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 assumed to occur between the light quarks within the diquarks. Using a simplified two-parameter interaction Hamiltonian, we obtain fits in which the isoscalar $J^{PC} = 1^{++}$ 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 $Z_c(3900)$ and $Z_c(4020)$ decay predominantly to $J/psi$ and $eta_c$, respectively, in accord with experiment. We explore implications of this model for the excited tetraquark multiplets and the pentaquarks.
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