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 T̄ and T which readily account for the discrepancies. An important implication of the tetraquark model is that the Dₛ⁺→ a₀(980)⁺π⁰+a₀(980)⁰π⁺ decay is not a purely W-annihilation process as in the diquark model of a₀(980); it receives dominant contributions from T̄ newly noticed in this work. Therefore, measurements of (D,Dₛ⁺)→ a₀(980)P decays lend strong support to the tetraquark picture of a₀(980).