Observation of B → D^(*)π^+π^−ℓ^−ν Decays in e^+e^− Collisions at the Υ(4S) Resonance

We report on measurements of the decays of B mesons into the semileptonic final states B → D^(*)π^+π^−ℓ−ν, where D(*) represents a D or D∗ meson and ℓ^− is an electron or a muon. These measurements are based on 471×10^6 BB pairs recorded with the BABAR detector at the SLAC asymmetric B factory PEP-II. We determine the branching fraction ratios R^(*)_(π+π−)=B(B → D^(*)π^+π^−ℓ^−ν)/B(B → D^(*)ℓ^−ν) using events in which the second B meson is fully reconstructed. We find R_(π+π−)=0.067±0.010±0.008 and R^∗_(π+π−) = 0.019 ± 0.005 ± 0.004, where the first uncertainty is statistical and the second is systematic. Based on these results and assuming isospin invariance, we estimate that B → D^(*)ππℓ^−ν decays, where π denotes either a π^± and π^0 meson, account for up to half the difference between the measured inclusive semileptonic branching fraction to charm hadrons and the corresponding sum of previously measured exclusive branching fractions