Calculation Shows Why Heavy Quarks Get Caught Up in the Flow

New results will help physicists interpret experimental data from particle collisions and better understand the interactions of quarks and gluons.

Image courtesy of Brookhaven National Laboratory
Heavy quarks (Q) interact most strongly with quark-gluon plasma (QGP)—exhibiting a short mean free path (zig zags)—near the transition temperature (near T/Tc = 1, in lower left), and less strongly with a longer mean free path at higher temperatures.

The Science

Using some of the world’s most powerful supercomputers, theorists have successfully calculated the heavy quark diffusion coefficient. This number describes how quickly a melted soup of quarks and gluons—the building blocks of protons and neutrons, which are set free in collisions of nuclei at powerful particle colliders—transfers its momentum to heavy quarks. The answer, it turns out, is very fast. In fact, it is at the limit of what quantum mechanics allows. The calculations show that the quarks and gluons liberated in these collisions have so many strong, short-range interactions with the heavier quarks that they pull the “boulder-like” heavy quarks along.

The Impact

The calculation will help scientists explain experimental results showing heavy quarks getting caught up in the flow of matter generated in heavy ion collisions. Researchers create these collisions at the Relativistic Heavy Ion Collider and the Large Hadron Collider. The new analysis also adds supporting evidence that the matter created in these collisions, a quark-gluon plasma (QGP), is a nearly perfect liquid. This liquid has a viscosity so low that it approaches the limits of quantum mechanics. Finally, the research showcases the strong international collaboration among theorists and the nuclear physics research community.


Seeing heavy quarks flow with QGP may seem as strange as seeing a heavy rock flow with a stream. But the low viscosity of the QGP—the hot soup of quarks and gluons liberated from protons and neutrons when two heavy ions collide—provides an explanation. It means that there are many strong interactions among those liberated particles. This implies that the “mean free path”—the distance a particle can travel before interacting with another—is extremely small. Heavy quarks with a similarly small mean free path would experience enough interactions to get pulled along.

Theorists in the HotQCD Collaboration calculated the heavy quark diffusion coefficient, which is proportional to how strongly the heavy quarks are interacting with the plasma, to check this understanding. They used powerful supercomputers and lattice QCD, a technique for solving the complex equations of quantum chromodynamics, the theory that describes the interactions of quarks and gluons. They found the heavy quark diffusion coefficient to be very large. The result reveals that the mean free path of heavy quarks within QGP is indeed quite short. The calculations will help theorists improve simulations of how heavy quarks are produced inside the QGP generated by the heavy ion collisions, and how their interactions change as the QGP evolves.


Swagato Mukherjee
Brookhaven National Laboratory

Peter Petreczky
Brookhaven National Laboratory


This work was supported by the Department of Energy Office of Science, Office of Nuclear Physics within the frameworks of Scientific Discovery through Advanced Computing (SciDAC) and the Heavy-Flavor Theory (HEFTY) topical theory collaboration, and by other funders for individual collaborators listed in the scientific paper. It made use of computational resources at the National Energy Research Scientific Computing Center, a DOE Office of Science user facility at Lawrence Berkeley National Laboratory, and facilities of the USQCD Collaboration.


Altenkort, L., et al. (HotQCD Collaboration), Heavy Quark Diffusion from 2+1 Flavor Lattice QCD with 320 MeV Pion Mass. Physical Review Letters 130, 231902 (2023). [DOI: 10.1103/PhysRevLett.130.231902]

Related Links

Calculation Shows Why Heavy Quarks Get Caught up in the Flow, Brookhaven Lab news release

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