21 research outputs found

    Measurement of Ωc0\Omega^0_{\rm c} baryon production and branching-fraction ratio BR(Ωc0→Ω−e+νe)/BR(Ωc0→Ω−π+){\rm BR(\Omega^0_c \rightarrow \Omega^- e^+\nu_e)} / {\rm BR(\Omega^0_c \rightarrow \Omega^- \pi^+)} in pp collisions at s\sqrt{s} = 13 TeV

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    International audienceThe inclusive production of the charm-strange baryon Ωc0\Omega^{0}_{\rm c} is measured for the first time via its semileptonic decay into Ω−e+νe\Omega^{-}\rm e^{+}\nu_{e} at midrapidity (∣y∣<0.8|y|<0.8) in proton−-proton (pp) collisions at the centre-of-mass energy s=13\sqrt{s}=13 TeV with the ALICE detector at the LHC. The transverse momentum (pTp_{\rm T}) differential cross section multiplied by the branching ratio is presented in the interval 2<pT<12 GeV/c2<p_{\rm T}<12~{\rm GeV}/c. The branching-fraction ratio BR(Ωc0→Ω−e+νe)/BR(Ωc0→Ω−π+){\rm BR}(\Omega^0_{\rm c} \rightarrow \Omega^{-}{\rm e}^{+}\nu_{\rm e})/ {\rm BR}(\Omega^0_{\rm c} \rightarrow \Omega^{-}{\pi}^{+}) is measured to be 1.12 ±\pm 0.22 (stat.) ±\pm 0.27 (syst.). Comparisons with other experimental measurements, as well as with theoretical calculations, are presented

    Probing strangeness hadronization with event-by-event production of multistrange hadrons

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    This Letter presents the first measurement of event-by-event fluctuations of the net number (difference between the particle and antiparticle multiplicities) of multistrange hadrons Ξ−\Xi^- and Ξ‾+\overline{\Xi}^+ and its correlation with the net-kaon number using the data collected by the ALICE Collaboration in pp, p-Pb, and Pb-Pb collisions at a center-of-mass energy per nucleon pair sNN=5.02 TeV\sqrt{s_{\mathrm{NN}}}=5.02\ \mathrm{TeV}. The statistical hadronization model with a correlation over three units of rapidity between hadrons having the same and opposite strangeness content successfully describes the results. On the other hand, string-fragmentation models that mainly correlate strange hadrons with opposite strange quark content over a small rapidity range fail to describe the data.This Letter presents the first measurement of event-by-event fluctuations of the net number (difference between the particle and antiparticle multiplicities) of multistrange hadrons Ξ−\Xi^- and Ξ‾+\overline{\Xi}^+ and its correlation with the net-kaon number using the data collected by the ALICE Collaboration in pp, p−-Pb, and Pb−-Pb collisions at a center-of-mass energy per nucleon pair sNN=5.02 TeV\sqrt{s_{\mathrm{NN}}}=5.02\ \mathrm{TeV}. The statistical hadronization model with a correlation over three units of rapidity between hadrons having the same and opposite strangeness content successfully describes the results. On the other hand, string-fragmentation models that mainly correlate strange hadrons with opposite strange quark content over a small rapidity range fail to describe the data

    Measurement of Ωc0\Omega^0_{\rm c} baryon production and branching-fraction ratio BR(Ωc0→Ω−e+νe)/BR(Ωc0→Ω−π+){\rm BR(\Omega^0_c \rightarrow \Omega^- e^+\nu_e)} / {\rm BR(\Omega^0_c \rightarrow \Omega^- \pi^+)} in pp collisions at s\sqrt{s} = 13 TeV

    No full text
    International audienceThe inclusive production of the charm-strange baryon Ωc0\Omega^{0}_{\rm c} is measured for the first time via its semileptonic decay into Ω−e+νe\Omega^{-}\rm e^{+}\nu_{e} at midrapidity (∣y∣<0.8|y|<0.8) in proton−-proton (pp) collisions at the centre-of-mass energy s=13\sqrt{s}=13 TeV with the ALICE detector at the LHC. The transverse momentum (pTp_{\rm T}) differential cross section multiplied by the branching ratio is presented in the interval 2<pT<12 GeV/c2<p_{\rm T}<12~{\rm GeV}/c. The branching-fraction ratio BR(Ωc0→Ω−e+νe)/BR(Ωc0→Ω−π+){\rm BR}(\Omega^0_{\rm c} \rightarrow \Omega^{-}{\rm e}^{+}\nu_{\rm e})/ {\rm BR}(\Omega^0_{\rm c} \rightarrow \Omega^{-}{\pi}^{+}) is measured to be 1.12 ±\pm 0.22 (stat.) ±\pm 0.27 (syst.). Comparisons with other experimental measurements, as well as with theoretical calculations, are presented

    Measurement of Ωc0\Omega^0_{\rm c} baryon production and branching-fraction ratio BR(Ωc0→Ω−e+νe)/BR(Ωc0→Ω−π+){\rm BR(\Omega^0_c \rightarrow \Omega^- e^+\nu_e)} / {\rm BR(\Omega^0_c \rightarrow \Omega^- \pi^+)} in pp collisions at s\sqrt{s} = 13 TeV

    No full text
    International audienceThe inclusive production of the charm-strange baryon Ωc0\Omega^{0}_{\rm c} is measured for the first time via its semileptonic decay into Ω−e+νe\Omega^{-}\rm e^{+}\nu_{e} at midrapidity (∣y∣<0.8|y|<0.8) in proton−-proton (pp) collisions at the centre-of-mass energy s=13\sqrt{s}=13 TeV with the ALICE detector at the LHC. The transverse momentum (pTp_{\rm T}) differential cross section multiplied by the branching ratio is presented in the interval 2<pT<12 GeV/c2<p_{\rm T}<12~{\rm GeV}/c. The branching-fraction ratio BR(Ωc0→Ω−e+νe)/BR(Ωc0→Ω−π+){\rm BR}(\Omega^0_{\rm c} \rightarrow \Omega^{-}{\rm e}^{+}\nu_{\rm e})/ {\rm BR}(\Omega^0_{\rm c} \rightarrow \Omega^{-}{\pi}^{+}) is measured to be 1.12 ±\pm 0.22 (stat.) ±\pm 0.27 (syst.). Comparisons with other experimental measurements, as well as with theoretical calculations, are presented

    Charm fragmentation fractions and cc‾{\rm c\overline{c}} cross section in p−-Pb collisions at sNN=5.02\sqrt{s_{\rm NN}}=5.02 TeV

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    The total charm-quark production cross section per unit of rapidity dσ(cc‾)/dy\mathrm{d}\sigma({\rm c\overline{c}})/\mathrm{d}y, and the fragmentation fractions of charm quarks to different charm-hadron species f(c→hc)f(\mathrm{c}\rightarrow {\rm h_{c}}), are measured for the first time in p−-Pb collisions at sNN=5.02\sqrt{s_\mathrm{NN}} = 5.02 TeV at midrapidity (−0.96<y<0.04-0.96<y<0.04 in the centre-of-mass frame) using data collected by ALICE at the CERN LHC. The results are obtained based on all the available measurements of prompt production of ground-state charm-hadron species: D0\mathrm{D}^{0}, D+\mathrm{D}^{+}, Ds+\mathrm{D}_\mathrm{s}^{+}, and J/ψ\mathrm{J/\psi} mesons, and Λc+\Lambda_\mathrm{c}^{+} and Ξc0\Xi_{\rm c}^{0} baryons. The resulting cross section is dσ(cc‾)/dy=219.6±6.3  (stat.)  −11.8+10.5  (syst.)  −2.9+7.6  (extr.)±5.4  (BR)±4.6  (lumi.)±19.5  (rapidity shape)+15.0  (Ωc0) \mathrm{d}\sigma({\rm c\overline{c}})/\mathrm{d}y =219.6 \pm 6.3\;(\mathrm{stat.}) {\;}_{-11.8}^{+10.5}\;(\mathrm{syst.}) {\;}_{-2.9}^{+7.6}\;(\mathrm{extr.})\pm 5.4\;(\mathrm{BR})\pm 4.6\;(\mathrm{lumi.}) \pm 19.5\;(\text{rapidity shape})+15.0\;(\Omega_{\rm c}^{0}) mb, which is consistent with a binary scaling of pQCD calculations from pp collisions. The measured fragmentation fractions are compatible with those measured in pp collisions at s=5.02\sqrt{s} = 5.02 and 1313 TeV, showing an increase in the relative production rates of charm baryons with respect to charm mesons in pp and p–Pb collisions compared with e+e−\mathrm{e^{+}e^{-}} and e−p\mathrm{e^{-}p} collisions. The pTp_\mathrm{T}-integrated nuclear modification factor of charm quarks, RpPb(cc‾)=0.91±0.04  (stat.)−0.09+0.08  (syst.)−0.03+0.04  (extr.)±0.03  (lumi.)R_\mathrm{pPb}({\rm c\overline{c}})= 0.91 \pm 0.04\;{\rm (stat.)}{}^{+0.08}_{-0.09}\;{\rm (syst.)}{}^{+0.04}_{-0.03}\;{\rm (extr.)}{}\pm 0.03\;{\rm (lumi.)}, is found to be consistent with unity and with theoretical predictions including nuclear modifications of the parton distribution functions.The total charm-quark production cross section per unit of rapidity dσ(cc‾)/dy\mathrm{d}\sigma({\rm c\overline{c}})/\mathrm{d}y, and the fragmentation fractions of charm quarks to different charm-hadron species f(c→hc)f(\mathrm{c}\rightarrow {\rm h_{c}}), are measured for the first time in p−-Pb collisions at sNN=5.02\sqrt{s_\mathrm{NN}} = 5.02 TeV at midrapidity (−0.96<y<0.04-0.96<y<0.04 in the centre-of-mass frame) using data collected by ALICE at the CERN LHC. The results are obtained based on all the available measurements of prompt production of ground-state charm-hadron species: D0\mathrm{D}^{0}, D+\mathrm{D}^{+}, Ds+\mathrm{D}_\mathrm{s}^{+}, and J/ψ\mathrm{J/\psi} mesons, and Λc+\Lambda_\mathrm{c}^{+} and Ξc0\Xi_{\rm c}^{0} baryons. The resulting cross section is dσ(cc‾)/dy=219.6±6.3  (stat.)  −11.8+10.5  (syst.)  −2.9+7.6  (extr.)±5.4  (BR)±4.6  (lumi.)±19.5  (rapidity shape)+15.0  (Ωc0)\mathrm{d}\sigma({\rm c\overline{c}})/\mathrm{d}y =219.6 \pm 6.3\;(\mathrm{stat.}) {\;}_{-11.8}^{+10.5}\;(\mathrm{syst.}) {\;}_{-2.9}^{+7.6}\;(\mathrm{extr.})\pm 5.4\;(\mathrm{BR})\pm 4.6\;(\mathrm{lumi.}) \pm 19.5\;(\text{rapidity shape})+15.0\;(\Omega_{\rm c}^{0}) mb, which is consistent with a binary scaling of pQCD calculations from pp collisions. The measured fragmentation fractions are compatible with those measured in pp collisions at s=5.02\sqrt{s} = 5.02 and 1313 TeV, showing an increase in the relative production rates of charm baryons with respect to charm mesons in pp and p−-Pb collisions compared with e+e−\mathrm{e^{+}e^{-}} and e−p\mathrm{e^{-}p} collisions. The pTp_\mathrm{T}-integrated nuclear modification factor of charm quarks, RpPb(cc‾)=0.91±0.04  (stat.)−0.09+0.08  (syst.)−0.03+0.04  (extr.)±0.03  (lumi.)R_\mathrm{pPb}({\rm c\overline{c}})= 0.91 \pm 0.04\;{\rm (stat.)}{}^{+0.08}_{-0.09}\;{\rm (syst.)}{}^{+0.04}_{-0.03}\;{\rm (extr.)}{}\pm 0.03\;{\rm (lumi.)}, is found to be consistent with unity and with theoretical predictions including nuclear modifications of the parton distribution functions

    Investigating strangeness enhancement in jet and medium via Ï•\phi(1020) production in p-Pb collisions at sNN\sqrt{s_{\rm NN}} = 5.02 TeV

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    This work aims to differentiate strangeness produced from hard processes (jet-like) and softer processes (underlying event) by measuring the angular correlation between a high-momentum trigger hadron (h) acting as a jet-proxy and a produced strange hadron (ϕ(1020)\phi(1020) meson). Measuring h−ϕ-\phi correlations at midrapidity in p−-Pb collisions at sNN\sqrt{s_{\rm NN}} = 5.02 TeV as a function of event multiplicity provides insight into the microscopic origin of strangeness enhancement in small collision systems. The jet-like and the underlying-event-like strangeness production are investigated as a function of event multiplicity. They are also compared between a lower and higher momentum region. The evolution of the per-trigger yields within the near-side (aligned with the trigger hadron) and away-side (in the opposite direction of the trigger hadron) jet is studied separately, allowing for the characterization of two distinct jet-like production regimes. Furthermore, the h−ϕ-\phi correlations within the underlying event give access to a production regime dominated by soft production processes, which can be compared directly to the in-jet production. Comparisons between h−ϕ-\phi and dihadron correlations show that the observed strangeness enhancement is largely driven by the underlying event, where the ϕ/h\phi/\mathrm{h} ratio is significantly larger than within the jet regions. As multiplicity increases, the fraction of the total ϕ(1020)\phi(1020) yield coming from jets decreases compared to the underlying event production, leading to high-multiplicity events being dominated by the increased strangeness production from the underlying event.This work aims to differentiate strangeness produced from hard processes (jet-like) and softer processes (underlying event) by measuring the angular correlation between a high-momentum trigger hadron (h) acting as a jet-proxy and a produced strange hadron (ϕ(1020)\phi(1020) meson). Measuring h−ϕ-\phi correlations at midrapidity in p−-Pb collisions at sNN\sqrt{s_{\rm NN}} = 5.02 TeV as a function of event multiplicity provides insight into the microscopic origin of strangeness enhancement in small collision systems. The jet-like and the underlying-event-like strangeness production are investigated as a function of event multiplicity. They are also compared between a lower and higher momentum region. The evolution of the per-trigger yields within the near-side (aligned with the trigger hadron) and away-side (in the opposite direction of the trigger hadron) jet is studied separately, allowing for the characterization of two distinct jet-like production regimes. Furthermore, the h−ϕ-\phi correlations within the underlying event give access to a production regime dominated by soft production processes, which can be compared directly to the in-jet production. Comparisons between h−ϕ-\phi and dihadron correlations show that the observed strangeness enhancement is largely driven by the underlying event, where the ϕ/h\phi/\mathrm{h} ratio is significantly larger than within the jet regions. As multiplicity increases, the fraction of the total ϕ(1020)\phi(1020) yield coming from jets decreases compared to the underlying event production, leading to high-multiplicity events being dominated by the increased strangeness production from the underlying event

    Investigating Λ\Lambda baryon production in p−-Pb collisions in jets and underlying event using angular correlations

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    This paper presents the first measurements of hadron(h)−Λ-\Lambda azimuthal angular correlations in p−-Pb collisions at sNN\sqrt{s_{\rm NN}} = 5.02 TeV using the ALICE detector at the LHC. These correlations are used to separate the production of associated Λ\Lambda baryons into three different kinematic regions, namely those produced in the direction of the trigger particle (near-side), those produced in the opposite direction (away-side), and those whose production is uncorrelated with the jet-axis (underlying event). The per-trigger associated Λ\Lambda yields in these regions are extracted, along with the near- and away-side azimuthal peak widths, and the results are studied as a function of associated particle pTp_{\rm T} and event multiplicity. Comparisons with the DPMJET event generator and previous measurements of the ϕ(1020)\phi(1020) meson are also made. The final results indicate that strangeness production in the highest multiplicity p−-Pb collisions is enhanced relative to low multiplicity collisions in the jet-like regions, as well as the underlying event. The production of Λ\Lambda relative to charged hadrons is also enhanced in the underlying event when compared to the jet-like regions. Additionally, the results hint that strange quark production in the away-side of the jet is modified by soft interactions with the underlying event.First measurements of hadron(h)−Λ-\Lambda azimuthal angular correlations in p−-Pb collisions at sNN\sqrt{s_{\rm NN}} = 5.02 TeV using the ALICE detector at the LHC are presented. These correlations are used to separate the production of associated Λ\Lambda baryons into three different kinematic regions, namely those produced in the direction of the trigger particle (near-side), those produced in the opposite direction (away-side), and those whose production is uncorrelated with the jet-axis (underlying event). The per-trigger associated Λ\Lambda yields in these regions are extracted, along with the near- and away-side azimuthal peak widths, and the results are studied as a function of associated particle pTp_{\rm T} and event multiplicity. Comparisons with the DPMJET event generator and previous measurements of the ϕ(1020)\phi(1020) meson are also made. The final results indicate that strangeness production in the highest multiplicity p−-Pb collisions is enhanced relative to low multiplicity collisions in the jet-like regions, as well as the underlying event. The production of Λ\Lambda relative to charged hadrons is also enhanced in the underlying event when compared to the jet-like regions. Additionally, the results hint that strange quark production in the away-side of the jet is modified by soft interactions with the underlying event

    Measurement of Λ3H{}_{\Lambda}^{3}\mathrm{H} production in Pb−-Pb collisions at sNN\sqrt{s_{\mathrm{NN}}} = 5.02 TeV

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    The first measurement of Λ3H_{\Lambda}^{3}\mathrm{H} and Λ‾3H‾^3_ {\overline{\Lambda}}\overline{\mathrm{H}} differential production with respect to transverse momentum and centrality in Pb−-Pb collisions at sNN=5.02\sqrt{s_{\mathrm{NN}}}=5.02~TeV is presented. The Λ3H_{\Lambda}^{3}\mathrm{H} has been reconstructed via its two-charged-body decay channel, i.e., Λ3H→3He+π−_{\Lambda}^{3}\mathrm{H} \rightarrow {}^{3}\mathrm{He} + \pi^{-}. A Blast-Wave model fit of the pTp_{\rm T}-differential spectra of all nuclear species measured by the ALICE collaboration suggests that the Λ3H_{\Lambda}^{3}\mathrm{H} kinetic freeze-out surface is consistent with that of other nuclei. The ratio between the integrated yields of Λ3H_{\Lambda}^{3}\mathrm{H} and 3He^3\mathrm{He} is compared to predictions from the statistical hadronisation model and the coalescence model, with the latter being favoured by the presented measurements.The first measurement of Λ3H_{\Lambda}^{3}\mathrm{H} and Λ‾3H‾^3_ {\overline{\Lambda}}\overline{\mathrm{H}} differential production with respect to transverse momentum and centrality in Pb−-Pb collisions at sNN=5.02\sqrt{s_{\mathrm{NN}}}=5.02~TeV is presented. The Λ3H_{\Lambda}^{3}\mathrm{H} has been reconstructed via its two-charged-body decay channel, i.e., Λ3H→3He+π−_{\Lambda}^{3}\mathrm{H} \rightarrow {}^{3}\mathrm{He} + \pi^{-}. A Blast-Wave model fit of the pTp_{\rm T}-differential spectra of all nuclear species measured by the ALICE collaboration suggests that the Λ3H_{\Lambda}^{3}\mathrm{H} kinetic freeze-out surface is consistent with that of other nuclei. The ratio between the integrated yields of Λ3H_{\Lambda}^{3}\mathrm{H} and 3He^3\mathrm{He} is compared to predictions from the statistical hadronisation model and the coalescence model, with the latter being favoured by the presented measurements

    Measurement of the production cross section of prompt Ξc0\Xi^0_{\rm c} baryons in p−-Pb collisions at sNN=5.02\sqrt{s_{\mathrm{NN}}}=5.02 TeV

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    The transverse momentum (pTp_{\rm T}) differential production cross section of the promptly-produced charm-strange baryon Ξc0\Xi_{\rm c}^{0} (and its charge conjugate Ξc0‾\overline{\Xi_{\rm c}^{0}}) is measured at midrapidity via its hadronic decay into π+Ξ−{\rm \pi^{+}}\Xi^{-} in p−-Pb collisions at a centre-of-mass energy per nucleon−-nucleon collision sNN = 5.02\sqrt{s_{\mathrm{NN}}}~=~5.02 TeV with the ALICE detector at the LHC. The Ξc0\Xi_{\rm c}^{0} nuclear modification factor (RpPbR_{\rm pPb}), calculated from the cross sections in pp and p−-Pb collisions, is presented and compared with the RpPbR_{\rm pPb} of Λc+\Lambda_{\rm c}^{+} baryons. The ratios between the pTp_{\rm T}-differential production cross section of Ξc0\Xi_{\rm c}^{0} baryons and those of D0\mathrm {D^0} mesons and Λc+\Lambda_{\rm c}^{+} baryons are also reported and compared with results at forward and backward rapidity from the LHCb Collaboration. The measurements of the production cross section of prompt Ξc0\Xi^0_{\rm c} baryons are compared with a model based on perturbative QCD calculations of charm-quark production cross sections, which includes only cold nuclear matter effects in p−-Pb collisions, and underestimates the measurement by a factor of about 50. This discrepancy is reduced when the data is compared with a model in which hadronisation is implemented via quark coalescence. The pTp_{\rm T}-integrated cross section of prompt Ξc0\Xi^0_{\rm c}-baryon production at midrapidity extrapolated down to pTp_{\rm T} = 0 is also reported. These measurements offer insights and constraints for theoretical calculations of the hadronisation process. Additionally, they provide inputs for the calculation of the charm production cross section in p−-Pb collisions at midrapidity.The transverse momentum (pTp_{\rm T}) differential production cross section of the promptly-produced charm-strange baryon Ξc0\Xi_{\rm c}^{0} (and its charge conjugate Ξc0‾\overline{\Xi_{\rm c}^{0}}) is measured at midrapidity via its hadronic decay into π+Ξ−{\rm \pi^{+}}\Xi^{-} in p−-Pb collisions at a centre-of-mass energy per nucleon−-nucleon collision sNN = 5.02\sqrt{s_{\mathrm{NN}}}~=~5.02 TeV with the ALICE detector at the LHC. The Ξc0\Xi_{\rm c}^{0} nuclear modification factor (RpPbR_{\rm pPb}), calculated from the cross sections in pp and p−-Pb collisions, is presented and compared with the RpPbR_{\rm pPb} of Λc+\Lambda_{\rm c}^{+} baryons. The ratios between the pTp_{\rm T}-differential production cross section of Ξc0\Xi_{\rm c}^{0} baryons and those of D0\mathrm {D^0} mesons and Λc+\Lambda_{\rm c}^{+} baryons are also reported and compared with results at forward and backward rapidity from the LHCb Collaboration. The measurements of the production cross section of prompt Ξc0\Xi^0_{\rm c} baryons are compared with a model based on perturbative QCD calculations of charm-quark production cross sections, which includes only cold nuclear matter effects in p−-Pb collisions, and underestimates the measurement by a factor of about 50. This discrepancy is reduced when the data is compared with a model in which hadronisation is implemented via quark coalescence. The pTp_{\rm T}-integrated cross section of prompt Ξc0\Xi^0_{\rm c}-baryon production at midrapidity extrapolated down to pTp_{\rm T} = 0 is also reported. These measurements offer insights and constraints for theoretical calculations of the hadronisation process. Additionally, they provide inputs for the calculation of the charm production cross section in p−-Pb collisions at midrapidity

    Measurement of Ωc0\Omega^0_{\rm c} baryon production and branching-fraction ratio BR(Ωc0→Ω−e+νe)/BR(Ωc0→Ω−π+){\rm BR(\Omega^0_c \rightarrow \Omega^- e^+\nu_e)} / {\rm BR(\Omega^0_c \rightarrow \Omega^- \pi^+)} in pp collisions at s\sqrt{s} = 13 TeV

    No full text
    International audienceThe inclusive production of the charm-strange baryon Ωc0\Omega^{0}_{\rm c} is measured for the first time via its semileptonic decay into Ω−e+νe\Omega^{-}\rm e^{+}\nu_{e} at midrapidity (∣y∣<0.8|y|<0.8) in proton−-proton (pp) collisions at the centre-of-mass energy s=13\sqrt{s}=13 TeV with the ALICE detector at the LHC. The transverse momentum (pTp_{\rm T}) differential cross section multiplied by the branching ratio is presented in the interval 2<pT<12 GeV/c2<p_{\rm T}<12~{\rm GeV}/c. The branching-fraction ratio BR(Ωc0→Ω−e+νe)/BR(Ωc0→Ω−π+){\rm BR}(\Omega^0_{\rm c} \rightarrow \Omega^{-}{\rm e}^{+}\nu_{\rm e})/ {\rm BR}(\Omega^0_{\rm c} \rightarrow \Omega^{-}{\pi}^{+}) is measured to be 1.12 ±\pm 0.22 (stat.) ±\pm 0.27 (syst.). Comparisons with other experimental measurements, as well as with theoretical calculations, are presented
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