Tetraquark bound states and resonances in a unitary microscopic quark model: A case study of bound states of two light quarks and two heavy antiquarks

Abstract

We address $qq\overline{Q}\overline{Q}$ exotic tetraquark bound states and resonances with a fully unitarized and microscopic quark model. We propose a triple string flip-flop potential, inspired by lattice QCD tetraquark static potentials and flux tubes, combining meson-meson and double Y potentials. Our model includes the color excited potential, but neglects the spin-tensor potentials, as well as all the other relativistic effects. To search for bound states and resonances, we first solve the two-body mesonic problem. Then we develop fully unitary techniques to address the four-body tetraquark problem. We fold the four-body Schr\odinger equation with the mesonic wave functions, transforming it into a two-body meson-meson problem with nonlocal potentials. We find bound states for some quark masses, including the one reported in lattice QCD. Moreover, we also find resonances and calculate their masses and widths, by computing the $T$ matrix and finding its pole positions in the complex energy plane, for some quantum numbers. However, a detailed analysis of the quantum numbers where binding exists shows a discrepancy with recent lattice QCD results for the $ll\overline{b}\overline{b}$ tetraquark bound states. We conclude that the string flip-flop models need further improvement.