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We report preliminary measurements of the exclusive charmless semileptonic
branching fractions of the B+ --> eta l+ nu and
B+ --> eta' l+ nu decays.
These measurements are based on 316 fb-1 of data collected at the
Y(4S) resonance by the BABAR detector.
In events in which the decay of one B meson to a hadronic final state is
fully reconstructed, the semileptonic decay of the recoiling B meson is
identified by the detection of a charged lepton and an eta or
eta'.
We measure the branching fraction
BR(B+ --> eta l+ nu) = (0.84 +/- 0.27 +/- 0.21) x 10-4, where the first error
is statistical and the second one systematic.
We also set an upper limit on the branching fraction of
BR(B+ --> eta l+ nu) < 1.4 x 10-4 and BR(B+ --> eta' l+ nu) < 1.3 x 10^-4 at
the 90% confidence level.
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