Improved Measurements of the Cabibbo Favored Decays $B_{(s)} \to D_{(s)} \pi\pi\pi$ and $\Lambda_b \to \Lambda_{c\pi\pi\pi}$ Branching Fractions

We report measurements of the branching fractions of the five and six-body decays $X_b\to X_c \pi^{-}\pi^{+}\pi^{-}$ relative to $X_b\to X_c\pi^{-}$, where $X_b(X_c)$ represents $\bar{B}^0$($D^+$), $B^-$ ($D^0$), $\bar{B}_s^0$ ($D_s^+$) and $\Lambda_b^0$ ($\Lambda_c^+$). The measurements are performed with the LHCb detector using 35 pb$^-$ of data collected at $\sqrt{s}$ = 7 TeV. The ratio of branching fractions are measured to be: \begin{align} {B(\bar{B}^0 \to D^{+}\pi^{-}\pi^{+}\pi^{-})\over B(\bar{B}^0 \to D^{+}\pi^{-})} = 2.35\pm0.11(stat)\pm0.24(syst) \nonumber \\ {B(B^- \to D^{0}\pi^{-}\pi^{+}\pi^{-})\over B(B^- \to D^{0}\pi^{-})} = 1.26\pm 0.07(stat)\pm0.12(syst) \nonumber \\ {B(\bar{B}^0_s \to D^+_s\pi^{-}\pi^{+}\pi^{-})\over B(\bar{B}^0_s \to D^{+}\pi^{-})} = 2.22\pm0.41(stat)\pm0.25(syst) \nonumber \\ {B(\Lambda^0_b \to \Lambda^+_b\pi^{-}\pi^{+}\pi^{-})\over B(\Lambda^0_b \to \Lambda^{+}_c\pi^{-})} = 1.32\pm0.15(stat)\pm0.14(syst) \nonumber \\ \end{align} These measurements are significantly better than or competitive with the world average values.