The top quark isn’t a loner after all: “toponium” is real!

Some particles just seem destined to be alone. Among atoms, helium and the other noble gases are famous for ignoring other atoms, displaying an energetics-based preference for remaining as isolated atoms over binding with any other atom, regardless of species. Among the fundamental particles, neutrinos (and antineutrinos) don’t appear to form any bound states, as they’re uncharged under both the strong nuclear and the electromagnetic force: the primary forces that bind particles together. The W-and-Z bosons are too short-lived to form bound states, as is the Higgs boson. But among particles with either an electric charge or a color charge (or both), there’s only one particle that was presumed to always remain in isolation: the top quark.

Of all the known fundamental particles, the top quark has both the greatest rest mass (at a little over 172 GeV/c²) and the shortest lifetime (at half a yoctosecond, or ~5 × 10^-25 s). The strong nuclear force — the force that binds quarks together into bound states like baryons and mesons — is an incredibly short-range force, but even “short-range” means that it requires a sufficient amount of time to enable the formation of bound states. Whereas all the other flavors of quarkonium (quark-antiquark pairs of the same species) have been observed, “toponium” was assumed to be forbidden, as top quarks and antiquarks were long thought to decay too quickly, preventing the formation of a bound state.

But new research from the CMS and ATLAS collaborations at CERN’s Large Hadron Collider tell a different story, with each team now demonstrating the existence of toponium at greater than 5-sigma significance: the gold standard for discovery in particle physics. Here’s how the Universe surprised us once again.

The quarks, antiquarks, and gluons of the Standard Model have a color charge, in addition to all the other properties like mass and electric charge. All of these particles, except gluons and photons, experience the weak interaction. Only the gluons and photons are massless; everyone else, even the neutrinos, have a non-zero rest mass.

You have to realize that, despite all that we’ve learned about the Universe from an astrophysical perspective, including:

• the existence and abundance of dark matter,
• the unexplained presence and value of dark energy,
• and the strong evidence (despite the lack of a mechanism) for something to have created a significant matter-antimatter asymmetry in the early Universe,

the only particles we know of in existence are the particles (and antiparticles) of the Standard Model. Despite the fact that we know there are additional forces and/or particles that must be present to explain the full suite of what’s presently observed, it’s only this fraction of reality — the quarks, leptons, and bosons that we know of, shown above — that we can experimentally test and measure.

The quarks and antiquarks of the Standard Model come in six different species, known as flavors: up, down, strange, charm, bottom, and top, sorted from least massive to most massive. The light species of quarks, like the up, down, and strange quarks, can all mix together from a quantum mechanical perspective, producing mixed (rather than pure) meson states like the π⁰, η, η′, ρ⁰ and ω mesons. There’s no up-antiup, down-antidown, or strange-antistrange mesons, but rather these “mixed state” mesons, all of which act as their own antiparticle.

However, the heavy quarks and antiquarks, like the charm and bottom quarks, can form into bound states that are made purely of charm-anticharm or bottom-antibottom quarks: examples of quarkonium.

Two examples of quarkonium: bottomonium (left) and charmonium (right), which are made of bottom-antibottom and charm-anticharm pairs of quarks and antiquarks, respectively. Only the heavy quarks, with significantly different masses from one another, can form distinct quarkonium states.

In order to create a quarkonium state, there are a few different things that need to happen.

• You need a particle physics event, like a collision, where there’s enough free energy in the center-of-mass reference frame to produce the particle-antiparticle pair needed to make quarkonium.
• The relevant particle-antiparticle pairs must remain close enough together to create a bound meson state, where gluons can be exchanged between them.
• And each member of that particle-antiparticle pair must remain stable against decay (which occurs through the weak interactions) so that the bound state can persist for long enough to allow the exchange of gluons.

In particle physics experiments, the first step is relatively easy; all you need to do is collide two particles (or a particle-antiparticle pair) together with a great enough center-of-mass energy, and you’ll have a chance of creating the quark and antiquark you’re interested in creating via Einstein’s mass energy equivalence: E = mc². The second step is also pretty easy, as when you have collisions that have lots of available energy to create new particles, some of that energy will go into particle (and antiparticle) creation and some of that energy will go into kinetic energy: the energy of motion of the new particles and the bound states they form. If a heavy quark-antiquark pair have large momenta relative to one another, they’ll produce mesons separately (one containing a heavy quark and another containing a heavy antiquark), but if they don’t, they can remain in a single, bound state together: quarkonium.

When a meson, such as a charm-anticharm particle shown here, has its two constituent particles pulled apart by too great an amount, it becomes energetically favorable to rip a new (light) quark/antiquark pair out of the vacuum and create two mesons where there was one before. A strong enough electric field, for long-enough lived mesons, can cause this to occur, with the needed energy for creating more massive particles coming from the underlying electric field, and with the amount of energy required to create these new particles (or particle-antiparticle pairs) described by E = mc².

That’s the key to making quarkonium: making heavy quark-antiquark pairs, but making them in such a way that the relevant heavy quark and antiquark are moving slowly relative to one another. However, there’s one more criterion that needs to be obeyed: both the quark and the antiquark have to live for sufficiently long periods of time that they can successfully exchange gluons between them: the key to making a bound state.

• For charm quarks (and antiquarks), this is no problem, as they live for up to a picosecond, with the charmonium particle (J/ψ) having a lifetime of around ~10^-20 seconds. This is long enough for a gluon to be exchanged over distances much larger than a femtometer (10^-15 meters), which is the typical size of a baryon or meson.
• For bottom quarks (and antiquarks), it’s even easier: they can form baryons living up to around a picosecond as well, with the bottomonium meson (ϒ) having a lifetime slightly longer than ~10^-20 seconds. Gluons have no trouble traversing the typical nuclear distances over these timescales.
• But for top quarks (and antiquarks), they have the shortest lifetimes of any known particle: just ~5 × 10^-25 seconds. A gluon can only travel about ~10^-16 meters over that timespan, which is less than a typical baryon or meson’s physical size.

To understand why this is so important, we need to look at a key idea in the physics of the strong nuclear force: asymptotic freedom.

At high energies (small distances), the strong force’s interaction strength drops to zero. At large distances, it increases rapidly. This is the idea of asymptotic freedom, which has been experimentally confirmed to great precision, and applies to quarks in any and all bound states.

Most of us are more familiar with forces like gravitation and electromagnetism: forces that are known as long-range forces in physics. A long-range force is strongest at the shortest distances, with no limit to how close you can get or how strong the force can get. However, as you go farther and farther away from the “source” of that force from a mass or a charge, respectively the force gets smaller and smaller, but never drops to zero. That’s the way gravity and electromagnetism each work.

But the strong nuclear force is different. Not only is it not a long-range force, it’s a completely different type of force.

• The force is zero at the shortest possible distances, which means if you put two “charged” (color charged, in this case) particles under that force right on top of one another (or as close as you dare imagine), the force between them drops to zero.
• The force then increases with separation, out to a distance of around ~10^-15 meters or so, which is the typical radius of confinement. If you tried to pull quarks farther apart than this, they would simply rip quark-antiquark pairs out of the vacuum, forming new bound states (hadrons).
• But then, beyond that key distance, the force again drops off tremendously, leaving only the residual strong force behind: the force that binds protons and neutrons together, only at extremely short distances.

This explains why baryons and mesons are all roughly the same size as one another, but it also leads to an expectation: that the top quark can’t form bound states at all.

This to-scale diagram shows the relative masses of the quarks and leptons, with neutrinos being the lightest particles and the top quark being the heaviest. No explanation, within the Standard Model alone, can account for these mass values. We now know that neutrinos can be no more massive than 0.45 eV/c² apiece, meaning that the difference between a neutrino’s mass and an electron’s mass is more than three times as large as the difference between the electron’s mass and the top quark’s mass.

Let’s think about the properties of the top quark. It has the greatest mass of any Standard Model particle: at ~172 GeV/c², or more than 35% heavier than the next-heaviest particle, the Higgs boson. It also has the shortest lifetime of any particle in the Standard Model, at just 5 × 10^-25 seconds, which is shorter-lived than the W-and-Z bosons or the Higgs boson, and much shorter than the lifetime of any other Fermion (i.e., a quark or lepton). With this short of a lifetime, a top quark and its antiquark counterpart would now run into a problem: they wouldn’t be able to form a bound state at all.

With such a large mass, it takes an enormous amount of energy to produce a top-antitop pair: around 345 GeV in the center-of-mass frame. That quark and antiquark, in theory, should be able to produce a quarkonium state together: toponium, so long as they live for long enough to exchange gluons between them. But gluons need to travel for about a femtometer in order to create a bound state, and that would require a lifetime of more like ~3 × 10^-24 seconds, which is about six times longer than a top quark (or antiquark) lives for.

In other words, we can just use a little simple math about:

• the separation distance between a quark and antiquark to form a meson,
• the amount of time required for a gluon exchange to occur,
• and the lifetime of top quarks and antiquarks,

to understand why the top-antitop form of quarkonium, toponium, simply shouldn’t exist.

This graph shows a series of top quark events that result in jets. The top-antitop production contribution is highlighted in red, while the total signal is shown in green and the jet background (not involving top-antitop events) is shown in blue. Note how the mass of the top quark is not constant at ~172 GeV, but rather is spread out over a wide range between ~150 and ~195 GeV before dipping below the background.

But now we have to remember one of the most important figures in this history of quantum mechanics: Heisenberg. Heisenberg is most famed for his uncertainty relations, such as between position and momentum. Want to measure a particle’s position? Great; you’ll have to make a measurement to do that, and that will give you its position to a certain level of precision. But there’s a cost to that: the product of the uncertainty in your position (Δx) and the uncertainty in your momentum (Δp) can be no less than one-half of the reduced Planck constant (ℏ). In terms of an equation, we could write:

Δx · Δp ≥ ℏ/2,

indicating that the product of the uncertainty in your position with the uncertainty in your momentum must always be greater than or equal to this quantum mechanical value of ℏ/2.

Of course, Heisenberg’s uncertainty principle applies to a lot more than just position and momentum; it applies to all conjugate pairs of quantities in quantum mechanics. Another such pair of quantities is energy and time. You might have noted that all electrons have the same rest mass as one another, and so you might think that all particles of the same species would have identical masses. After all, we can declare that the top quark’s mass is 172.52 GeV/c², as determined by the best CMS and ATLAS measurements. However, some top quarks live for shorter periods of time (they have a small Δt), and they have a larger uncertainty in their rest mass (and hence, their energy, ΔE).

On the other hand, some top quarks (and antiquarks) will be outliers, and will live for longer than ~5 × 10^-25 seconds, just like some radioactive materials can live for far longer than their half-life or mean lifetime.

If one knows how carbon-14 decays and can measure how much carbon-14 (relative to carbon-12) is present today, it’s straightforward to learn how much carbon-14 was present when a specific event occurred in a ‘fossilized’ relic from the past. The process of carbon-dating uses precisely this method, where the atoms remaining allow us to infer what the conditions were at the moment the carbon-containing organism stopped uptaking new carbon.

While most top quarks, on average, live for a specific mean lifetime, some live shorter and some live longer. It’s sort of like half-life: even though most of your radioactive particles decay after more than one half-life, a few will remain even after five, ten, or more. For a top quark to live long enough to experience the strong interactions, however, you would naively expect it not to need merely six half-life timescales to elapse (after which about ~1.5% of all top quarks would survive), but around twenty of them, after which fewer than 1-in-1,000,000 top quarks would survive. This is why, at least naively, you would think that the formation of toponium would be impossible.

But toponium, perhaps counterintuitively, would be made of very massive particles: a top quark and antiquark, and this would give it a much smaller bound-state radius compared with other baryons and mesons: of right around ~10^-17 meters. Toponium’s mean lifetime is very short: determined to be around ~2.5 × 10^-25 seconds, but this is importantly even shorter than the top quark’s mean lifetime. It was just less than two years ago that quantum entanglement was observed between top-antitop pairs of particles, and a few months ago, the CMS collaboration announced that collisions that resulted in the creation of top-antitop events found an excess of events that indicated a new bound state right at ~341 GeV/c², right near where you’d expect to produce toponium, if it were possible. Just days ago, the ATLAS collaboration announced that they found the same excess.

This view of the ATLAS detector, being worked on in between data runs at the Large Hadron Collider, showcases the largest and one of the two most precise particle detectors of all-time. Pinpointing and tracking the masses, energies, and momenta of every particle that streams out from the collision point is key to reconstructing what particles and antiparticles were produced: even unstable ones that decay before leaving a telltale signature in the detector.

How can you make toponium, and why isn’t it strictly forbidden?

It’s if you produce a top and antitop quark together at right around the energy threshold for creating them, they’ll be moving very slowly with respect to one another, and they might:

• see each other,
• exchange one gluon (or more than one),
• and begin to orbit one another, even briefly,

before one and then the other decays away. The small separation distance (or what physicists think of as the Bohr radius) between the internal particles of the quark-antiquark pair in toponium helps, but there’s an additional key prediction of quantum physics for toponium: it should show up not just at the smallest possible energies for making a top-antitop pair, but there should be very specific quantum spin states that it displays.

Invariant mass of the top-pair system close to the production threshold as a function of angular variables after the fit to data. The orange line in the second panel shows the contribution of the non-relativistic effects compared to the prediction without this process. Even after background subtraction, a substantial signal remains: indicating the formation of a bound state and consistent with that bound state being toponium.

As with all things, there’s a “standard background” we’d expect, as in the case where you didn’t have toponium, and then there’s “what signal do we actually observe,” and do we see a significant enough excess to declare a discovery? You have to compare your signal with your predicted theoretical background, and see if it’s significant enough.

• In late March of 2025, the CMS collaboration announced seeing an excess of events at the top-antitop threshold above the perturbative QCD (strong force) predictions at 6.3-sigma significance.
• Then, in early July of 2025, the ATLAS collaboration announced that same excess, at the same top-antitop energy threshold, above the perturbative QCD predictions at the 7.7-sigma significance level.

Although there’s more work to be done just to make sure this isn’t some sort of coincidental new, beyond-the-Standard Model particle, we’ve clearly discovered some sort of resonant production of a bound state, and it is consistent in every measurable way with what’s predicted for toponium.

This shows the event display for a candidate top-antitop bound state event. The event was recorded on October 14, 2017, and leads to an invariant mass in the top-antitop pair of 342 GeV, and also with the expected spin-sensitive observables. The momentum of the top quark is less than 10% of the total energy of the toponium state.

It’s a testament to searching for everything you can search for, even including things you might not naively expect. It’s part of why we do physics and why it’s ultimately an experimental science: theory can guide you and tell you what you might expect, but only the experiment can tell you what’s real. It may not be a Nobel-worthy achievement, but the fact that we now know that quarkonium can be made between top and antitop quarks — and that we even learned under what conditions it gets made — certainly represents an advance in science.

The fact that this discovery occurred in 2025 at CERN, however, and not a decade (or more) earlier at the Superconducting Supercollider, should emphasize the importance that science is and must be a global endeavor: the knowledge we gain from it benefits all of humanity. It’s by building machines, tools, observatories, and instruments that maximize our discovery potential, or what we can learn by daring to look in a new, more powerful way, that we gain the ability to not only push past the current frontiers of what is known, but how we give ourselves the opportunities to be surprised by what nature has in store.

Whenever a scientific superpower abandons its leadership role, it opens up new opportunities for other nations and consortiums to make that discovery. For particle physics at the energy frontier, Europe has taken up leadership. For many other scientific endeavors being abandoned by the US in 2025, it’s not only Europe but also China, Russia, and Japan, among others, who will be able to seize those opportunities.

And rest assured, there are indeed valuable new opportunities out there, and whoever makes the needed investment will reap the benefits. It’s easy to declare, “We already know everything worth knowing, and therefore we won’t invest any more in these endeavors,” and it’s easy to convince ourselves that we’re right. Without search, there can be no discovery. However, the very spirit of science — of curiosity, of continued investigation, and of looking at the Universe in ways we’ve never looked at it previously — compels us to continue on, even, and perhaps especially, when face-to-face with what’s presently unknown.