Searching for Stable States in the TDD1 Systems Based on a Chiral Quark Model

Experimentally, the \(1⁺\) state \(X(3872)\) was first discovered, and subsequently, its partner state \(Y(4260)\), with the same quark content \((cq̄qc̄) \) and quantum number \(1⁻\) was also observed. Inspired by this pattern, we systematically investigate the newly discovered \(1⁺\) state \(Tcc\) and its possible \(1⁻\) partner, the \(T_{DD₁}\) system with the same quark content \((cq̄cq̄)\). Within the framework of the chiral quark model, we perform a comprehensive study of the bound and resonance states of \(TDD_1\) using the Gaussian expansion method (GEM). Two quark configurations, the molecular structure and the diquark structure, are considered in our calculations. Our results indicate the existence of a shallow bound state dominated by the \(DD_1*\) channel, which is analogous to the experimentally observed \(Tcc\), as well as two compact resonant states with narrow widths around 4.5 GeV. To avoid the influence of model parameters on the results, we additionally fitted a new set of parameters and obtained consistent conclusions. According to our calculation results, although the color-octet and diquark configurations have relatively high energies, the channel-coupling effects induced by them play a crucial role in the formation of these stable states. We strongly encourage experimental efforts to search for the stable states predicted in the \(TDD_1\) system.