In the final day of the ICNFP 2022 conference in Kolympari (Greece), we could listen to an enlightening presentation by Prof. Marek Karliner (Tel Aviv University), who is an absolute authority on the matter of the theory of hadron spectroscopy. 
Below is a unrefined transcript of his presentation, wherein I hope I did not include too many typing mistakes (typically omissions, as my speed at the keyboard is not as good as it used to be). As a warning, the text is quite technical and not suitable for non-physicists. The gist of it, if you are curious but can't delve into it, is that we are discovering a lot of interesting new structure in particle made of quarks - a whole underlying level below the Mendeleev table of elements, more fundamental but not less rich of interesting twists. E.g., these new exotic hadrons may store very large binding energy - way larger than that we have exploited since the 1940ies for atomic warfare as well as for nuclear plants. Probably this will remain forever an academic observation only, but one never knows!

In this presentation we will see what we understand in terms of theory, regarding multi-quark states. 
Quarks are fundamental building blocks of hadrons, or to paraphrase Orwell, "All quarks are equal, but heavy quarks are more equal than others", in the sense that they are easier to analyze in experiment and theory. 

In recent years we have seen several discoveries. LHCb found a doubly charmed pentaquark; there is a robust theoretical prediction for a stable (B-B-ubar-dbar) tetraquark; and there is a large number of so-called hadronic molecules, the most conspicuous is the pentaquark discovered by LHCb and other states discovered by Belle and BESIII. We are, in other words, discovering a new layer of the periodic table.

We can summarize the situation by saying that there is by now quite robust experimental evidence for multiquark states, exotic hadrons, non-qqbar' mesons [e.g. (Q-Qbar-q-qbar), (Q-Q-qbar-qbar) states], and non-qq'q'' baryons [e.g. of the kind (Qbar-Q-q-q'-q'')].

Two questiosn are key: which additional exotics should we expect? And how are quarks organized inside them? For some of the objects detected there is a clear answer, not for all.

In September last year LHCb discovered the exotic narrow doubly charmed tetraquark. It is the first one which has two heavy quarks inside it instead of a heavy quark and a heavy antiquark. They saw a narrow strcture decaying into two D0 mesons and a positive pion. This particle lays below the threshold mass. There is a question of whether these discoveries are backed by theoretical predictions. In this case, yes!

The new tetraquark is extremely narrow, with a width of less than half a MeV. This could be of about 50 keV. The question is, is this a four-quark bag or a molecule of D0 mesons? The partial answer to the question is provided by predictions. There were many predictions for it, and our own from 2017 was based on the assumption of a tightly bound tetraquark. But in retrospect it is possible that it is a mixture, as it is close to threshold and its quantum numbers are the same of those of a mixture.

Tightly bound tetraquarks are simpler than other hadrons, as they have weak spin interactions and heavy quarks inside them are almost static. This is key to accurate predictions of heavy b-quark exotics.

In 2014 we applied the theoretical technique to doubly heavy baryons like (ccu), and later to tetraquarks. In 2014 the prediction for (ccq), a state, was 3627+-12 MeV, later found as 3621.6+-0.4 MeV by LHCb. This gave us confidence to extend the technique to exotics. We predicted the lifetime of that particle in concordance to observed value. For the mass, the prediction relies on the amount of interaction between the two charm quarks. For that we had to make an assumption, rather bold at the time, that the interaction is exactly equal to half of that of a charm and anticharm, which we know from experiment. We did not know how good that assumption could be, despite it being motivated by past experience. A posteriori this seems very well satisfied. The binding of two charm quarks is rather large, providing a decrease of the mass of the bound state by 130 MeV. 

The same toolbox now predicts a stable, deeply bound (B-B-ubar-dbar) tetraquark, which is 215 MeV below the BB* threshold. This would be the first manifestly exotic stable baryon.

Everybody now agrees that this particular tetraquark is bound and the strong interaction has no open decay channels, so it is a stable particle just like the lambda baryon from the point of view of QCD. It would be extremely interesting when it is eventually discovered, to see what the mass is. Our prediction is 10389+-12 MeV.

In a sense, the doubly heavy tetraquarks are very similar to doubly heavy baruons. A baryon (C-C-q) is like a (C-C-ubar-dbar) tetraquark, because of fermi statistics: a colour antitriplet CC binds to a colour triplet q. In the tetraquark, a (ubar-dbar) combination is a colour triplet. Then you have a spin-1 diquark, a spin-zero diquark, and they bind into a 1^+ particle. The spin of the particle is most likely 1 and the parity is positive. So it would be interesting to see what happens with the double B tetraquark.

As quarks get heavier, the bounds in heavy quarks becomes stronger. The distance to threshold is essentially zero for double charm, and it gets significant below threshold for (b-c), and it is deep for double bottom.

CMS recently saw a  good quality signal for the X(3872), which is very likely a tetraquark, in lead-lead collisions. This gives optimism that we may use heavy ion collisions to see more exotic tetraquarks such as the . The cross sections in heavy ion collisions is much larger, but backgrounds are larger. If it can be done for the X(3872), maybe it can be done for others.

To summarize, the first manifestly exotic stable hadron is T(B-Bubar-dbar). We can study exotich hadrons that are hadronic molecules. There are five states that are particularly interesting, and they share the characteristic of being close to the two meson threshold, they decay into quarkonia and pions, there is a very large phase space available for this decay, yet despite this they have a ridiculously small width. E.g. the Z_b(10650) has a large 1 GeV of phase space but it has a width of 2 MeV. This is a very strong hint that the particle is a hadronic molecule. Such states decay into two mesons more often than to quarkonium, by a factor 100.

The lightest hadronic molecule made of a baryon and a meson was predicted and then discovered just a few weeks afterwards. Later LHCb found three such states, close to threshold. Stability was understood because in order to decay, the charm and anticharm in the two hadrons must overlap their wavefunctions; but they are far away, so the probability for creating a bound quarkonium is small.

In summary, there is a narrow (C-C-ubar-dbar) state discovered by LHCb; it could be observed in heavy ions. It was found exactly where we predicted it to be. There should be more such objects. This leads to predictions that there exists a doubly bottom tetraquark that should be accessible at LHCb. Narrow exotics seem to be hadronic molecules, and quite a few have been seen. There are some additional states; e.g., one (C-Cbar-C-Cbar) state decaying into two J/Psi. So, there is new exciting spectroscopy and it is a nice example of theory and experiment collaborating tightly, which in our field is a luxury these days.