Observation of D a₀ (980) in the decays D^0 ^+^- and D^+ ^+^0

We report the first amplitude analysis of the decays D^0 ^+ ^- and D^+ ^+^0 using a data sample taken with the BESIII detector at the center-of-mass energy of 3. 773 GeV, corresponding to an integrated luminosity of 7. 9 fb^-1. The contribution from the process D^0 (+) a₀ (980) ^+ ^- (0) is significantly larger than the D^0 (+) a₀ (980) ^- (0) ^+ contribution. The ratios B (D^0 a₀ (980) ^+^-) /B (D^0 a₀ (980) ^-^+) and B (D^+ a₀ (980) ^+^0) /B (D^+ a₀ (980) ^0^+) are measured to be 7. 5^+2. 5-₀. ₈\, ₒₓ₀ₓ. 1. 7ₒₘₒₓ. and 2. 60. 6ₒₓ₀ₓ. 0. 3ₒₘₒₓ. , respectively. The measured D^0 ratio disagrees with the theoretical predictions by orders of magnitudes, thus implying a substantial contribution from final-state interactions.