Spectroscopy and stability of meson–antimeson tetraquarks using a 3D pion-exchange potential

In this work, we investigate the spectroscopy and decay properties of neutral tetraquark systems modeled as loosely bound meson-antimeson meson - antimeson pairs (e.g., DD̄^* D D ¯ ∗ , D^*D̄^* D ∗ D ¯ ∗ , BB̄^* B B ¯ ∗ , and B^*B̄^* B ∗ B ¯ ∗ ). All our calculations are strictly performed for the color-neutral meson–antimeson configurations. The homogeneous Lippmann–Schwinger equation is solved using a one-pion-exchange potential (OPEP) that incorporates explicit spin-dependent components. The configuration-space kernel is Fourier transformed and projected into the helicity basis, enabling a transparent treatment of spin structures. We focus on PV and VV systems near open-charm and open-bottom thresholds and extract binding energies, wave functions, and partial decay widths within a single-channel approximation that neglects coupled-channel effects. For representative channels, we obtain EB ≈ 45~MeV E B ≈ 45 MeV for DD̄^* D D ¯ ∗ with JPC=1⁺⁺ J PC = 1 + + , EB ≈ 60~MeV E B ≈ 60 MeV