The kinematic dependences of the relative production rates, $f_{\Lambda_b^0}/f_d$, of $\Lambda_b^0$ baryons and $\bar{B}^0$ mesons are measured using $\Lambda_b^0 \rightarrow \Lambda_c^+ \pi^$ and $\bar{B}^0 \rightarrow D^+ \pi^$ decays. The measurements use protonproton collision data, corresponding to an integrated luminosity of 1 fb$^{1}$ at a centreofmass energy of 7 TeV, recorded in the forward region with the LHCb experiment. The relative production rates are observed to depend on the transverse momentum, $p_T$, and pseudorapidity, $\eta$, of the beauty hadron, in the studied kinematic region $1.5 < p_T < 40$ GeV/$c$ and $2 < \eta < 5$. Using a previous LHCb measurement of $f_{\Lambda_b^0}/f_d$ in semileptonic decays, the branching fraction $\mathcal{B}(\Lambda_b^0 \rightarrow \Lambda_c^+ \pi^) = \Big( 4.30 \pm 0.03 ^{+0.12}_{0.11} \pm 0.26 \pm 0.21 \Big) \times 10^{3}$ is obtained, where the first uncertainty is statistical, the second is systematic, the third is from the previous LHCb measurement of $f_{\Lambda_b^0}/f_d$ and the fourth is due to the $\bar{B}^0 \rightarrow D^+ \pi^$ branching fraction. This is the most precise measurement of a $\Lambda_b^0$ branching fraction to date.
Ratio of total selection efficiencies in bins of the (a) $p_{\rm T}$ and (b) $\eta$ of the $b$ hadron. The horizontal error bars indicate the range of each bin in $p_{\rm T}$ or $\eta$ respectively. 
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Invariant mass distributions of (a,c) $\Lambda ^+_ c \pi ^ $ candidates and (b,d) $ D ^+ \pi ^ $ candidates for specific ranges in $p_{\rm T}$ and $\eta$ of the $b$ hadron, with fit projections overlaid. The different components are defined in the legend, where "part reco" refers to the sum of partially reconstructed decays. 
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(a) Dependence of the efficiencycorrected ratio of yields, $\mathcal{R}$, between $\Lambda ^0_ b \rightarrow \Lambda ^+_ c \pi ^ $ and $\overline{ B }{} ^0 \rightarrow D ^+ \pi ^ $ decays on the $p_{\rm T}$ of the beauty hadron, fitted with an exponential function. The error bars on the data show the statistical and systematic uncertainties added in quadrature. (b) The resulting parametrisation is then fitted to the rescaled $ f_{\Lambda ^0_ b }/f_ d $ measurements from the semileptonic analysis [7], to obtain the scale factor $\mathcal{S}$. The error bars include only the statistical uncertainty. 
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Dependence of $ f_{\Lambda ^0_ b }/f_ d $ on the (a) $p_{\rm T}$ and (b) $\eta$ of the beauty hadron. To obtain this figure, the ratio of efficiencycorrected event yields is scaled to the absolute value of $ f_{\Lambda ^0_ b }/f_ d $ from the semileptonic analysis [7]. The error bars include the statistical and systematic uncertainties associated with the hadronic measurement. The dashed red lines indicate the uncertainty on the scale of $ f_{\Lambda ^0_ b }/f_ d $ from the semileptonic analysis. 
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Animated gif made out of all figures. 
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Relative systematic uncertainties for the measurements of $\mathcal{R}(x)$ (first five columns) and $\cal B$ ( $\Lambda ^0_ b \rightarrow \Lambda ^+_ c \pi ^ $ ) (last column). The uncertainties from the various sources are uncorrelated and added in quadrature to obtain the total uncertainty. Sample size refers to the size of the simulated events sample. 
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Supplementary material full pdf 
supple[..].pdf [203 KiB] 

This zip files contains supplementary material for the publication LHCbPAPER2014004. The files are: supplementary.pdf: An overview of the extra material *pdf,*png,*eps,*C: Fig1 in supplementary.pdf in various formats *txt: Tables 1 and 2 in supplementary.pdf 
Fig1S.pdf [17 KiB] HiDef png [160 KiB] Thumbnail [136 KiB] *C file 
Created on 14 January 2021.