| Summary: | We present searches for the rare decay modes D[superscript 0]→e[superscript +]e[superscript -], D0→μ[superscript +]μ[superscript -], and D0→e[superscript ±]μ[superscript ∓] in continuum e[superscript +]e[superscript -]→cc̅ events recorded by the BABAR detector in a data sample that corresponds to an integrated luminosity of 468 fb[superscript -1]. These decays are highly Glashow–Iliopoulos–Maiani suppressed but may be enhanced in several extensions of the standard model. Our observed event yields are consistent with the expected backgrounds. An excess is seen in the D[superscript 0]→μ[superscript +]μ[superscript -] channel, although the observed yield is consistent with an upward background fluctuation at the 5% level. Using the Feldman–Cousins method, we set the following 90% confidence level intervals on the branching fractions: B(D[superscript 0]→e[superscript +]e[superscript -])<1.7×10[superscript -7], B(D[superscript 0]→μ[superscript +]μ[superscript -]) within [0.6,8.1]×10[superscript -7], and B(D[superscript 0]→e[superscript ±]μ[superscript ∓])<3.3×10[superscript -7].
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