Doubly heavy tetraquarks, qq'(QQ)over-bar', in a nonrelativistic quark model with a complete set of harmonic oscillator bases

We improve our previous variational method based nonrelativistic quark model by introducing a complete set of three-dimensional harmonic oscillator bases as the spatial part of the total wave function. To assess the validity of our approach, we compare the binding energy thus calculated with the exact value for the hydrogen model. After fitting to the masses of the ground state hadrons, we apply our new method to analyzing the doubly heavy tetraquark states qq'(Q) over bar(Q) over bar' and compare the results for the binding energies to results in other works. We also calculate the ground state masses of T-sc(ud (s) over bar(c) over bar) T-sb(ud (s) over bar(b) over bar) with (I, S) = (0, 1), (0, 2). We find that T-bb(ud (b) over bar(b) over bar and us (b) over bar(b) over bar, both with (I, S) = (0, 1), are stable against the two lowest threshold meson states with binding energies -145 and -42 MeV, respectively. We further find that T-cb(ud (c) over bar(b) over bar) is near the lowest threshold. The spatial sizes for the tetraquarks are also discussed.

Automated summary

The study improves the nonrelativistic quark model by introducing a complete set of three-dimensional harmonic oscillator bases and validates the method by comparing calculated binding energies with exact values for the hydrogen model. The new method is applied to analyze double heavy tetraquark states and calculate ground state masses, with certain states found to be stable against the two lowest threshold meson states. The study also discusses the spatial sizes of the tetraquarks.