Observation of D^{+}→K_{S}^{0}a_{0}(980)^{+} in the Amplitude Analysis of D^{+}→K_{S}^{0}π^{+}η.

We perform for the first time an amplitude analysis of the decay D^{+}→K_{S}^{0}π^{+}η and report the observation of the decay D^{+}→K_{S}^{0}a_{0}(980)^{+} using 2.93  fb^{-1} of e^{+}e^{-} collision data taken at a center-of-mass energy of 3.773 GeV with the BESIII detector. As the only W-annihilation-free decay among D to a_{0}(980) pseudoscalar, D^{+}→K_{S}^{0}a_{0}(980)^{+} is the ideal decay in extracting the contributions of the W-emission amplitudes involving a_{0}(980) and to study the final-state interactions. The absolute branching fraction of D^{+}→K_{S}^{0}π^{+}η is measured to be (1.27±0.04_{stat}±0.03_{syst})%. The branching fractions of intermediate processes D^{+}→K_{S}^{0}a_{0}(980)^{+} with a_{0}(980)^{+}→π^{+}η and D^{+}→π^{+}K[over ¯]_{0}^{*}(1430)^{0} with K[over ¯]_{0}^{*}(1430)^{0}→K_{S}^{0}η are measured to be (1.33±0.05_{stat}±0.04_{syst})% and (0.14±0.03_{stat}±0.01_{syst})%, respectively.