Observation of the Decay B→J/ψηK and Search for X(3872)→J/ψη

We report the observation of the B meson decay B±→J/ψηK± and evidence for the decay B0→J/ψηKS0, using 90×106 BB̅ events collected at the Υ(4S) resonance with the BABAR detector at the SLAC PEP-II e+e- asymmetric-energy storage ring. We obtain branching fractions of B(B±→J/ψηK±)=[10.8±2.3(stat)±2.4(syst)]×10-5 and B(B0→J/ψηKS0)=[8.4±2.6(stat)±2.7(syst)]×10-5. We search for the new narrow mass state, the X(3872), recently reported by the Belle Collaboration, in the decay B±→X(3872)K±,X(3872)→J/ψη and determine an upper limit of B[B±→X(3872)K±→J/ψηK±]<7.7×10-6 at 90% confidence level.