Abstract
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 $q{q}^{\ensuremath{'}}\overline{Q}\overline{{Q}^{\ensuremath{'}}}$ and compare the results for the binding energies to results in other works. We also calculate the ground state masses of ${T}_{sc}(ud\overline{s}\overline{c})$ and ${T}_{sb}(ud\overline{s}\overline{b})$ with $(I,S)=(0,1),(0,2)$. We find that ${T}_{bb}(ud\overline{b}\overline{b})$ and $us\overline{b}\overline{b}$, both with $(I,S)=(0,1)$, are stable against the two lowest threshold meson states with binding energies $\ensuremath{-}145$ and $\ensuremath{-}42\text{ }\text{ }\mathrm{MeV}$, respectively. We further find that ${T}_{cb}(ud\overline{c}\overline{b})$ is near the lowest threshold. The spatial sizes for the tetraquarks are also discussed.
Highlights
Since the observation of X(3872) [1] and several exotic hadron candidates that followed, the structure of these particles and other potential flavor exotic configurations have become a central theme of study
We introduce a complete set of threedimensional harmonic oscillator bases with a rescaling factor that can be flexibly used for better convergence relative to the harmonic oscillator bases in Ref. [10], and apply them to constructing the spatial part of the total wave function in a nonrelativistic quark model with hyperfine potential given in Eq (1)
We show the details in constructing the spatial wave function with the complete set of harmonic oscillator bases for the meson as well as the baryon structure
Summary
Since the observation of X(3872) [1] and several exotic hadron candidates that followed, the structure of these particles and other potential flavor exotic configurations have become a central theme of study. [8,10], the harmonic oscillator bases were applied to the construction of the spatial part of the wave function for the baryon structure. Silvestre-Brac and Semay [8] discussed the validity of the harmonic oscillator bases within the light baryons, which are composed only of u, d, and s quarks They extended their work to tetraquarks in Refs. [10], and apply them to constructing the spatial part of the total wave function in a nonrelativistic quark model with hyperfine potential given in Eq (1). We show the details in constructing the spatial wave function with the complete set of harmonic oscillator bases for the meson as well as the baryon structure. In Appendix C, we present the method for constructing the bases for the proton
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