Bound state energy and wave function of tetraquark b̄b̄ud from lattice QCD potential

Abstract

In this study, the bound state energy of a four-quark system was analytically calculated as a two heavy–heavy anti-quarks [Formula: see text] and two light–light quarks [Formula: see text]. Tetraquark was assumed to be a bound state of two-body system consisting of two mesons, each containing a light quark and a heavy antiquark. Due to the presence of heavy mesons in the tetraquark, Born–Oppenheimer approximation was used to study its bound states. To assess the bounding energy, Schrödinger equation was solved using lattice QCD [Formula: see text] potential, having expanded the tetraquark potential [Formula: see text] up to 11th term. Binding energy state and wave function, however, were obtained in the scalar [Formula: see text] channel. Graphical results for wave functions obtained versus antiquark–antiquark distance [Formula: see text] confirmed the existence of the tetraquark [Formula: see text]. Analytical bound state energy obtained here was in good agreement with several numerical ones published in the literature, confirming the accuracy of the approach taken here.