Analysis of the Decay D^0 to K^0_S pi^0 pi^0

We present the results of a Dalitz plot analysis of D^0 to K^0_S pi^0 pi^0 using the CLEO-c data set of 818 inverse pico-barns of e^+ e^- collisions accumulated at sqrt{s} = 3.77 GeV. This corresponds to three million D^0 D^0-bar pairs from which we select 1,259 tagged candidates with a background of 7.5 ± 0.9 percent. Several models have been explored, all of which include the K^(892), K^_2(1430), K^(1680), the f_0(980), and the sigma(500). We find that the combined pi^0 pi^0 S-wave contribution to our preferred fit is (28.9 ± 6.3 ± 3.1)% of the total decay rate while D^0 to K^(892)^0 pi^0 contributes (65.6 ± 5.3 ± 2.5)%. Using three tag modes and correcting for quantum correlations we measure the D^0 to K^0_S pi^0 pi^0 branching fraction to be (1.059 ± 0.038 ± 0.061)%.