Beauty-full exotic bound states at the LHC

Article: Beauty-full Tetraquarks
Authors: Yang Bai, Sida Lu, and James Osborn

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 \varphi in Figure 2) into two bound states of pairs of b quarks, which themselves are referred to as \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 (\varphi) which then decays to two bound states of bottom quark pairs called \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:




Further reading and video:

1) TASI 2014 has some great introductory lectures and notes on QCD:

A Quark Gluon Plasma Primer

Artist's rendition of a proton breaking down into free quarks after a critical temperature. Image credit Lawrence Berkeley National Laboratory.
Figure 1: Artist’s rendition of a proton breaking down into free quarks after a critical temperature. Image credit Lawrence Berkeley National Laboratory.

Quark gluon plasma, affectionately known as QGP or “quark soup”, is a big deal, attracting attention from particle, nuclear, and astrophysicists alike. In fact, scrolling through past ParticleBites, I was amazed to see that it hadn’t been covered yet! So consider this a QGP primer of sorts, including what exactly is predicted, why it matters, and what the landscape looks like in current experiments.

To understand why quark gluon plasma is important, we first have to talk about quarks themselves, and the laws that explain how they interact, otherwise known as quantum chromodynamics. In our observable universe, quarks are needy little socialites who can’t bear to exist by themselves. We know them as constituent particles in hadronic color-neutral matter, where the individual color charge of a single quark is either cancelled by its anticolor (as in mesons) or by two other differently colored quarks (as with baryons). But theory predicts that at a high enough temperature and density, the quarks can rip free of the strong force that binds them and become deconfined. This resulting matter is thus composed entirely of free quarks and gluons, and we expect it to behave as an almost perfect fluid. Physicists believe that in the first few fleeting moments after the Big Bang, all matter was in this state due to the extremely high temperatures. In this way, understanding QGP and how particles behave at the highest possible temperatures will give us a new insight into the creation and evolution of the universe.

The history of experiment with QGP begins in the 80s at CERN with the Super Proton Synchrotron (which is now used as the final injector into the LHC.) Two decades into the experiment, CERN announced in 2000 that it had evidence for a ‘new state of matter’; see Further Reading #3 for more information. Since then, the LHC and the Brookhaven Relativistic Heavy Ion Collider (RHIC) have taken up the search, colliding heavy lead or gold ions and producing temperatures on the order of trillions of Kelvin. Since then, both experiments have released results claiming to have produced QGP; see Figure 2 for a phase diagram that shows where QGP lives in experimental space.

Phases of QCD and the energy scales probed by experiment.
Phases of QCD and the energy scales probed by experiment.

All this being said, the QGP story is not over just yet. Physicists still want a better understanding of how this new matter state behaves; evidence seems to indicate that it acts almost like a perfect fluid (but when has “almost” ever satisfied a physicist?) Furthermore, experiments are searching to know more about how QGP transitions into a regular hadronic state of matter, as shown in the phase diagram. These questions draw in some other kinds of physics, including statistical mechanics, to examine how bubble formation or ‘cavitation’ occurs when chemical potential or pressure is altered during QGP evolution (see Further Reading 5). In this sense, observation of a QGP-like state is just the beginning, and heavy ion collision experiments will surely be releasing new results in the future.


Further Reading:

  1. “The Quark Gluon Plasma: A Short Introduction”, arXiv hep-ph 1101.3937
  2. “Evidence for a New State of Matter”, CERN press release
  3. “Hot stuff: CERN physicists create record-breaking subatomic soup”, Nature blog
  4. “The QGP Discovered at RHIC”, arXiv nucl-th 0403.032
  5. “Cavitation in a quark gluon plasma with finite chemical potential and several transport coefficients”, arXiv hep-ph 1505.06335