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

Abstract

We use the leading order (LO) contact interactions and OPE potentials to investigate the newly observed double-charm state $T_{cc}^{+}$. The $DD\pi$ 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 $DD\pi$ 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 $D\bar{D}\pi$ and $D{\bar{D}}^{\ast }$ 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.

arXiv comment25 pages, 10 figures, 6 tables

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• Trilepton and tetralepton bound and resonant states: the QED counterpart of multiquark states
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• The $\varphi NN,J/\psi NN,{\eta }_{c}NN$ systems based on HAL QCD interactions
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• Analysis of bound and resonant states of doubly heavy tetraquarks with spin $J\le 2$
• Investigating the two-pion exchange of the double charm $D{D}^{\ast }$ chiral interactions and $T_{cc}$
• Bound and Resonant States of Muonic Few-Body Coulomb Systems: Extended Stochastic Variational Approach