Investigation on the stabilities of doubly heavy tetraquark states

In our recent work [S. Noh and W. Park, Nonrelativistic quark model analysis of 𝑇𝑐⁢𝑐, Phys. Rev. D 108, 014004 (2023)], the mass and binding energy of 𝑇𝑐⁢𝑐 are found to be 3873 MeV and −2  MeV, respectively, which align with the observations reported at LHCb [R. Aaij (LHCb Collaboration), Observation of an exotic narrow doubly charmed tetraquark, Nat. Phys. 18, 751 (2022)]. Based on our latest quark model approach, we extend our search for other potentially stable configurations of doubly heavy tetraquarks using our nonrelativistic quark model described in Noh and Park, [Nonrelativistic quark model analysis of 𝑇𝑐⁢𝑐, Phys. Rev. D 108, 014004 (2023)]. Our numerical calculations indicate that the ¯𝑢⁢¯𝑠⁢𝑐⁢𝑏 configuration is deeply bound. However, the ¯𝑢⁢¯𝑑⁢𝑐⁢𝑏 configuration with the isospin symmetry in the light quark sector is relatively less bound. In this study, we emphasize a compulsory aspect for requiring a complete set of three-dimensional harmonic oscillator bases through the discussion of the ¯𝑢⁢¯𝑠⁢𝑐⁢𝑏 configuration and investigate the essential differences between the ¯𝑢⁢¯𝑠⁢𝑐⁢𝑏 and ¯𝑢⁢¯𝑑⁢𝑐⁢𝑏 configurations.