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

Abstract

In this work, we investigate the spectroscopy and decay properties of neutral tetraquark systems modeled as loosely bound meson − antimeson pairs (e.g., DD¯ ∗, D∗D¯ ∗, BB¯ ∗, and 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 coupledchannel effects. For representative channels, we obtain EB ≈ 45 MeV for DD¯ ∗ with J PC = 1++, EB ≈ 60 MeV for D∗D¯ ∗ with 0++, and EB ≈ 35–50 MeV in the BB¯ ∗ and B∗B¯ ∗ sectors, yielding masses within a few MeV of known near-threshold resonances. Width estimates based on overlap integrals tend to exceed the experimentally narrow values, reflecting the absence of coupled-channel dynamics and final-state interactions. Overall, the results delineate the applicability of the momentum–helicity formalism to nearthreshold molecular states and motivate extensions incorporating short-range contact terms and channel coupling.