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

From the amplitude analysis of the Ds+→π+π0η decay, the BESIII Collaboration first observed the Ds+→a0(980)+π0 and Ds+→a0(980)0π+ decay modes, which are expected to occur through the pure W-annihilation processes. The measured branching fraction B[Ds+→a0(980)+(0)π0(+),a0(980)+(0)→π+(0)η] 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 Ds+ 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 Ds+→π+π0η decay by taking into account the contributions from the tree diagram Ds+→ρ+η→π+π0η and the intermediate ρ+η and K∗K̄/KK̄∗ triangle diagrams. The intermediate a0(980) state can be dynamically generated from the final state interactions of coupled KK̄ and πη channels, and it is shown that the experimental data can be described fairly well, which supports the interpretation of a0(980) as a molecular state.