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We search for B0 meson decays into two-body combinations of K0, η, η′, and ϕ mesons in 324×10^6 BB̅ pairs collected with the BABAR detector at the PEP-II asymmetric-energy e+e- collider at SLAC. We measure the following branching fractions (upper limits at 90% confidence level) in units of 10-6: B(B0→ηK0)=1.8-0.6+0.7±0.1(<2.9), B(B0→ηη)=1.1-0.4+0.5±0.1(<1.8), B(B0→ηϕ)=0.1±0.2±0.1(<0.6), B(B0→η′ϕ)=0.2-0.3+0.4±0.1(<1.0), and B(B0→η′η′)=1.0-0.6+0.8±0.1(<2.4), where the first error is statistical and the second systematic

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Searches for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>B</mml:mi><mml:mn>0</mml:mn></mml:msup></mml:math>decays to<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>η</mml:mi><mml:msup><mml:mi>K</mml:mi><mml:mn>0</mml:mn></mml:msup></mml:math>,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>η</mml:mi><mml:mi>η</mml:mi></mml:math>,<mml:math xmlns:mml="http://www.w3.org/1998/Math/…

Searches forB0decays toηK0,ηη,