Tetraquark bound states in constituent quark models: Benchmark test calculations

We investigate the tetraquark bound states that are manifestly exotic using three distinct few-body methods; Gaussian expansion method (GEM), resonating group method (RGM), and diffusion Monte Carlo (DMC). We refer to manifestly exotic states that do not involve a mixture with the conventional mesons through the creation and annihilation of nn̄, where $n=u$, d. Our calculations are conducted with two types of quark models; the pure constituent quark model featuring one-gluon-exchange interactions and confinement interactions, and the chiral constituent quark model, supplemented by extra one-boson-exchange interactions. This study represents a comprehensive benchmark test of various few-body methods and quark models. Our findings reveal the superiority of GEM over RGM and DMC methods based on present implements for the tetraquark bound states. Additionally, we observe a tendency for the chiral quark model to overestimate the binding energies. We systematically explore the fully, triply, doubly, and singly heavy tetraquark states with JP=0⁺,1⁺,2⁺, encompassing over 150 states in total. We successfully identify several bound states, including [ccn̄n̄]_JP=1⁺I=0, [bbn̄n̄]_JP=1⁺I=0, [bcn̄n̄]_JP=0⁺,1⁺,2⁺I=0, [bsn̄n̄]_JP=0⁺,1⁺I=0, [csn̄n̄]_JP=0⁺I=0, and [bbn̄s̄]_JP=1⁺, all found to be bound states below the dimeson thresholds.