Category: quark bound states

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.

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 in Figure 2) into two bound states of pairs of b quarks, which themselves are referred to as  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.

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