Tetraquark nature of the a₀ (980) meson in hadronic D decays

The internal structure of the light scalar meson a₀ (980) is explored in the three-body D decays of D a₀ (980) P P₁P₂P through the intermediate state a₀ (980), where P denotes a pseudoscalar meson. The quasi-two-body D a₀ (980) ^+P decays are governed by the external W-emission diagram in which a₀ (980) ^+ is emitted. The predicted branching fractions in the q q model of a₀ (980) are too small by one to two orders of magnitude compared to experiment as the amplitude is suppressed by the smallness of the a₀ (980) ^+ decay constant, while those for D^+ a₀ (980) ⁰ P and D⁰ a₀ (980) ^-P are usually too large. These discrepancies can be resolved provided that a₀ (980) is a tetraquark state. In this case, there exist two additional T-like topological amplitudes, denoted by T and T which readily account for the discrepancies. An important implication of the tetraquark model is that the Dₛ^+ a₀ (980) ^+⁰+a₀ (980) ⁰^+ decay is not a purely W-annihilation process as in the diquark model of a₀ (980) ; it receives dominant contributions from T newly noticed in this work. Therefore, measurements of (D, Dₛ^+) a₀ (980) P decays lend strong support to the tetraquark picture of a₀ (980).