Rare quark jolts could reveal the secrets of the universe’s first fluid

Rare jolts could reveal details of the universe’s first fluid that average particle motion misses. New calculations predict that a heavy quark racing through hot plasma can experience unusually large momentum changes. Those events occur more often than a simple bell curve predicts, and large slowing events are more likely than comparable speeding-up events.

Jean Du Plessis of MIT and Bruno Scheihing-Hitschfeld of the University of California, Santa Barbara, report the work in Physical Review Letters. Their theory examines heavy particles traveling at relativistic speeds, close to the speed of light, where familiar approximations for random motion become incomplete. It offers a possible new way to investigate the microscopic properties of quark-gluon plasma.

“Our result reveals a new source of information carried by heavy quarks in rare, unusually large changes in their motion,” said Du Plessis, a graduate student at MIT’s Center for Theoretical Physics. “How often those large changes occur depends on the microscopic nature of the plasma, raising the possibility that they could provide a new way to learn what the quark-gluon plasma is actually like inside.”

The starting point is Brownian motion, the irregular movement of particles buffeted by a fluid’s microscopic constituents. Botanist Robert Brown observed this jittering in water, and Albert Einstein later explained its molecular origin. The same general problem of random microscopic motion remains important when scientists study much smaller systems, although their physical conditions can differ enormously.

Two effects work together: drag tends to slow a moving particle, while thermal fluctuations give it random kicks. In an appropriate Brownian model, these effects balance so the particle can eventually reach thermal equilibrium with its surroundings. That connection links the visible consequences of thermal motion to the invisible interactions producing them.

A common approximation represents momentum fluctuations with a Gaussian distribution, the familiar bell curve. Small departures from the average dominate, while extreme departures become rapidly less likely. The problem arises when this simplified description is carried into relativistic heavy-quark motion, where microscopic calculations of drag and fluctuations no longer obey the usual Einstein relation.

Here, momentum describes a particle’s motion, and momentum transfer records how interactions change it over an interval. The distribution therefore describes possible changes and their probabilities, not a map of where quarks sit inside the plasma. Keeping that distinction makes the proposed probe more concrete: the researchers are asking how the medium changes a passing particle’s motion.

The researchers worked with quantum chromodynamics, the theory describing quarks, gluons and the strong interaction. They began with weakly coupled plasmas, where interactions are sufficiently tractable for a controlled calculation. Their goal was to retain more information about momentum exchange than an approximation based only on average drag and fluctuation width.

The calculation combined contributions from relatively large momentum transfers with the collective physics governing smaller transfers. Matching those contributions required removing their overlap so the same processes were not counted twice. This allowed the team to calculate the distribution of momentum changes along the quark’s direction of motion, including effects of gluon interactions.

This was a theoretical investigation, not an experiment tracking a newly observed quark trajectory. The analysis also used a large-mass approximation that neglects certain finite-mass effects. Its significance lies in showing how a more complete treatment of momentum exchange can recover the balance needed for equilibration when a purely Gaussian description cannot.

Near its center, the calculated distribution resembles the familiar bell curve. Farther away, its tails fall exponentially rather than with the steeper Gaussian suppression. The difference changes the predicted frequency of rare, large momentum transfers, showing why the shape of a distribution matters alongside its average in particle-physics models.

The tails are also unequal for a moving quark. A large event that slows it more than average drag would suggest is more likely than an equally large event that speeds it up. That asymmetry matters because heavy quarks must exchange momentum with their surroundings in a way consistent with eventually reaching thermal equilibrium.

“The usual Brownian picture assumes that large kicks become exceedingly rare,” Du Plessis said. “For heavy quarks, however, these rare kicks are more common than the bell curve predicts, and are not equally likely in opposite directions: A large kick that slows the quark down more than expected from drag is more likely than an equally large kick that leaves it moving faster than expected.”

Many small contributions can still make the center increasingly Gaussian over long intervals. That familiar statistical behavior does not erase the tails or make them irrelevant to equilibration. For a realistic particle, a rare large transfer can change its subsequent motion appreciably, even when such events account for only a small fraction of possible outcomes.

The team found the same qualitative structure in weakly coupled versions of different gauge theories. It also identified that structure in an earlier strongly coupled calculation using an idealized supersymmetric plasma. Shared features across these models suggest that the pattern could survive beyond one mathematical setting, but do not establish identical behavior in every form of matter.

In particular, the strongly coupled comparison is not a complete calculation of real quantum chromodynamics under collider conditions. The authors argue that a Gaussian center with exponential tails is likely to be a robust feature of realistic quark-gluon plasma. Establishing its quantitative consequences for nuclear collisions requires further work, rather than assuming the idealized models supply a finished experimental prediction.

The distinction also prevents an overstatement about Einstein’s work. The result extends the description needed for this extreme setting; it does not invalidate ordinary Brownian motion or overturn relativity. The familiar Gaussian picture retains a useful central role, while the rare events outside that central region contain additional information it leaves out.

Nor does finding an exponential tail make the different theoretical media indistinguishable. Its steepness contains information about the medium’s microscopic physics, and can differ between weakly and strongly interacting models. The shared mathematical outline is therefore a starting point for comparison, while the detailed rate of rare events supplies the potentially discriminating information.

Quark-gluon plasma existed during the early universe’s first microseconds, before quarks became confined into particles such as protons and neutrons. Physicists recreate tiny, fleeting droplets through high-energy ion collisions in particle accelerators. Heavy quarks passing through that medium can act as probes because their changing motion reflects interactions with its constituents.

Researchers could compare transport models incorporating these rare kicks with collider measurements. The paper proposes describing the tails with an additional parameter that measures how rapidly their probabilities decline. That could help connect microscopic calculations with inferred transport properties, without pretending that experiments directly record every kick experienced by an individual quark.

Real heavy quarks have finite masses, and collision plasmas evolve over extremely short lifetimes. A particularly large kick can alter a quark’s velocity enough to change the distribution governing its subsequent motion. The next challenge is to incorporate such dynamics into realistic models and determine whether rare momentum transfers leave a measurable signature in heavy-quark observables.

These resources explain thermal equilibration, complementary calculations and the experimental motivation for studying primordial matter.

Universal Equilibration Condition for Heavy Quarks
This theoretical study generalizes the equilibrium condition beyond Gaussian fluctuations and the usual Einstein relation. (Physical Review Letters, December 2025)

Dynamics of heavy quarks in strongly coupled N = 4 SYM plasma
This calculation explores non-Gaussian momentum exchange in an idealized strongly interacting plasma. (Journal of High Energy Physics, July 2025)

Quark Mass Dependence of Heavy Quark Diffusion Coefficient from Lattice QCD
Lattice calculations examine how quark mass affects diffusion, providing a complementary reference for transport models. (Physical Review Letters, February 2024)

How much do heavy quarks thermalize in a heavy ion collision?
This foundational work connects heavy-quark diffusion, energy loss and Brownian-style transport descriptions. (Physical Review C, June 2005)

The early universe
CERN outlines how early-universe matter evolved from quarks into protons, neutrons and atoms. (CERN)

Research findings are available online in the journal Physical Review Letters.

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