Category: quark bound states

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Did CMS discover an unexpected quasiparticle? New search observes what looks to be ‘toponium’

While searching for new Higgs bosons the CMS experiment at the Large Hadron Collider (LHC) may have just found a surprise. They have observed an excess of events that look to be a new particle, and are reporting high statistical evidence for their claim. The only question is what exactly is this new particle?

The search was initially designed to look for new, heavier, versions of the Higgs boson decaying to a top quark and an anti-top quark. Its well known that the Higgs boson of the Standard Model, discovered jointly by ATLAS and CMS in 2012, underlies the mechanism which gives all fundamental particles their masses. The Higgs boson itself interacts with particles in proportion to their mass, preferring heavier particles over lighter ones. It therefore interacts the most strongly with the heaviest known fundamental particle, the top quark, which has a mass of ~173 GeV. The Higgs boson itself only has a bass of 125 GeV, meaning conservation of energy dictates it can’t decay into a top quark-antiquark pair.

However many theories of physics beyond the the Standard Model predict additional Higgs bosons, heavier cousins of the current one. If these new heavy Higgs bosons had a mass larger than 350 GeV, they would likely decay to a top quark-antiquark pair quite often. CMS therefore was analyzed its data searching for this signature, hoping to find signs of a new Higgs boson. To do so, they had scrutinize very carefully the known production of top quark-antiquark pairs, which are produced copiously at the LHC from other processes. If a new particle was being produced and decaying to top quarks, the mass of the new particle would give the top quarks a characteristic energy. One key sign of a new particle would therefore be an excess of top quark-antiquark events at a particular energy, corresponding to the mass of the new particle. 

When CMS scrutinized their data looking for such an excess they found one. But curiously right ~350 GeV, the minimum energy required to produce the top quark-antiquark pair. It would be quite the coincidence for a new particle to show up right at this minimum threshold, which made CMS consider alternative possibilities.

 

 

A comparison of the observed CMS data and their estimate of backgrounds as a function of the invariant mass of the top quark antiquark system. CMS observes an excess of events at ~350 GeV, which is well fit with a toponium model (red line).

 One unorthodox explanation that seems to fit the bill is ‘toponium’, a short lived bound state of the top quark-antiquark pair is being formed. Toponium would be the heaviest version of ‘quarkonia’ we have seen, bound states of quark antiquark pairs that form bound states similar to atoms. We have observed and measured quarkonia states of the other quarks for decades, however it was long thought that the top quark, whose large mass causes it to decay in just 10^(-25) seconds, would decay too quickly to create observable bound state effects at a hadron collider. Toponium production would happen most often if the top quarks were produced just at the energy threshold, such that they don’t any extra energy. These low energy top quarks would spend more time close to each other than normal, rather than immediately flying away, so they could have time to briefly form a toponium state before decaying. However, once small hints of intriguing excesses started appearing in LHC analyses, updated calculations in the last few years suggested that perhaps such an effect could be observable.

These calculations are approximate, and more work is still being done to refine them. But the preliminary predictions they give for the properties of toponium seem to match well with what CMS is seeing, both in terms of the rate of toponium production and the quantum properties of the toponium state (spin and parity).

Still CMS is being cautious before claiming a discovery of toponium. They claim observation of an ‘excess at the top quark pair production threshold’ which is consistent with toponium. However given the limited present data and incomplete theoretical models of toponium, they cannot rule out that the excess they are seeing is coming from a new Higgs-like particle.

CMS measurement of the cross section of the two different hypothetical particles
CMS measurement tries to disentangle the quantum properties of the observed excess. The x-axis shows the estimated rate of production a ‘pseudoscalar’ particle producing the excess. The y-axis shows a similar estimate for a ‘scalar’ particle. The allowed region for the scalar still includes zero, while the zero pseudoscalar hypothesis is clearly excluded at larger than 5 standard deviations.

Further work will be needed to develop improved theoretical models of toponium, and detailed studies from CMS assessing the properties of their observed excess. The excess will also need confirmation from CMS’s rival LHC experiment, ATLAS, to ensure it has not merely made a mistake in its analysis.

However, the smart money would say this very likely looks like toponium. Which, while not signaling the long sought overthrow of the standard model, would be an unexpected and cool surprise from the LHC. Understanding the properties of this previously-thought-impossible quasiparticle will spawn much fruitful research in the years to come. Physicists love a surprise!

Paper:

“Observation of a pseudoscalar excess at the top quark pair production threshold” https://arxiv.org/abs/2503.22382

Additional CMS Paper considering Heavy-Higgs interpretation “Search for heavy pseudoscalar and scalar bosons decaying to top quark pairs in proton-proton collisions”

Read more

CERN Courier “CMS observes top–antitop excess“

Symmetry Magazine “Don’t call it toponium“

Discloure: The author is a member of the CMS collaboration but did not directly work on this analysis

Erratum 4/15/2025 : The article was updated to clarify that in the theory literature prior to the LHC toponium was thought possible to form, just that it was thought to be too small an effect to be observable. The article previously incorrectly stated it had been previously thought impossible to form

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Quark nuggets of wisdom

Article title: “Dark Quark Nuggets”

Authors: Yang Baia, Andrew J. Long, and Sida Lu

Reference: arXiv:1810.04360

Information, gold and chicken. What do they all have in common? They can all come in the form of nuggets. Naturally one would then be compelled to ask: “what about fundamental particles? Could they come in nugget form? Could that hold the key to dark matter?” Lucky for you this has become the topic of some ongoing research.

A ‘nugget’ in this context refers to large macroscopic ‘clumps’ of matter formed in the early universe that could possibly survive up until the present day to serve as a dark matter candidate. Much like nuggets of the edible variety, one must be careful to combine just the right ingredients in just the right way. In fact, there are generally three requirements to forming such an exotic state of matter:

  1. (At least) two different vacuum states separated by a potential ‘barrier’ where a phase transition occurs (known as a first-order phase transition).
  2. A charge which is conserved globally which can accumulate in a small part of space.
  3. An excess of matter over antimatter on the cosmological scale, or in other words, a large non-zero macroscopic number density of global charge.

Back in the 1980s, before much work was done in the field of lattice quantum chromodynamics (lQCD), Edward Witten put forward the idea that the Standard Model QCD sector could in fact accommodate such an exotic form of matter. Quite simply this would occur at the early phase of the universe when the quarks undergo color confinement to form hadrons. In particular Witten’s were realized as large macroscopic clumps of ‘quark matter’ with a very large concentration of baryon number, $latex N_B > 10^{30}$. However, with the advancement of lQCD techniques, the phase transition in which the quarks become confined looks more like a continuous ‘crossover’ (i.e. a second-order phase transition), making the idea in the Standard Model somewhat unfeasible.

Theorists, particularly those interested in dark matter, are not confined (for lack of a better term) to the strict details of the Standard Model and most often look to the formation of sometimes complicated ‘dark sectors’ invisible to us but readily able to provide the much needed dark matter candidate.

Dark QCD?

The problem of obtaining a first-order phase transition to form our quark nuggets need not be a problem if we consider a QCD-type theory that does not interact with the Standard Model particles. More specifically, we can consider a set of dark quarks, dark gluons with arbitrary characteristics like masses, couplings, numbers of flavors or numbers of colors (which of course are quite settled for the Standard Model QCD case). In fact, looking at the numbers of flavors and colors of dark QCD in Figure 1, we can see in the white unshaded region a number of models that can exist with a first-order phase transition, as required to form these dark quark nuggets.

Figure 1: The white unshaded region corresponds to dark QCD models which may permit a first-order phase transition and thus the existence of ‘dark quark nuggets’.

As with normal quarks, the distinction between the two phases actually refers to a process known as chiral symmetry breaking. When the temperature of the universe cools to this particular scale, color confinement of quarks occurs around the same time, such that no single-color quark can be observed on its own – only in colorless bound states.

Forming a nugget

As we have briefly mentioned so far, the dark nuggets are formed as the universe undergoes a ‘dark’ phase transition from a phase where the dark color is unconfined to a phase where it is confined. At some critical temperature, due to the nature of first-order phase transitions, bubbles of the new confined phase (full of dark hadrons) begin to nucleate out of the dark quark-gluon plasma. The growth of these bubbles are driven by a difference in pressure, characteristic of the fact that the unconfined and confined phase vacuums states are of different energy. With this emerging bubble wall, the almost massless particles from the dark plasma scatter from the wall containing heavy dark (anti)baryons and hence a large amount of dark baryon number accumulates in this phase. Eventually, as these bubbles merge and coalesce, we would expect local regions of remaining dark quark-gluon plasma, unconfined and stable from collapse due to the Fermi degeneracy pressure (see reference below for more on this). An illustration is shown in Figure 2. Calculations with varying energy scales of confinement estimate their masses are anywhere between $latex 10^{-7}$ to $latex 10^{23}$ grams with radii from $latex 10^{-15}$ to $latex 10^8$ cm and so can truly be classed as macroscopic dark objects!

Figure 2: Dark Quark Nuggets are a phase of unconfined dark quark-gluon plasma kept stable by the balance between Fermi degeneracy pressure and vacuum pressure from the separation between the unconfined and confined phases.

How do we know they could be there? 

There are a number of ways to infer the existence of dark quark nuggets, but two of the main ones are: (i) as a dark matter candidate and (ii) through probes of the dark QCD model that provides them. Cosmologically, the latter can imply the existence of a dark form of radiation which ultimately can lead to effects on the Cosmic Microwave Background Radiation (CMB). In a similar vein, one recent avenue of study today is the production of a steady background of gravitational waves emerging from the existence of a first-order phase transition – one of the key requirements for dark quark nugget formation. More importantly, they can be probed through astrophysical means if they share some coupling (albeit small) with the Standard Model particles. The standard technique of direct detection with Earth-based experiments could be the way to go – but furthermore, there may be the possibility of cosmic ray production from collisions of multiple dark quark nuggets. Among these are a number of other observations over the massive range of nugget sizes and masses shown in Figure 3.

Figure 3: Range of dark quark nugget masses and sizes and their possible detection methods.

To conclude, note that in such a generic framework, a number of well-motivated theories may predict (or in fact have unavoidable) instances of quark nuggets that may serve as interesting dark matter candidates with a lot of fun phenomenology to play with. It is only up to the theorist’s imagination where to go from here!

References and further reading:

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Beauty-full exotic bound states at the LHC

Article: Beauty-full Tetraquarks
Authors: Yang Bai, Sida Lu, and James Osborn
Reference: https://arxiv.org/abs/1612.00012

Good Day Nibblers,

As you probably already know, a single quark in isolation has never been observed in Nature. The Quantum Chromo Dynamics (QCD) strong force prevents this from happening by what is called ‘confinement. This refers to the fact that when quarks are produced in a collision for example, instead of flying off alone each to be detected separately, the strong force very quickly forces them to bind into composite states of two or more quarks called hadrons. These multi-quark bound states were first proposed in 1964 by Murray Gell-Mann as a way to explain observations at the time.

The quarks are bound together by QCD via the exchange of gluons (e.g. see Figure 1) and there is an energy associated with how strongly they are bound together. This binding energy between the quarks contributes to the ‘effective mass’ for the composite states and in fact it is what is largely responsible for the mass of ordinary matter (Footnote 1). Most of the theoretical and experimental progress has been in two or three quark bound states, referred to as mesons and baryons respectively. The most familiar examples of quark bound states are the neutron and proton, both of which are baryons composed of three quarks bound together and form the basis for atomic nuclei.

Figure 1: Bound state of four bottom quarks (blue) held together by the QCD strong force which is transmitted via the exchange of gluons (pink).

Of course four and even more quark bound states are possible and some have been observed, but things get much trickier theoretically in these cases. For four quark bound states (called tetra-quarks) the theoretical progress had been largely limited to the case where at least one of the quarks was a light quark, like an up or a down quark.

The paper highlighted here takes a step towards understanding four quark bound states in the case where all four quarks are heavy. These heavy four body systems are extra tricky because they cannot be decomposed into pairs of two body systems which we could solve much more easily. Instead, one must solve the Schrödinger equation for the full four body system for which approximation methods are needed. The example the current authors focus on is the four bottom quark bound state or 4b state for short (see Figure 1). In this paper they use sophisticated numerical methods to solve the non-relativistic Schrödinger equation for a four-body system bound together by QCD. Specifically they solve for the energy of the ground state, or lowest energy state, of the 4b system. This lowest energy state can effectively be interpreted as the mass of the 4b composite state.

In the ground state the four bottom quarks arrange themselves in such a way that the composite system appears as spin-0 particle. So in effect the authors have computed the mass of a composite spin-0 particle which, as opposed to being an elementary scalar like the Standard Model Higgs boson, is made up of four bottom quarks bound together. They find the ground state energy, and thus the mass of the 4b state, to be about 18.7 GeV. This is a bit below the sum of the masses of the four (elementary) bottom quarks which means the binding energy between the quarks actually lowers the effective mass of the composite system.

The interesting thing about this study is that so far no tetra-quark states composed only of heavy quarks (like the bottom and top quarks) have been discovered at colliders. The prediction of the mass of the 4b resonance is exciting because it means we know where we should look at the LHC and can optimize a search strategy accordingly. This of course increases the prospects of observing a new state of matter when the 4b state decays, which it can potentially do in a number of ways.

For instance it can decay as a spin-0 particle (depicted as $latex \varphi$ in Figure 2) into two bound states of pairs of b quarks, which themselves are referred to as $latex \Upsilon$ mesons. These in turn can be observed in their decays to light Standard Model particles giving many possible signatures at the LHC. As the authors point out, one such signature is the four lepton final state which, as I’ve discussed before, is a very precisely measured channel with small backgrounds. The light mass of the 4b state also allows for it to potentially be produced in large rates at the LHC via the strong force. This sets up the exciting possibility that a new composite state could be discovered at the LHC before long simply by looking at events with four leptons with total energy around 18 – 19 GeV.

Figure 2: Production of a four bottom quark bound state ($latex \varphi$) which then decays to two bound states of bottom quark pairs called $latex \Upsilon$ mesons.

Of course, one could argue this is less exciting than discovering a new elementary particle since if the 4b state is observed it won’t be the discovery of a new particle but instead of yet another manifestation of the QCD strong force. At the end of the day though, it is still an exotic state of nature which has never been observed. Furthermore, these exotic states could be interesting testing grounds for beyond the Standard Model theories which include new forces that communicate with the bottom quark.

We’ll have to wait and see if the QCD strong force can indeed manifest itself as a four bottom quark bound state and if the prediction of its mass made by the authors indeed turns out to be correct. In the meantime, it gives plenty of motivation to experimentalists at the LHC to search for these and other exotic bound states and gives us perhaps some hope for finding physics beyond the Standard Model at the LHC.

Footnote 1: I know what you are thinking, but I thought the Higgs gave mass to matter!? Well yes, but…The Higgs gives mass to the elementary particles of the Standard Model. But most of the matter (that is not dark!) in the universe is not elementary, but instead made up of protons and neutrons which are composed of three quarks bound together. The mass of protons and neutrons is dominated by the binding and kinetic energy of the three quarks systems and therefore it is this that is largely responsible for the mass of normal matter we see in the universe and not the Higgs mechanism.

Other recent studies on heavy quark bound states:

1) https://arxiv.org/abs/1601.02092

2) https://arxiv.org/abs/1605.01647

3) https://arxiv.org/abs/1611.00348

Further reading and video:

1) TASI 2014 has some great introductory lectures and notes on QCD: https://physicslearning.colorado.edu/tasi/tasi_2014/tasi_2014.htm