjee stated. “It would have to undergo many collisions to get dragged along with the plasma.”
If the QGP is a perfect fluid, the mean free path for the heavy quark interactions should be short enough to make that possible.
Calculating the heavy quark diffusion coefficient was a way to check this understanding.
Supercomputers helped to pave the way for the new calculation
The calculations needed to solve the equations of quantum chromodynamics (QCD) — the theory that describes quark and gluon interactions — are mathematically complex.
Many powerful supercomputers and advances in theory helped pave the way for the new calculation.
“In 2010/11, we started using a mathematical shortcut, which assumed the plasma consisted only of gluons, no quarks,” said Olaf Kaczmarek of Bielefeld University, who led the German part of this effort.
The team was able to work out their method using lattice QCD by thinking only of gluons.
In this method, scientists ran simulations of particle interactions on a discretised four-dimensional space-time lattice.
They placed the particles in discrete positions on an imaginary 3D grid to model their interactions with neighbouring particles. They then saw how those interactions changed over time.
The team used many different starting arrangements and included varying distances between particles.
They then figured out how to add in the complexity of the quarks.
The team loaded a large number of sample configurations of quarks and gluons onto the 4D lattice. They used repeated random sampling to find the most probable distribution of quarks and gluons within the lattice.
“By averaging over those configurations, you get a correlation function related to the heavy quark diffusion coefficient,” said Luis Altenkort, a University of Bielefeld graduate student who also worked on this research at Brookhaven Lab.
As an analogy, think about estimating the air pressure in a room by sampling the positions and motion of the molecules. “You try to use the most probable distributions of molecules based on another variable, such as temperature, and exclude improbable configurations—such as all the air molecules being clustered in one corner of the room,” Altenkort said.
The QGP was simulated at a range of fixed temperatures. The heavy quark diffusion coefficient for each temperature was calculated. This could be used to map out the temperature dependence of the heavy quark interaction strength.
“These demanding calculations were possible only by using some of the world’s most powerful supercomputers,” Kaczmarek said.
As Mukherjee noted, “These powerful machines don’t just do the job for us while we sit back and relax; it took years of hard work to develop the codes that can squeeze the most efficient performance out of these supercomputers to do our complex calculations.”
The heavy quark diffusion coefficient is largest at the temperature at which the QGP forms
The calculations show that the heavy quark diffusion coefficient is the largest at the temperature at which the QGP forms. It then decreases with increasing temperatures.
The result implies that the QGP comes to an equilibrium very quickly.
“You start with two nuclei, with essentially no temperature, then you collide them and in less than one quadrillionth of a second, you get a thermal system,” Petreczky said.
The heavy quarks also get thermalised.
For that to happen, the heavy quarks must undergo many scatterings with other particles very quickly. This implies that the mean free path of these interactions must be very small.
The calculations show that the mean free path of the heavy quark interactions is very close to the shortest distance allowable at the transition to QGP.
The quantum limit is established by the inherent uncertainty of knowing both a particle’s position and momentum simultaneously.
The scientists argue that this independent measure provides corroborating evidence for the low viscosity of the QGP.
Improving understanding of how heavy ion collision systems evolve
Now that it is confirmed that the heavy quark interactions with the QGP vary with temperature, the team can improve their understanding of how the actual heavy ion collision systems evolve.
“My colleagues are trying to develop more accurate simulations of how the interactions of the QGP affect the motion of heavy quarks,” Petreczky said.
“To do that, they need to take into account the dynamical effects of how the QGP expands and cools down — all the complicated stages of the collisions.
“Now that we know how the heavy quark diffusion coefficient changes with temperature, they can take this parameter and plug it into their simulations of this complicated process and see what else needs to be changed to make those simulations compatible with the experimental data at RHIC and the LHC.
“We’ll be able to better model the motion of heavy quarks in the QGP, and then have a better theory to data comparison.”
