Analysis of the decay D 0 → K S 0 π 0 π 0

We present the results of a Dalitz plot analysis of ${D}^{0}\\ensuremath{\\rightarrow}{K}_{S}^{0}{\\ensuremath{\\pi}}^{0}{\\ensuremath{\\pi}}^{0}$ using the CLEO-c data set of $818\\text{ }\\text{ }{\\mathrm{pb}}^{\\ensuremath{-}1}$ of ${e}^{+}{e}^{\\ensuremath{-}}$ collisions accumulated at $\\sqrt{s}=3.77\\text{ }\\text{ }\\mathrm{GeV}$. This corresponds to $3\\ifmmode\\times\\else\\texttimes\\fi{}{10}^{6}$ ${D}^{0}{\\overline{D}}^{0}$ pairs from which we select 1259 tagged candidates with a background of $7.5\\ifmmode\\pm\\else\\textpm\\fi{}0.9$ percent. Several models have been explored, all of which include the ${K}^{*}(892)$, ${K}_{2}^{*}(1430)$, ${K}^{*}(1680)$, the ${f}_{0}(980)$, and the $\\ensuremath{\\sigma}(500)$. We find that the combined ${\\ensuremath{\\pi}}^{0}{\\ensuremath{\\pi}}^{0}$ $S$-wave contribution to our preferred fit is $(28.9\\ifmmode\\pm\\else\\textpm\\fi{}6.3\\ifmmode\\pm\\else\\textpm\\fi{}3.1)%$ of the total decay rate while ${D}^{0}\\ensuremath{\\rightarrow}{\\overline{K}}^{*}(892{)}^{0}{\\ensuremath{\\pi}}^{0}$ contributes $(65.6\\ifmmode\\pm\\else\\textpm\\fi{}5.3\\ifmmode\\pm\\else\\textpm\\fi{}2.5)%$. Using three tag modes and correcting for quantum correlations we measure the ${D}^{0}\\ensuremath{\\rightarrow}{K}_{S}^{0}{\\ensuremath{\\pi}}^{0}{\\ensuremath{\\pi}}^{0}$ branching fraction to be $(1.058\\ifmmode\\pm\\else\\textpm\\fi{}0.038\\ifmmode\\pm\\else\\textpm\\fi{}0.073)%$.