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 DD * molecule with J P = 1 + in the framework of the one-boson-exchange potential model. The isospin breaking effect and S − D wave coupling are taken into account carefully. We adopt the complex scaling method (CSM) to study the DD * system and obtain a quasibound state corresponding to the T + cc . Its binding energy relative to the D 0 D * + and width are −354 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 DD * system. As a by-product, we study the X(3872) as a (D D * − D * D)/ √ 2 molecule with J P C = 1 ++ . We also find a quasibound state corresponding to the X(3872). Its binding energy relative to the D 0 D * 0 threshold and width are −111 keV and 26 keV respectively. The S−wave (D 0 D * 0 − D * 0 D0 )/ √ 2 component dominates this state with the probability of 92.7%.