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

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Abstract

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 B^0-bar($D^+$), $B^-$ ($D^0$), B_s^0-bar ($D_s^+$) 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 B(B^0-bar -> D^+\pi^-\pi^+\pi^-)/ B(B^0-bar -> D^+\pi^-) = 2.38\pm0.11\pm0.21 B(B^- -> D^0\pi^-\pi^+\pi^-) / B(B^- -> D^0\pi^-) = 1.27\pm0.06\pm0.11 B(B_s^0-bar -> D_s^+\pi^-\pi^+\pi^-) / B(B_s^0-bar -> D_s^+\pi^-) = 2.01\pm0.37\pm0.20 B(\Lambda_b^0->\Lambda_c^+\pi^-\pi^+\pi^-) / B(\Lambda_b^0 -> \Lambda_c^+\pi^-) = 1.43\pm0.16\pm0.13. 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.

Figures and captions

Feynman diagrams for $H_b\rightarrow H_c\pi^-$ and $H_b\rightarrow H_c\pi^-\pi^+\pi^-$ decays. Figs. (a) and (b) show external tree diagrams, (c) and (d) show color-suppressed tree diagrams ($B^-$ and $\Lambda_b^0$ only), and (e) shows the Cabibbo-suppressed external tree diagram, only accessible to $B^0$ meson.

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Lb2LcPiDecayInternal.eps
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TreeB2DPiDecayCS.eps

Invariant mass distributions for $\overline{ B }{} ^0 \rightarrow D^+\pi^-\pi^+\pi^-$ (top left), $B^-\rightarrow D^0\pi^-\pi^+\pi^-$ (top right), $\overline{ B }{} ^0_s \rightarrow D_s^+\pi^-\pi^+\pi^-$ (bottom left), and $\Lambda_b^0\rightarrow \Lambda_c^+\pi^-\pi^+\pi^-$ (bottom right). Fits showing the signal and background components are indicated, and are described in the text.

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b2dcha1_trigsel_35pb_Paper.eps
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bs2dsa1_trigsel_35pb_Paper.eps
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lb2lca1_trigsel_35pb_Paper.eps

Invariant mass distributions for $\overline{ B }{} ^0 \rightarrow D^+\pi^-$ (top left), $B^{-}\rightarrow D^0\pi^{-}$ (top right), $\overline{ B }{} ^0_s \rightarrow D_s^+\pi^-$ (bottom left), and $\Lambda_b^0\rightarrow \Lambda_c^+\pi^-$ (bottom right). Fits showing the signal and background components are indicated, and are described in the text.

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lb2lcpi_trigsel_35pb_Paper.eps

Comparisons of the $p_T$ and IP spectra for the daughters from the $D^+$ in $\overline{ B }{} ^0 \rightarrow D^+\pi^-$ [(a) and (b)], and from the $D^+$ in $\overline{ B }{} ^0 \rightarrow D^+\pi^-\pi^+\pi^-$ [(c) and (d)]; Points with error bars are data and the solid lines are simulation.

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ddau_3H_paper.eps

Comparisons of the $p_T$ and IP spectra for the bachelor pion in $\overline{ B }{} ^0 \rightarrow D^+\pi^-$ [(a) and (b)], and for the 3 pions in $\overline{ B }{} ^0 \rightarrow D^+\pi^-\pi^+\pi^-$ [(c) and (d)]. Points with error bars are data and the solid lines are simulation.

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kdau_3H_paper.eps

Invariant mass of the $3\pi$ system in $\overline{ B }{} ^0 \rightarrow D^+\pi^-\pi^+\pi^-$ (top left), $B^-\rightarrow D^0\pi^-\pi^+\pi^-$ (top right), $\overline{ B }{} ^0_s \rightarrow D_s^+\pi^-\pi^+\pi^-$ (bottom left) and $\Lambda_b^0\rightarrow \Lambda_c^+\pi^-\pi^+\pi^-$ (bottom right) decays. The data are the points with error bars and the simulations are the solid lines and shaded regions.

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PiPiPiMass_Lb2LcA1.eps

$\pi^+\pi^-$ invariant mass (2 combinations per $\overline{ B }{} ^0 $ candidate) in the $3\pi$ system for $\overline{ B }{} ^0 \rightarrow D^+\pi^-\pi^+\pi^-$ when (a) $M(\pi^-\pi^+\pi^-)<1.5$ GeV/$c^2$ and (b) $M(\pi^-\pi^+\pi^-)\ge 1.5$ GeV/$c^2$. The corresponding plots for $B^-\rightarrow D^0\pi^-\pi^+\pi^-$ are shown in (c) and (d).

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pipiMass_B2D0A1.eps

Invariant mass difference $M(D\pi^-\pi^+) - M(D)$, for (a) $\overline{ B }{} ^0 \rightarrow D^+\pi^-\pi^+\pi^-$ signal candidates, (b) $B^-\rightarrow D^0\pi^-\pi^+\pi^-$ signal candidates, (c) $B^-\rightarrow D^0\pi^-\pi^+\pi^-$ through a $D^{*+}$ intermediate state, and (d) $B^-\rightarrow D^0\pi^-\pi^+\pi^-$ not through a $D^{*+}$ intermediate state. The signal components are the white region (and lightly shaded regions for $B^-\rightarrow D^0\pi^-\pi^+\pi^-$), and the background component is the darker shaded region.

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Bp2D03Pi_ExcCharmDStar_TrigSel_Paper.eps
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Bp2D03Pi_ExcCharmnonDStar_TrigSel_Paper.eps

Intermediate resonances contributing to the $\Lambda_b^0\rightarrow \Lambda_c^+\pi^-\pi^+\pi^-$ decay. Shown are distributions for (a) $M(\Lambda_c^+\pi^-\pi^+) - M(\Lambda_c^+)$, with $\Lambda_c(2595)^+$ and $\Lambda_c(2625)^+$ contributions, (b) $M(\Lambda_c^+\pi^{\pm}) - M(\Lambda_c^+)$ (3 combinations per $\Lambda_b^0$ candidate) (c) $M(\Lambda_c^+\pi^{-}) - M(\Lambda_c^+)$ (2 combinations per $\Lambda_b^0$ candidate), and (d) $M(\Lambda_c^+\pi^{+}) - M(\Lambda_c^+)$ (1 combination per $\Lambda_b^0$ candidate), showing the intermediate $\Sigma_c$ states. The line is a fit as described in the text, and the shaded region is the fitted background.

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Lb2Lc3piTrigSel_SigmaCpppipi.eps

Animated gif made out of all figures.

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Tables and captions

Summary of efficiencies for decay channels under study. Here, $\epsilon_{\rm kin}$ is the total kinematic selection efficiency, $\epsilon_{\rm trig}$ is the trigger efficiency, and $\epsilon_{\rm tot}$ is their product. The uncertainties shown are statistical only.

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Table_1.pdf

Summary of yields for the branching fraction computation. Uncertainties are statistical only.

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Table_2.pdf

Summary of corrections and systematic uncertainties to the ratio of branching fractions $\cal{B}(H_b\rightarrow H_c\pi^-\pi^+\pi^-)/\cal{B}(H_b\rightarrow H_c\pi^-)$.

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Table_3.pdf

Summary of yields for the signal and normalization modes. Below $D_1$ and $D_2^*$ refer to the $D_1(2420)$ and $D_2^*(2460)$ mesons, respectively.

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Table_4.pdf

Summary of the relative reconstruction and selection efficiencies ($\epsilon_{\rm sel}^{\rm rel}$) and trigger efficiencies ($\epsilon_{\rm trig|sel}^{\rm rel}$) for the excited charm hadron intermediate states with respect to the inclusive $H_c\pi^-\pi^+\pi^-$ final states. Below $D_1$ and $D_2^*$ refer to $D_1(2420)$ and $D_2^*(2460)$, respectively. The uncertainties shown are statistical only.

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Table_5.pdf

Created on 18 October 2019.