A search for rare charmless decays of B0d and B0s mesons has been performed in the exclusive channels B0d(s) →ηη0, B0d(s) →ηπ0 and B0d(s) →π0π0. The data sample consisted of three million hadronic Z decays collected by the L3 experiment at LEP from 1991 through 1994. No candidate event has been observed and the following upper limits at 90% confidence level on the branching ratios have been set:
Br(B0d→ηη) <4.1 x 10−4, Br(B0s →ηη) < 1.5 x 10−3, Br(B0d→ηπ0) < 2.5 x 10−4, Br(B0s→ηπ0) < 1.0 x 10−3, Br(B0d→π0π0) < 6.0 x 10−5, Br(B0s→π0π0) < 2.1 x 10−4.
These are the first experimental limits on Bd0→ηη and on the Bs0 neutral charmless modes.