Equivalence among color-singlet, color-octet, and diquark structures in a chiral quark model

Since the quark model was put forward, theoretical researchers have always attached great importance to the study of hidden color channels (including color octets and diquark structure). Because of the influence of color van der Waals forces, the hidden color channel itself has strong attraction, which provides a dynamic mechanism for the formation of a resonance state or bound state. In this paper, taking the $T_{cc}$ system as an example, under the framework of the Gaussian expansion method, a set of relatively complete color singlets (that is, the ground state of the color singlet plus its corresponding higher-order component) is used to replace the contribution of the color octet. Similarly, we endeavor to replace the diquark structure with a relatively complete set of molecular states, encompassing both the ground state and excited states. Our results demonstrate that the color-octet structure can be effectively replaced by a set of relatively complete color-singlet bases, while the diquark structure cannot be entirely substituted by an equivalently comprehensive set of molecular state bases.