Simple spectrum of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>c</mml:mi><mml:mover accent="true"><mml:mrow><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="false">¯</mml:mo></mml:mrow></mml:mover><mml:mi>c</mml:mi><mml:mover accent="true"><mml:mrow><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="false">¯</mml:mo></mml:mrow></mml:mover></mml:mrow></mml:math> states in the dynamical diquark model
Jesse Giron, Richard F. Lebed
Abstract
We develop the spectroscopy of $c\overline{c}c\overline{c}$ 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 nonorbital spin couplings connect only quarks within each diquark), the spectroscopy is extremely simple. Namely, the $S$-wave multiplets contain precisely three degenerate states (${0}^{++}$, ${1}^{+\ensuremath{-}}$, ${2}^{++}$) 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 $X(6900)$ 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.