Tetraquark nature of the $a_0(980)$ meson in hadronic $D$ decays

Abstract

The internal structure of the light scalar meson $a_0(980)$ is explored in the three-body $D$ decays of $D\to a_0(980)P\to P_1{P}_{2}P$ through the intermediate state $a_0(980)$, where $P$ denotes a pseudoscalar meson. The quasi-two-body $D\to a_0(980{)}^{+}P$ decays are governed by the external $W$-emission diagram in which $a_0(980{)}^{+}$ is emitted. The predicted branching fractions in the $q\bar{q}$ model of $a_0(980)$ are too small by one to two orders of magnitude compared to experiment as the amplitude is suppressed by the smallness of the $a_0(980{)}^{+}$ decay constant, while those for $D^{+}\to a_0(980{)}^{0}P$ and $D^0\to a_0(980{)}^{-}P$ are usually too large. These discrepancies can be resolved provided that $a_0(980)$ is a tetraquark state. In this case, there exist two additional $T$-like topological amplitudes, denoted by $\overline{T}$ and $\tilde{T}$ which readily account for the discrepancies. An important implication of the tetraquark model is that the $D_s^{+}\to a_0(980{)}^{+}\ddot{I}{€}^0+a_0(980{)}^0\ddot{I}{€}^{+}$ decay is not a purely $W$-annihilation process as in the diquark model of $a_0(980)$; it receives dominant contributions from $\overline{T}$ newly noticed in this work. Therefore, measurements of $(D,D_s^{+})\to a_0(980)P$ decays lend strong support to the tetraquark picture of $a_0(980)$.

15 pages, 1 figure, version accepted by PRD