The Simple Spectrum of $c\bar c c\bar c$ States in the Dynamical Diquark Model

TL;DR

This paper develops a simple, minimal dynamical diquark model to describe the spectrum of all-heavy tetraquark states, matching recent LHCb observations and predicting additional multiplets and their properties.

Contribution

It introduces a minimal dynamical diquark model for all-heavy tetraquarks, providing a straightforward spectrum with specific multiplet structures and mass predictions.

Findings

Identifies $X(6900)$ as a $2S$ multiplet candidate.

Associates a state at 6740 MeV with the $1P$ multiplet.

Predicts locations of other multiplets like $1S$ and $1D$.

Abstract

We develop the spectroscopy of $c\bar c c\bar c$ 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 non-orbital spin couplings connect only quarks within each diquark), the spectroscopy is extremely simple. Namely, the $S$-wave multiplets contain precisely 3 degenerate states ($0^{++}$, $1^{+-}$, $2^{++}$) and the 7 $P$-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 $X(6900)$ 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.