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Search for the decay<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>D</mml:mi><mml:mn>0</mml:mn></mml:msup><mml:mo>→</mml:mo><mml:mi>γ</mml:mi><mml:mi>γ</mml:mi></mml:math>and measurement of the branching fraction for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>D</mml:mi><mml:mn>0</mml:mn></mml:msup><mml:mo>→</mml:mo><mml:msup><mml:mi>π</mml:mi><mml:mn>0</mml:mn></mml:msup><mml:msup><mml:mi>π</mml:mi><mml…
We search for the rare decay of the ${D}^{0}$ meson to two photons, ${D}^{0}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}$, and present a measurement of the branching fraction for a ${D}^{0}$ meson decaying to two neutral pions, $B({D}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0})$. The data sample analyzed corresponds to an integrated luminosity of $470.5\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ collected by the BABAR detector …