Can the nature of a0(980) be tested in the Ds+. π+ π0η decay?

From the amplitude analysis of the D-s(+). pi(+)pi(0)eta decay, the BESIII Collaboration first observed the D-s(+). a(0) (980)(+)pi(0) and D-s(+). a(0)(980)(0)pi(+) decay modes, which are expected to occur through the pure Wannihilation processes. The measured branching fraction B[D-s(+) -> a(0) (980)(+(0))pi(0(+)), a(0) (980)(+(0)) -> pi(+(0))eta] is, however, found to be larger than those of known W-annihilation decays by 1 order of magnitude. This apparent contradiction can be reconciled if the two decays are induced by internal W-conversion or external W-emission mechanisms instead of a W-annihilation mechanism. In this work, we propose that the D-s(+) decay proceeds via both the external and internal W-emission instead of W-annihilation mechanisms. In such a scenario, we perform a study of the D-s(+) -> pi(+) pi(0)eta decay by taking into account the contributions from the tree diagram D-s(+) -> rho(+)eta -> pi(0)eta and the intermediate. and K* (K) over bar /K (K) over bar* triangle diagrams. The intermediate a(0)(980) state can be dynamically generated from the final state interactions of coupled K (K) over tilde and pi eta channels, and it is shown that the experimental data can be described fairly well, which supports the interpretation of a(0)(980) as a molecular state.