The production cross sections of $\mathrm {D^0}$, $\mathrm {D^+}$, and $\mathrm {\Lambda_{c}^{+}}$ hadrons originating from beauty-hadron decays (i.e. non-prompt) were measured for the first time at midrapidity in proton$-$lead (p$-$Pb) collisions at the center-of-mass energy per nucleon pair of $\sqrt{s_{\mathrm{NN}}} = 5.02$ TeV. Nuclear modification factors ($R_{\mathrm {pPb}}$) of non-prompt $\mathrm {D^0}$, $\mathrm {D^+}$, and $\mathrm {\Lambda_{c}^{+}}$ are calculated as a function of the transverse momentum ($p_{\mathrm T}$) to investigate the modification of the momentum spectra measured in p$-$Pb collisions with respect to those measured in proton$-$proton (pp) collisions at the same energy. The $R_{\mathrm {pPb}}$ measurements are compatible with unity and with the measurements in the prompt charm sector, and do not show a significant $p_{\mathrm T}$ dependence. The $p_{\mathrm T}$-integrated cross sections and $p_{\mathrm T}$-integrated $R_{\mathrm {pPb}}$ of non-prompt $\mathrm {D^0}$ and $\mathrm {D^+}$ mesons are also computed by extrapolating the visible cross sections down to $p_{\mathrm T}$ = 0. The non-prompt D-meson $R_{\mathrm {pPb}}$ integrated over $p_{\mathrm T}$ is compatible with unity and with model calculations implementing modification of the parton distribution functions of nucleons bound in nuclei with respect to free nucleons. The non-prompt $\mathrm {\Lambda_{c}^{+}/D^{0}}$ and $\mathrm{D^+/D^0}$ production ratios are computed to investigate hadronisation mechanisms of beauty quarks into mesons and baryons. The measured ratios as a function of $p_{\mathrm T}$ display a similar trend to that measured for charm hadrons in the same collision system.
Non-prompt $\mathrm{D}^0$ $p_\mathrm{{T}}$-differential production cross section $\mathrm{d}^2\sigma/\mathrm{d}p_\mathrm{T}\mathrm{d}y$ in p--Pb collisions at $\sqrt{{s_\mathrm{NN}}}=5.02~\mathrm{{TeV}}$ in the rapidity interval $-0.96 < y_{\mathrm{cms}} < 0.04$.
Non-prompt $\mathrm{D}^+$ $p_\mathrm{{T}}$-differential production cross section $\mathrm{d}^2\sigma/\mathrm{d}p_\mathrm{T}\mathrm{d}y$ in p--Pb collisions at $\sqrt{{s_\mathrm{NN}}}=5.02~\mathrm{{TeV}}$ in the rapidity interval $-0.96 < y_{\mathrm{cms}} < 0.04$.
Non-prompt $\Lambda_{c}^{+}$ $p_\mathrm{{T}}$-differential production cross section $\mathrm{d}^2\sigma/\mathrm{d}p_\mathrm{T}\mathrm{d}y$ in p--Pb collisions at $\sqrt{{s_\mathrm{NN}}}=5.02~\mathrm{{TeV}}$ in the rapidity interval $-0.96 < y_{\mathrm{cms}} < 0.04$.
A measurement of the production of prompt $\Lambda_{\rm c}^{+}$ baryons in Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 5.02 $ TeV with the ALICE detector at the LHC is reported. The $\Lambda_{\rm c}^{+}$ and $\overline{\Lambda}_{\rm c}^{-}$ were reconstructed at midrapidity ($|y| < 0.5$) via the hadronic decay channel $\Lambda_{\rm c}^{+}\rightarrow {\rm p} {\rm K}_{\rm S}^{0}$ (and charge conjugate) in the transverse momentum and centrality intervals $6 < p_{\rm T} <12$ GeV/$c$ and 0-80%. The $\Lambda_{\rm c}^{+}$/D$^0$ ratio, which is sensitive to the charm quark hadronisation mechanisms in the medium, is measured and found to be larger than the ratio measured in minimum-bias pp collisions at $\sqrt{s} = 7$ TeV and in p-Pb collisions at $\sqrt{s_{\rm NN}} = 5.02 $ TeV. In particular, the values in p-Pb and Pb-Pb collisions differ by about two standard deviations of the combined statistical and systematic uncertainties in the common $p_{\rm T}$ interval covered by the measurements in the two collision system. The $\Lambda_{\rm c}^{+}$/D$^0$ ratio is also compared with model calculations including different implementations of charm quark hadronisation. The measured ratio is reproduced by models implementing a pure coalescence scenario, while adding a fragmentation contribution leads to an underestimation. The $\Lambda_{\rm c}^{+}$ nuclear modification factor, $R_{\rm AA}$, is also presented. The measured values of the $R_{\rm AA}$ of $\Lambda_{\rm c}^{+}$, D$_{\rm s}$ and non-strange D mesons are compatible within the combined statistical and systematic uncertainties. They show, however, a hint of a hierarchy $(R_{\rm AA}^{{\rm D}^{0}}
$\Lambda_{\rm {c}}^{+}$/${\rm D}^{0}$ ratio in 0-80% most central Pb-Pb collisions at $\sqrt{s_{\rm {NN}}} = 5.02$ TeV in the transverse momentum interval 6 < $p_{\rm {T}}$ < 12 GeV/${\it {c}}$
The nuclear modification factor $R_\mathrm{AA}$ of prompt $\Lambda_{\rm {c}}^{+}$ baryons in 0-80% most central Pb-Pb collisions at $\sqrt{s_{\rm {NN}}} = 5.02$ TeV in the transverse momentum interval 6 < $p_{\rm {T}}$ < 12 GeV/${\it {c}}$
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