Resonant final-state interactions in D^0 -> \bar{K}^{0} {\eta}, \bar{K}^{0} \eta' Decay

We have investimated the effect of the isospin 1/2, J^P = 0^+ resonant state K^*_0(1950) on the decays D^0 ->\bar{K}^{0}\eta and D^0 ->\bar{K}^0 \eta' as a function of the branching ratio sum r =Br(K^*_0(1950)->\bar{K}^0\eta)+ Br(K^*_0(1950)->\bar{K}^0 \eta' and coupling constants g_{K^*_0\bar{K}^0\eta}, g_{K^*_0\bar{K}^0\eta'}. We have used a factorized input for D^0 -> K^*_0(1950) weak transition through a \pi K loop. We estimated both on- and off-shell contributions from the loop. Our calculation shows that the off-shell effects are significant. For $r\geq 30$ a fit to the decay amplitude A(D^0 -> \bar{K}^0 \eta') was possible, but the amplitude A(D^0 ->\bar{K}^0 \eta) remained at its factorized value. For small values of r, $r\leq 18$, we were able to fit A(D^0 -> \bar{K}^0 \eta), and despite the fact that A(D^0 -> \bar{K}^0 \eta') could be raised by almost 100 % over its factorized value, it still falls short of its experimental value. A simultaneous fit to both amplitudes A(D^0 -> \bar{K}^0 \eta') and A(D^0 -> \bar{K}^0 \eta) was not possible. We have also determined the strong phase of the resonant amplitudes for both decays. PACS numbers:13.25.Ft, 13.25.-k, 14.40.Lb