A Study of $T_{cc}(3875)^+$ Nature : Compact v.s. Molecule

Abstract

A central question in exotic-hadron physics is their internal structure whether these states are loosely bound hadronic molecules or compact multiquark configurations. To shed light on this issue, we develop a model that incorporates mixing between hadronic-molecular and compact multiquark components. We then apply this framework to the specific case of the $T_{cc}(3875)^+$ and analyze the peak structure in the $D^0D^0π^+$ invariant-mass spectrum reported by LHCb. We find that a scenario based on a predominantly compact tetraquark provides the best fitted solution which can explain the $T_{cc}(3875)^+$. We also find that the model admits two more solutions of comparable quality, both of which imply that the $T_{cc}(3875)^+$ is a molecular state: (1) the $T_{cc}(3875)^+$ is a $D^{*+}D^0$ molecule and there is a $D^{*0}D^+$ molecular state in addition; (2) the $T_{cc}(3875)^+$ is a $D^{*0}D^+$ molecule and an aditional $D^{*+}D^0$ molecular state is found below $D^0D^0π^+$ threshold. These molecular states are not simple $I = 0$ states, but mixtures of $I = 0$ and $I = 1$ states. We show that all three scenarios are also consistent with the experimentally observed near-threshold $D^0D^0$ and $D^0D^+$ invariant-mass distributions.

Figures (3)

• Figure 1: Fitted results of $D^0D^0\pi^+$ invariant mass spectrum of each three scenarios: Mol.+Compact (solid, orange), Mol. 1 (dotted, blue), and Mol. 2 (dashed, red) with the parameters in Table \ref{['tbl:Best Fitted parameters']}. Experimental 200 keV binned $D^0D^0\pi^+$ data are shown by black points with statistical error bars. Vertical gray dashed lines mark the $D^{*+}D^0$ and $D^{*0}D^+$ thresholds.
• Figure 2: The binding energies obtained in each scenario. Red horizontal bars indicate the pole locations. Two poles are obtained in Mol. 1 and Mol. 2, while only one single near-threshold pole is found in the Mol.+Compact scenario. Blue arrows annotate the binding energies measured from the threshold of the dominant channel assigned analyzing the residue of the scattering amplitude. For the M+C scenario, the value $-954\,$ keV is measured from the $m_{4q}$. The values shown in parentheses are the differences from the $D^{*+}D^0$ threshold. The orange band shows the LHCb determination of mass of $T_{cc}^+$.
• Figure 3: Expected $DD$ invariant-mass distributions derived from the $D^0D^0\pi^+$ analysis. Left:$T_{cc}^+\!\to D^0D^0\pi^+$. Right:$T_{cc}^+\!\to D^0D^+\pi^0$ predicted from the $D^0D^+\pi^0$ amplitude computed with the same parameter set that was fitted to the 200 keV-binned $D^0D^0\pi^+$ spectrum.