Study of the kinematic dependences of ${\mathrm{\Lambda }}_b^0$ production in $pp$ collisions and a measurement of the ${\mathrm{\Lambda }}_b^0\to {\mathrm{\Lambda }}_c^{+}{\pi }^{-}$ branching fraction

The kinematic dependences of the relative production rates, $f_{{\mathrm{\Lambda }}_b^0}\mathrm{/}{f}_d$, of ${\mathrm{\Lambda }}_b^0$ baryons and ${\bar{B}}^0$ mesons are measured using ${\mathrm{\Lambda }}_b^0\to {\mathrm{\Lambda }}_c^{+}{\pi }^{-}$ and $\bar{B}^0 \rightarrow D^+ \pi^-$ decays. The measurements use proton-proton collision data, corresponding to an integrated luminosity of 1 fb${}^{-1}$ at a centre-of-mass 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 $f_{{\mathrm{\Lambda }}_b^0}\mathrm{/}{f}_d$ 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 $f_{{\mathrm{\Lambda }}_b^0}\mathrm{/}{f}_d$ and the fourth is due to the $\bar{B}^0 \rightarrow D^+ \pi^-$branchingfraction\mathrm{.}Thisisthemostprecisemeasurementofa$\Lambda_b^0$ branching fraction to date.