The dynamical diquark model: fine structure and isospin

Abstract

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.

Spectrum of the $$uudc \bar{c}$$ hidden charm pentaquark with an SU(4) flavor-spin hyperfine interaction

“…However, some support in favor of a flavor-spin interaction in exotics is given by Ref. [37]. Although restricted to tetraquarks described in a diquark basis, it has been shown that the mass difference observed in some charmed tetraquarks can be explained by an isospin dependent interaction, which is an SU(2) flavor-spin interaction.…”

Spectrum of p -wave hidden-charm exotic mesons in the diquark model

“…While it is possible to fit the 3 constants M 0 , κ qQ , V 0 using nothing but the 3 PDG-averaged mass eigenvalues of X(3872), Z c (3900), and Z c (4020), and indeed such a restrictive fit gives results virtually identical to those in Ref. [24]:…”

“…We inferred in Ref. [24] that the isospin-dependent couplings, at least in the S wave, appear to see only the light quarks, and do not view the diquarks as pointlike constituents. Indeed, one of the major thrusts of Ref.…”

“…Meanwhile, Ref. [24] presents an analysis of mass splittings among the 12 hidden-charm 1S states (both known and predicted), and shows that the X(3872) can emerge naturally as the lightest member of the multiplet. Building upon this analysis, the current paper focuses upon the 1P states, all of which carry P = −.…”

“…In fact, by minimally extending the Hamiltonian of Ref. [24] to include spin-orbit and tensor terms, we provide a large number of testable predictions for the unknown sectors of the multiplet, and with this explicit Hamiltonian in hand, one can adjust detailed fits easily to incorporate any future experimental modifications to the known spectrum. A study of the P -wave δ-δ states using QCD sum rules appears in Refs.…”