Investigation of heavy tetraquark states as di-meson molecules by solving the bethe–salpeter equation

In this paper, we report a systematic investigation of the spectroscopy and structure of heavy tetraquark states by adopting a scheme that interposes a QCD-motivated meson-meson potential and Bethe–Salpeter Equation (BSE) formalism. Heavy-mesonic interaction is described by an effective potential that has a confining linear term regularized by a super-Gaussian cutoff and is subsequently moved into momentum space for numerical solution. Solution of the BSE is accomplished by employing advanced numerical methods, such as adaptive Gauss–Kronrod quadrature for evaluating integrals and logarithmically discretized momentum space for resolving low-momentum regions more efficiently, and discretization by the Nyström method, and inverse power iteration for determining bound states. By applying this scheme to examples like [Formula: see text]-[Formula: see text] and other states of quark content [Formula: see text] and [Formula: see text], we calculate Root-Mean-Square (RMS) radii and binding energies. We find that our findings, contrasted with LHCb, Belle and BESIII experimental and other theoretical data suggest a meson-meson molecular structure predominantly for those states, with appreciable spatial extents ([Formula: see text]–[Formula: see text] [Formula: see text]fm) much larger than those for their individual mesonic constituents. This paper elucidates the molecular character of some exotic hadrons and offers a theoretical device for charting the multiquark spectrum.