Search for the Decay D⁰ → γγ and Measurement of the Branching Fraction for D⁰ → π⁰π⁰

We search for the rare decay of the D⁰ meson to two photons, D⁰ → γγ, and present a measurement of the branching fraction for a D⁰ meson decaying to two neutral pions, B(D⁰ → π⁰π⁰). The data sample analyzed corresponds to an integrated luminosity of 470.5 fb⁻¹ collected by the BABAR detector at the PEP-II asymmetric-energy e⁺e⁻ collider at SLAC. We place an upper limit on the branching fraction, B(D⁰ → γγ) < 2.2 × 10⁻⁶ at 90% confidence level. This limit improves on the existing limit by an order of magnitude. We also find B(D⁰→π⁰π⁰) = (8.4 ± 0.1 ± 0.4 ± 0.3) × 10⁻⁴.