Inspired by the resonance $T_{cc}^{+}(3875)$ recently observed by the LHCb Collaboration, we systematically explore the $S$- and $P$-wave $cc\overline{q}{\overline{q}}^{\prime }$ $(\overline{q},{\overline{q}}^{\prime }=\overline{u},\overline{d},\overline{s})$ systems in a chiral SU(3) quark model. The Hamiltonian contains the kinetic energy, the one-gluon-exchange (OGE) potential, the confinement potential, and the one-boson-exchange (OBE) potential stemming from the coupling of quark and chiral fields. The Schrödinger equation is solved by use of the variational method with the spacial trial wave functions chosen as Gaussian functions. It is found that the lowest state has a mass 3879 MeV, isospin and spin-parity $I{J}^P=01^{+}$, and quark constituent $cc\overline{u}\overline{d}$, in agreement with the experimentally observed $T_{cc}^{+}(3875)$. This state is approximately at the calculated $D{D}^{*}$ threshold and has a root-mean-square radius of about 0.48 fm. These demonstrate that the $T_{cc}^{+}(3875)$ can be accommodated as a stable and compact tetraquark sate in the chiral SU(3) quark model. All the other $S$- and $P$-wave $cc\overline{q}{\overline{q}}^{\prime }$ $(\overline{q},{\overline{q}}^{\prime }=\overline{u},\overline{d},\overline{s})$ states lie about 100 to a few hundreds MeV higher than the corresponding meson-meson thresholds and thus are not suggested to be candidates of stable and compact tetraquark states due to their fall-apart decays to two mesons.

中文翻译：

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手性 SU(3) 夸克模型中 S 波和 P 波 ccq̀q̀′ (q̀,q̀′=ù,d̀,s̀) 系统的光谱

受到共鸣的启发${\mathrm{时间}}_{CC}^{+}（3875）$最近，LHCb 合作组织观察到，我们系统地探索了$S$- 和$磷$-海浪$CC\stackrel{￣}{q}{\stackrel{￣}{q}}^{\prime }$ $（\stackrel{￣}{q},{\stackrel{￣}{q}}^{\prime }=\stackrel{￣}{你},\stackrel{￣}{d},\stackrel{￣}{s}）$手性 SU(3) 夸克模型中的系统。哈密​​顿量包含动能、一胶子交换 (OGE) 势、约束势和源自夸克和手性场耦合的一玻色子交换 (OBE) 势。采用变分法求解薛定谔方程，空间试验波函数选择为高斯函数。发现最低态质量为3879 MeV，同位旋和自旋宇称$我J^{磷}=01^{+}$，和夸克成分$CC\stackrel{￣}{你}\stackrel{￣}{d}$，与实验观察到的一致${\mathrm{时间}}_{CC}^{+}（3875）$。该状态大约在计算的$D{D}^{*}$阈值，均方根半径约为 0.48 fm。这些表明${\mathrm{时间}}_{CC}^{+}（3875）$可以作为稳定且致密的四夸克状态容纳在手性 SU(3) 夸克模型中。所有其他的$S$- 和$磷$-海浪$CC\stackrel{￣}{q}{\stackrel{￣}{q}}^{\prime }$ $（\stackrel{￣}{q},{\stackrel{￣}{q}}^{\prime }=\stackrel{￣}{你},\stackrel{￣}{d},\stackrel{￣}{s}）$这些态比相应的介子-介子阈值高约100到几百MeV，因此不建议作为稳定和致密四夸克态的候选者，因为它们会衰变成两个介子。