Search for neutral B-meson decays to a0π, a0K, ηρ0, and ηf0

We present a search for B0 decays to charmless final states involving an η meson, a charged pion, and a second charged pion or kaon. The data sample corresponds to 383×106 BB̅ pairs collected with the BABAR detector operating at the PEP-II asymmetric-energy B factory at SLAC. We find no significant signals and determine the following 90% C.L. upper limits: B(B0→a0-π+)×B(a0-→ηπ-)<3.1×10-6, B(B0→a0-K+)×B(a0-→ηπ-)<1.9×10-6, B(B0→a0(1450)-π+)×B(a0(1450)-→ηπ-)<2.3×10-6, B(B0→a0(1450)-K+)×B(a0(1450)-→ηπ-)<3.1×10-6, B(B0→ηρ0)<1.5×10-6, and B(B0→ηf0(980))×B(f0(980)→π+π-)<0.4×10-6.