Hydrogen-like structures in the strong interaction

TL;DR

This paper models doubly heavy hadrons as hydrogen-like structures using the Born-Oppenheimer approximation, deriving their mass spectra and predicting potential stable tetraquark states, including the nature of the T_{cc}^+.

Contribution

It introduces a systematic approach to study heavy flavor hadrons as hydrogen-like systems and predicts new stable tetraquark states with specific quantum numbers.

Findings

T_{cc}^+ is likely a compact tetraquark state.

Predicted stable tetraquark states with narrow widths.

Model successfully fits known hadron spectra.

Abstract

Heavy flavor hadrons, especially doubly heavy baryons and doubly heavy tetraquarks, have always received extensive attention in theoretical and experimental research. Given the separation of quark masses $m_Q \gg m_q$ ($Q = c, b$ and $q = u, d, s$), this type of heavy flavor hadrons can be well regarded as hydrogen-like structures in the strong interaction. In the theoretical framework of Born-Oppenheimer approximation, we derive the Schr{\"o}dinger equation for the motion of light quarks in the effective potential field of heavy quarks. Taking proper account of the color-spin hyperfine interaction, we carry out a systematic study on the mass spectra of $S$-wave doubly heavy baryons and doubly heavy tetraquarks. The model parameters required for the calculation are obtained by fitting conventional hadrons. The investigation on the doubly heavy baryon systems indicates the reliability of our theoretical approach. Our calculation results show that the experimentally discovered $T_{cc}^+$ is most likely a compact tetraquark $|(cc)_0^{6}(\bar{u}\bar{d})_1^{\bar{6}}\rangle$ state with quantum numbers $(I,J^P)=(0, 1^+)$. Forthermore, for different quantum number assignments, some stable tetraquark states are found and may be very narrow peaks. The predictions for other heavy flavor hadrons are expected to be confirmed in new theories and future experiments.