$T_{cc}^+$ and $X(3872)$ with the complex scaling method and $DD(\bar{D})π$ three-body effect

作者：Zi-Yang Lin, Jianbo Cheng, Shi-Lin Zhu · 发表于：arXiv (Cornell University) · 年份：2022 · DOI：10.48550/arxiv.2205.14628 · 被引用次数：5 · 研究领域：Quantum Chromodynamics and Particle Interactions、Nuclear physics research studies、Atomic and Molecular Physics

We use the leading order (LO) contact interactions and OPE potentials to investigate the newly observed double-charm state $T_{cc}^+$. The $DDπ$ three-body effect is important in this system since the intermediate states can go on shell. We keep the dependence of the pion propagators on the center-of-mass energy, which results in a unitary cut of the OPE potential at the $DDπ$ three-body threshold. By solving the complex scaled Schrödinger equation, we find a pole corresponding to the $T_{cc}^+$ on the physical Riemann sheet. Its width is around 80 keV and nearly independent of the choice of the cutoff. Assuming the $D\bar{D}π$ and $D\bar{D}^*$ channels as the main decay channels, we apply the similar calculations to the $X(3872)$, and find its width is even smaller. Besides, the isospin breaking effect is significant for the $X(3872)$ while its impact on the $T_{cc}^+$ is relatively small.