Measurements of the branching fractions for B<inf>(s)</inf>→D <inf>(s)</inf>πππ and Λb0→Λc+πππ

Branching fractions of the decays H _bH _cπ ^-π ⁺π ^- relative to H _b→ H _cπ ^- are presented, where H _b (H _c) represents B ^̄0 (D ⁺), B ^- (D0), B̄s0 (Ds+), and Λb0 (Λc+). The measurements are performed with the LHCb detector using 35pb ^-1 of data collected at √s=7TeV. The ratios of branching fractions are measured to be [B(B ^̄0→D ⁺π ^-π ⁺π ^-)]/[B(B ^̄0→D ⁺π ^-)]=2.38±0. 11±0.21, [B(B ^-→D0π ^-π ⁺π ^-)]/[B(B ^-→D0π ^-)]=1.27±0.06±0.11, [B(B̄s0→Ds+π ^-π ⁺π ^-)]/ [B(B̄s0→Ds+π ^-)]=2.01±0.37±0.20, [B(Λb0→Λc+π ^-π ⁺π ^-)]/ [B(Λb0→Λc+π ^-)]=1.43±0.16±0.13 We also report measurements of partial decay rates of these decays to excited charm hadrons. These results are of comparable or higher precision than existing measurements.