Analysis of the decay $D^0\to K_S^0{\pi }^0{\pi }^0$

We present the results of a Dalitz plot analysis of $D^0\to K_S^0{\pi }^0{\pi }^0$ using the CLEO-c data set of $818{\mathrm{pb}}^{-1}$ of $e^{+}{e}^{-}$ collisions accumulated at $\sqrt{s}=3.77\mathrm{GeV}$. This corresponds to $3\times {10}^6$ $D^0{\overline{D}}^0$ pairs from which we select 1259 tagged candidates with a background of $7.5\pm 0.9$ 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 $(28.9\pm 6.3\pm 3.1)\%$ of the total decay rate while $D^0\to {\overline{K}}^{*}(892{)}^0{\pi }^0$ contributes $(65.6\pm 5.3\pm 2.5)\%$. Using three tag modes and correcting for quantum correlations we measure the $D^0\to K_S^0{\pi }^0{\pi }^0$ branching fraction to be $(1.058\pm 0.038\pm 0.073)\%$.

Figure 1

Signalside $\Delta E$ distribution. The solid line shows the results of fitting with a double Gaussian to represent the signal plus a constant background (horizontal dashed line). The vertical dashed lines indicate the signal region.

Figure 2

$D^0\to K_S^0{\pi }^0{\pi }^0$ Dalitz plot showing two entries per candidate, one for each possible $K_S^0{\pi }^0$ combination.

Figure 3

$m^2(K\pi )$ projections for Model 1. The data are represented by the points with error bars and the total fit by the thick solid line. The other fit components are discussed in the text.

Figure 4

$m^2(\pi \pi )$ projection for Model 1. The data are represented by the points with error bars and the total fit by the thick solid line. The other fit components are discussed in the text.