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Diabatic Dynamical Diquark Model of Hidden-Strangeness Tetraquarks

Shahriyar Jafarzade, Richard F. Lebed

TL;DR

This paper advances the diabatic formulation of the dynamical diquark model to hidden-strangeness tetraquarks, incorporating explicit hadronic thresholds to study multichannel mixing. By constructing a diabatic potential matrix and solving coupled Schrödinger equations, the authors find that the heavy diquark–antidiquark core remains the dominant component across S- and P-wave states, while di-hadron admixtures are generally small. They identify and analyze candidates such as φ(2170), η(2370), X(2300), f2(2340), and X(2600), showing their structures are largely compact with modest threshold mixing and predict additional isoscalar states. The results support a unified interpretation of hidden-strangeness exotics within a compact tetraquark framework, with threshold dynamics playing a secondary but non-negligible role.

Abstract

We generalize our recent analysis of hidden-strangeness tetraquarks within the dynamical diquark model from its adiabatic form (in which each state is described solely by a diquark-antidiquark potential) to its diabatic form (which incorporates effects of di-hadron thresholds upon the states). We tabulate all relevant thresholds and compute the di-hadron content of each predicted state. Our results produce no particular hidden-strange tetraquark candidate whose structure is dominated by di-hadron structure, in contrast to the charm sector, where many exotic states are strongly associated with such thresholds: The hidden-strange states tend to remain compact and less influenced by di-hadron thresholds. Multiple states above 2~GeV with peculiar decay properties, including $φ(2170)$, $f_2(2340)$, and $η(2370)$, continue to serve as excellent hidden-strange tetraquark candidates.

Diabatic Dynamical Diquark Model of Hidden-Strangeness Tetraquarks

TL;DR

This paper advances the diabatic formulation of the dynamical diquark model to hidden-strangeness tetraquarks, incorporating explicit hadronic thresholds to study multichannel mixing. By constructing a diabatic potential matrix and solving coupled Schrödinger equations, the authors find that the heavy diquark–antidiquark core remains the dominant component across S- and P-wave states, while di-hadron admixtures are generally small. They identify and analyze candidates such as φ(2170), η(2370), X(2300), f2(2340), and X(2600), showing their structures are largely compact with modest threshold mixing and predict additional isoscalar states. The results support a unified interpretation of hidden-strangeness exotics within a compact tetraquark framework, with threshold dynamics playing a secondary but non-negligible role.

Abstract

We generalize our recent analysis of hidden-strangeness tetraquarks within the dynamical diquark model from its adiabatic form (in which each state is described solely by a diquark-antidiquark potential) to its diabatic form (which incorporates effects of di-hadron thresholds upon the states). We tabulate all relevant thresholds and compute the di-hadron content of each predicted state. Our results produce no particular hidden-strange tetraquark candidate whose structure is dominated by di-hadron structure, in contrast to the charm sector, where many exotic states are strongly associated with such thresholds: The hidden-strange states tend to remain compact and less influenced by di-hadron thresholds. Multiple states above 2~GeV with peculiar decay properties, including , , and , continue to serve as excellent hidden-strange tetraquark candidates.
Paper Structure (12 sections, 27 equations, 1 figure, 12 tables)

This paper contains 12 sections, 27 equations, 1 figure, 12 tables.

Table of Contents

  1. Introduction
  2. Tetraquark States within the Dynamical Diquark Model
  3. Hadronic Thresholds
  4. Diabatic Description of the Dynamical Diquark Model
  5. Results
  6. $S$-Wave $s\bar{s}q\bar{q}$ States
  7. $P$-Wave $s\bar{s}q\bar{q}$ States
  8. $\bm{\phi(2170)}$ and $\bm{\eta(2370)}$
  9. $S$-Wave $s\bar{s}s\bar{s}$ States
  10. $\bm{X}$(2300) and $\bm{f_{2}(2340)}$
  11. $P$-Wave $s\bar{s}s\bar{s}$ States
  12. Conclusions

Figures (1)

  • Figure 1: Spectrum of $s\bar{s} s\bar{s}$ and $s\bar{s} q\bar{q}$ states of given quantum numbers within the dynamical diquark model, expressed such that the differing di-hadron threshold effects for each state (but not yet including fine-structure effects in the underlying states) produce a spread for each multiplet indicated by a shaded band. These results are compared to the measured values of the isoscalar, light-unflavored meson resonances (masses and decay widths) tabulated by the PDG and by BESIII.