Measurements of the Branching fractions for $B_{(s)} \to D_{(s)}\pi\pi\pi$ and $\Lambda_b^0 \to \Lambda_c^+\pi\pi\pi$

Branching fractions of the decays $H_b\to H_c\pi^-\pi^+\pi^-$ relative to $H_b\to H_c\pi^-$ are presented, where $H_b$ ($H_c$) represents $\overline{B^0}$ ($D^+$), $B^-$ ($D^0$), $\overline{B_s^0}$ ($D_s^+$) and $\Lambda_b^0$ ($\Lambda_c^+$). The measurements are performed with the LHCb detector using 35~${\rm pb^{-1}}$ of data collected at $\sqrt{s}=7$~TeV. The ratios of branching fractions are measured to be \begin{eqnarray*} {{\cal{B}}(\overline{B^0}\to D^+\pi^-\pi^+\pi^-)\over{\cal{B}}(\overline{B^0}\to D^+\pi^-)} = 2.38\pm0.11\pm0.21 \nonumber \\ {{\cal{B}}(B^-\to D^0\pi^-\pi^+\pi^-)\over{\cal{B}}(B^-\to D^0\pi^-)} = 1.27\pm0.06\pm0.11 \nonumber \\ {{\cal{B}}(\overline{B_s^0}\to D_s^+\pi^-\pi^+\pi^-)\over{\cal{B}}(\overline{B_s^0}\to D_s^+\pi^-)} = 2.01\pm0.37\pm0.20 \nonumber \\ {{\cal{B}}(\Lambda_b^0\to\Lambda_c^+\pi^-\pi^+\pi^-)\over{\cal{B}}(\Lambda_b^0\to\Lambda_c^+\pi^-)} = 1.43\pm0.16\pm0.13. \nonumber \\ \end{eqnarray*} 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.