Amplitude Analysis of D_{s}^{+}→π^{+}π^{0}η and First Observation of the W-Annihilation Dominant Decays D_{s}^{+}→a_{0}(980)^{+}π^{0} and D_{s}^{+}→a_{0}(980)^{0}π^{+}.

We present the first amplitude analysis of the decay D_{s}^{+}→π^{+}π^{0}η. We use an e^{+}e^{-} collision data sample corresponding to an integrated luminosity of 3.19  fb^{-1} collected with the BESIII detector at a center-of-mass energy of 4.178 GeV. We observe for the first time the W-annihilation dominant decays D_{s}^{+}→a_{0}(980)^{+}π^{0} and D_{s}^{+}→a_{0}(980)^{0}π^{+}. We measure the absolute branching fraction B(D_{s}^{+}→a_{0}(980)^{+(0)}π^{0^{(}+)},a_{0}(980)^{+(0)}→π^{+(0)}η)=(1.46±0.15_{stat}±0.23_{sys})%, which is larger than the branching fractions of other measured pure W-annihilation decays by at least one order of magnitude. In addition, we measure the branching fraction of D_{s}^{+}→π^{+}π^{0}η with significantly improved precision.