Measurement of branching fractions in radiative B decays to ηKγ and search for B decays to η'Kγ

We present measurements of the B ->eta K gamma branching fractions and upper limits for the B ->eta K-'gamma branching fractions. For B+->eta K+gamma we also measure the time-integrated charge asymmetry. The data sample, collected with the BABAR detector at the Stanford Linear Accelerator Center, represents 232x10(6) produced B (B) over bar pairs. The results for branching fractions and upper limits at 90% confidence level in units of 10(-6) are: B(B-0 ->eta K-0 gamma)=11.3(-2.6)(+2.8)+/- 0.6, B(B+->eta K+gamma)=10.0 +/- 1.3 +/- 0.5, B(B-0 ->eta K-'(0)gamma)< 6.6, B(B+->eta K-'(+)gamma)< 4.2. The charge asymmetry in the decay B+->eta K+gamma is A(ch)=-0.09 +/- 0.12 +/- 0.01. The first errors are statistical and the second systematic.