Double-charm tetraquark under the complex scaling method

Abstract

The LHCb Collaboration discovered a double-charm tetraquark ${T}_{cc}^{+}$ with a very small width. We investigate the ${T}_{cc}^{+}$ as a $D{D}^{*}$ molecule with ${J}^{P}={1}^{+}$ in the framework of the one-boson-exchange potential model. The isospin breaking effect and $S\ensuremath{-}D$ wave coupling are taken into account carefully. We adopt the complex scaling method to study the $D{D}^{*}$ system and obtain a quasibound state corresponding to the ${T}_{cc}^{+}$. Its binding energy relative to the ${D}^{0}{D}^{*+}$ and width are $\ensuremath{-}354\text{ }\text{ }\mathrm{keV}$ and 61 keV respectively. The isospin breaking effect is found to be enormous, and the $S$-wave ${D}^{0}{D}^{*+}$ and ${D}^{+}{D}^{*0}$ components give dominant contributions with the probabilities of 72.1% and 27.1% respectively. In addition, we do not find any resonances in the $D{D}^{*}$ system. As a by-product, we study the $X(3872)$ as a $(D{\overline{D}}^{*}\ensuremath{-}{D}^{*}\overline{D})/\sqrt{2}$ molecule with ${J}^{PC}={1}^{++}$. We also find a quasibound state corresponding to the $X(3872)$. Its binding energy relative to the ${D}^{0}{\overline{D}}^{*0}$ threshold and width are $\ensuremath{-}111\text{ }\text{ }\mathrm{keV}$ and 26 keV, respectively. The $S$-wave $({D}^{0}{\overline{D}}^{*0}\ensuremath{-}{D}^{*0}{\overline{D}}^{0})/\sqrt{2}$ component dominates this state with the probability of 92.7%.