The multihadron decays $\Lambda_b^0\rightarrow D^+ p \pi^-\pi^-$ and $\Lambda_b^0\rightarrow D^{ *+} p \pi^-\pi^-$ are observed in data corresponding to an integrated luminosity of 3fb$^{ -1}$, collected in proton-proton collisions at centre-of-mass energies of 7 and 8TeV by the LHCb detector. Using the~decay $\Lambda_b^0\rightarrow \Lambda_c^+ \pi^+ \pi^-\pi^-$ as a normalisation channel, the ratio of branching fractions is measured to be $$ \frac { { \mathcal{ B}} ( \Lambda_b^0\rightarrow D^+ p \pi^-\pi^- ) } { { \mathcal{ B}} ( \Lambda_b^0\rightarrow \Lambda_c^+ \pi^+ \pi^-\pi^- ) } \times \frac { { \mathcal{ B}} ( D^+ \rightarrow K^-\pi^+\pi^+) } { { \mathcal{ B}} ( \Lambda_c^+ \rightarrow p K^-\pi^+ ) } = ( 5.35 \pm 0.21 \pm 0.16 ) \% \,, $$ where the first uncertainty is statistical and the second systematic. The ratio of branching fractions for $\Lambda_b^0\rightarrow D^{ *+} p \pi^-\pi^-$ and $\Lambda_b^0\rightarrow D^+ p \pi^-\pi^-$ decays is found to be $$ \frac{ { \mathcal{ B}} ( \Lambda_b^0\rightarrow D^{ *+} p \pi^-\pi^- )} { { \mathcal{ B}} ( \Lambda_b^0\rightarrow D^{ +} p \pi^-\pi^- )} \times ( { \mathcal{ B}}( D^{ *+} \rightarrow \pi^0 ) + { \mathcal{ B}}( D^{ *+} \rightarrow \gamma )) = ( 61.3 \pm 4.3 \pm 4.0 ) \% \,. $$
Categories: hep-ex