We produce the first numerical predictions of the dynamical diquark model of multiquark exotic hadrons. Using Born-Oppenheimer potentials calculated numerically on the lattice, we solve coupled and uncoupled systems of Schrödinger equations to obtain mass eigenvalues for multiplets of states that are, at this stage, degenerate in spin and isospin. Assuming reasonable values for these fine-structure splittings, we obtain a series of bands of exotic states with a common parity eigenvalue that agree well with the experimentally observed charmoniumlike states, and we predict a number of other unobserved states. In particular, the most suitable fit to known pentaquark states predicts states below the charmonium-plus-nucleon threshold. Finally, we examine the strictest form of Born-Oppenheimer decay selection rules for exotics and, finding them to fail badly, we propose a resolution by relaxing the constraint that exotics must occur as heavy-quark spin-symmetry eigenstates.

We incorporate fine-structure corrections into the dynamical diquark model of multiquark exotic hadrons. These improvements include effects due to finite diquark size, spin-spin couplings within the diquarks, and most significantly, isospin-dependent couplings in the form of pionlike exchanges expected to occur between the light quarks within the diquarks. Using a simplified two-parameter interaction Hamiltonian, we obtain fits in which the isoscalar J P C = 1 ++ state-identified as the X(3872)-appears naturally as the lightest exotic (including all states that are predicted by the model but have not yet been observed), while the Zc(3900) and Zc(4020) decay predominantly to J/ψ and ηc, respectively, in accord with experiment. We explore implications of this model for the excited tetraquark multiplets and the pentaquarks.

We study the fine structure in the spectrum of known and predicted negative-parity hidden-charm exotic meson states, which comprise the lowest P -wave multiplet in the dynamical diquark model. Starting with a form previously shown to successfully describe the S-wave states, we develop a 5parameter Hamiltonian that includes spin-orbit and tensor terms. After discussing the experimental status of the observed J P C = 1 −− states Y with respect to masses and decay modes (classified by eigenvalues of heavy-quark spin), we note a number of inconsistencies between measurements from different experiments that complicate a unique determination of the spectrum. Outlining a variety of scenarios for interpreting the Y data, we perform fits to each one, obtaining results that demonstrate differing possibilities for the P -wave spectra. Choosing one of these fits for illustration, we predict masses for all 28 isomultiplets in this 1P multiplet, compare the results to tantalizing hints in the data, and discuss the rich discovery potential for new states.

We develop the spectroscopy of cccc and other all-heavy tetraquark states in the dynamical diquark model. In the most minimal form of the model (e.g., each diquark appears only in the color-triplet combination; the nonorbital spin couplings connect only quarks within each diquark), the spectroscopy is extremely simple. Namely, the S-wave multiplets contain precisely three degenerate states (0 þþ , 1 þ− , 2 þþ) and the seven P-wave states satisfy an equal-spacing rule when the tensor coupling is negligible. When comparing numerically to the recent LHCb results, we find the best interpretation is assigning Xð6900Þ to the 2S multiplet, while a lower state suggested at about 6740 MeV fits well with the members of the 1P multiplet. We also predict the location of other multiplets (1S, 1D, etc.) and discuss the significance of the cc open-flavor threshold.

The observation by BESIII and LHCb of states with hidden charm and open strangeness (ccqs) presents new opportunities for the development of a global model of heavy-quark exotics. Here we extend the dynamical diquark model to encompass such states, using the same values of Hamiltonian parameters previously obtained from the nonstrange and hidden-strange sectors. The large mass splitting between Zcs(4000) and Zcs(4220) suggests substantial SU(3) flavor mixing between all J P = 1 + states, while their average mass compared to that of other sectors offers a direct probe of flavor octet-singlet mixing among exotics. We also explore the inclusion of η-like exchanges within the states, and find their effects to be quite limited. In addition, using the same diquark-mass parameters, we find Pc(4312) and Pcs(4459) to fit well as corresponding nonstrange and openstrange pentaquarks.