Measurement of the cross sections of $\Xi^0_{\rm c}$ and $\Xi^+_{\rm c}$ baryons and branching-fraction ratio BR($\Xi^0_{\rm c} \rightarrow \Xi^-{\rm e}^+\nu_{\rm e}$)/BR($\Xi^0_{\rm c} \rightarrow \Xi^-\pi^+$) in pp collisions at 13 TeV

The $p_{\rm T}$-differential cross sections of prompt charm-strange baryons $\Xi^0_{\rm c}$ and $\Xi^+_{\rm c}$ were measured at midrapidity ($|y|<0.5$) in proton$-$proton (pp) collisions at a centre-of-mass energy $\sqrt{s}=13$ TeV with the ALICE detector at the LHC. The $\Xi^0_{\rm c}$ baryon was reconstructed via both the semileptonic decay ($\Xi^{-}{\rm e^{+}}\nu_{\rm e}$) and the hadronic decay ($\Xi^{-}{\rm \pi^{+}}$) channels. The $\Xi^+_{\rm c}$ baryon was reconstructed via the hadronic decay ($\Xi^{-}\pi^{+}\pi^{+}$) channel. The branching-fraction ratio $\rm {\rm BR}(\Xi_c^0\rightarrow \Xi^-e^+\nu_e)/\rm {\rm BR}(\Xi_c^0\rightarrow \Xi^{-}\pi^+)=$ 1.38 $\pm$ 0.14 (stat) $\pm$ 0.22 (syst) was measured with a total uncertainty reduced by a factor of about 3 with respect to the current world average reported by the Particle Data Group. The transverse momentum ($p_{\rm T}$) dependence of the $\Xi^0_{\rm c}$- and $\Xi^+_{\rm c}$-baryon production relative to the ${\rm D^0}$-meson and to the $\Sigma^{0,+,++}_{\rm c}$- and $\Lambda^+_{\rm c}$-baryon production are reported. The baryon-to-meson ratio increases towards low $p_{\rm T}$ up to a value of approximately 0.3. The measurements are compared with various models that take different hadronisation mechanisms into consideration. The results provide stringent constraints to these theoretical calculations and additional evidence that different processes are involved in charm hadronisation in electron$-$positron ($\rm e^+e^-$) and hadronic collisions.

The Ξ 0 c → Ξ − e + ν e analysis was performed using the technique reported in Ref. [21].The Ξ 0 c candidates were defined from opposite-sign charge eΞ pairs with an opening angle smaller than 90 • .In order to reject electrons from photon conversions occurring in the detector material, the electron-candidate tracks are required to have associated hits in the two innermost layers of the ITS [41,42].Further rejection of background electrons originating from Dalitz decays of neutral mesons and photon conversions was performed using a technique based on the invariant mass of e + e − pairs [43,44].The electron (positron) candidates were paired with opposite-sign charge tracks from the same event and are rejected if they form at least one e + e − pair with an invariant mass smaller than 50 MeV/c 2 .A correction for the misidentification probability was implemented, estimated to be 2% by applying the algorithm to same-sign charge e ± e ± pairs.The background in the e + Ξ − pair distribution is estimated by exploiting the fact that Ξ 0 c baryons decay into e + Ξ − νe , but not into e − Ξ − νe , while most of the background sources contribute equally to both samples.The yield of same-sign charge pairs is therefore used to estimate the background.The Ξ 0 c raw yield was then obtained by subtracting the distribution of same-sign charge eΞ-pairs from the distribution of opposite-sign charge pairs, and integrating the invariant-mass distribution for M(eΞ) < 2.5 GeV/c 2 .The procedure was verified with PYTHIA 8.2 [39] simulations and the GEANT 3 transport code.A similar procedure was adopted by the ARGUS and CLEO Collaborations [45,46].The same-sign charge pairs also contain a contribution from Ξ 0,− b → e − Ξ − νe X decays not present in the distribution of opposite-sign charge pairs, leading to an oversubtraction.It was corrected for based on the assumptions reported in Ref. [21] and ranges from 1% to 4%, depending on p T .The p T distribution of e + Ξ − pairs was corrected for the missing momentum of the undetected neutrino using the Bayesian unfolding technique [47] implemented in the RooUnfold package [48].Additional information on the unfolding procedure is reported in the additional material [49].
The raw yields were divided by the acceptance-times-efficiency for prompt hadrons, (Acc × ε) prompt , and were corrected for the beauty feed-down contribution.The (Acc × ε) prompt corrections were obtained from a Monte Carlo simulation with the same configuration of the one used for the BDT training.The simulated Ξ c p T distributions were modified by a two step iterative procedure in order to mimic data.In the first step, the Ξ c reconstruction efficiency is obtained with the p T distribution generated with Systematic uncertainties were estimated considering several sources.For the hadronic decay channels, the systematic uncertainty on the raw-yield extraction was evaluated by repeating the fit of the invariantmass distribution with varied fit interval, functional form of the background contribution, and width of the Gaussian function used to describe the signal peak.For the Ξ 0 c in the semileptonic decay channel, the raw-yield extraction systematic uncertainty was estimated by varying the selection criteria on the opening angle and on the invariant mass of the pair.The systematic uncertainties were defined as the RMS of the distribution of the signal yields obtained from these variations.The relative uncertainty on raw-yield extraction ranges from 7% to 11% depending on the p T .The uncertainty on the track reconstruction efficiency was evaluated by varying the track-selection criteria and by comparing the probability to prolong the tracks from the TPC to the ITS hits in data and simulations.A 5% (7%) uncertainty was assigned for the Ξ 0 c (Ξ + c ).The uncertainty on the selection efficiency originates mainly from imperfections in the description of the detector response and alignment in the simulation.It was estimated from the ratios of the corrected yields obtained by varying the BDT and topological selections applied; an uncertainty ranging from 2% to 5% was assigned.The systematic uncertainty due to the shape of the Ξ c p T distributions used for the calculation of (Acc × ε) prompt was estimated by considering different p T shapes in the simulation, obtained by varying the weights mentioned above within their uncertainty [21] and it amounts to 1% for p T < 3 GeV/c.The systematic uncertainty on the subtraction of feed-down from beauty-hadron decays was evaluated as in Ref.
[15] and additionally by scaling up the Ξ c /Λ + c ratio by a conservative factor of two and scaling it down to the Ξ − b /Λ 0 b ratio measured by the LHCb Collaboration [50], important in the case that BR . The assigned uncertainty ranges from 1% to 9% depending on p T .Additional uncertainties related only to the Ξ 0 c semileptonic decay channel were estimated as follows.The uncertainties related to the unfolding procedure were estimated by varying the number of iterations of the algorithm, the p T range and the widths of the p T intervals used in the Bayesian unfolding procedure, and the unfolding method itself to the Singular Value Decomposition [51], and ranges from 2% to 12% depending on p T .The systematic uncertainty related to the oversubtraction due to the Ξ b contribution in the same-sign charge eΞ pairs was estimated by scaling the assumed Ξ b momentum distribution by a conservative 50% [52].A maximum of 2% uncertainty was assigned at high p T .A 2% uncertainty was assigned to account for possible differences in the acceptance of e + Ξ − pairs in data and simulation, which is evaluated by performing the measurement in different rapidity intervals between |y| < 0.5 and 0.8.The cross sections have an additional global normalisation uncertainty due to the uncertainties on the integrated luminosity [34] and the BRs [30,31].The Ξ 0 c measurements in the two decay channels agree within statistical and uncorrelated systematic uncertainties [49].The results from the two decay channels were combined to obtain a more precise measurement of the prompt p T -differential Ξ 0 c -baryon cross section.The tracking and feed-down systematic uncertainties were propagated as correlated between the two measurements.Figure 1 shows the average of the cross sections, computed considering as weights the inverse square of the relative statistical and p T -uncorrelated systematic uncertainties [53].The prompt Ξ + c -baryon cross section, also shown in  = 14.9 ± 2.0 (stat) ± 6.6 (syst) ± 0.2 (lumi) µb.In calculating the p T -integrated cross section and the ratio of the branching fractions, the systematic uncertainty related to unfolding, for the Ξ 0 c → Ξ − e + ν e , was considered as p T uncorrelated and the other uncertainties as fully p T correlated.For the hadronic decay channels, the uncertainty related to the raw-yield extraction was considered p T uncorrelated, because the signal-over-background ratio is observed to largely vary as a function of p T , while the others as fully p T correlated.The p T -integrated Ξ 0 c cross section at midrapidity was obtained by extrapolating the visible cross section to the full p T range.The p T dependence of the Catania model [28], which better describes the shape of the measured cross section with respect to other model calculations as seen in Fig. 2, was used to calculate the extrapolation factor, which is 1.29 +0.12 −0.08 .The systematic uncertainty was estimated considering calculations [22,23,27] that describe the shape of the cross section in the measured p T interval.The p T -extrapolated cross section for the Ξ 0 c is dσ pp, 13 TeV /dy |y|<0.5 = 193.1 ± 26.8 (stat) ± 46.0 (syst) ± 3.1 (lumi) +17.6  −11.9 (extrap) µb.The measurement of the Ξ 0 c -baryon cross sections, not corrected by the BRs, in the two different decay channels allowed the computation of the BR(Ξ 0 c → Ξ − e + ν e )/BR(Ξ 0 c → Ξ − π + ) ratio.The p T -dependent ratio of the two measurements, which was observed to be flat in p T [49], was averaged over p T using the inverse uncorrelated relative uncertainties as weights [53].The final systematic uncertainty on the ratio was obtained by summing in quadrature the p T -correlated and uncorrelated systematic uncertainties.The measured ratio is BR(Ξ 0 c → Ξ − e + ν e )/BR(Ξ 0 c → Ξ − π + ) = 1.38 ± 0.14 (stat) ± 0.22 (syst).The result is consistent with the global average reported by the PDG (1.3 ± 0.8) [30] and has a total uncertainty reduced by a factor of 3. The result is also consistent with the one released by the Belle Collaboration [54]., while the Ξ c /D 0 ratio is generally lower.This result provides strong indications that the fragmentation functions of baryons and mesons differ significantly.The PYTHIA 8.2 event generator with the Monash tune [39], and tunes that implement colour reconnection (CR) beyond the leading-colour approximation [22], which lead to an increased baryon production, were compared to the measurements.The Monash tune significantly underestimates the data by a factor of 23-43 in the low-p T region and by a factor of about 5 in the highest p T interval.All three CR modes give a similar magnitude and p T -dependence of Ξ c /D 0 , and although they predict a larger baryon-to-meson ratio with respect to the Monash tune, they still underestimate the measured Ξ c /D 0 ratio by a factor 4-9 for p T < 4 GeV/c.The measured Ξ c /D 0 ratio was also compared to a SHM [23] that includes additional excited charm-baryon states not yet observed but predicted by the RQM [24] and by lattice QCD [25].While this model describes the Λ + c /D 0 and Σ 0,+,++ c /D 0 ratios [15,26], it underestimates the Ξ c /D 0 ratio.The measured ratios were also compared with models that include hadronisation via coalescence.In the quark (re-)combination mechanism (QCM) [27], the charm quark can pick up a comoving light antiquark or two comoving quarks to form a single-charm meson or baryon.The model does not describe the Ξ c /D 0 ratio.The Catania model [28,55] implements charm-quark hadronisation via both coalescence and fragmentation, and it is the model that is closer to the measured ratio over the full p T interval.hadronisation in pp collisions.Finally, the ratio BR(Ξ 0 c → Ξ − e + ν e )/BR(Ξ 0 c → Ξ − π + ) was measured with a total uncertainty reduced by a factor 3 with respect to the global average reported by the PDG [30].
Ξ 0 c and Ξ + c production in pp collisions at √ s = 13 TeV ALICE Collaboration Fig 1, is compatible within the uncertainties with the Ξ 0 c measurement.lumi.unc.not shown ±

Figure 1 :
Figure 1: Cross sections of prompt Ξ 0 c (full circles) and Ξ + c (open circles) baryons as a function of p T in pp collisions at √ s = 13 TeV.The error bars and empty boxes represent the statistical and systematic uncertainties, respectively.The systematic uncertainties on the BR are shown as shaded boxes.

Figure 2
Figure2(left) shows the Ξ c /D 0 ratios measured as a function of p T .The systematic uncertainties related to the track-reconstruction efficiency, feed-down subtraction, and luminosity were propagated as correlated in the ratio.The observed p T dependence of the Ξ c /D 0 ratio is similar to what was measured for the Λ + c /D 0 ratio [15], while the Ξ c /D 0 ratio is generally lower.This result provides strong indications that the fragmentation functions of baryons and mesons differ significantly.The PYTHIA 8.2 event generator with the Monash tune[39], and tunes that implement colour reconnection (CR) beyond the leading-colour approximation[22], which lead to an increased baryon production, were compared to the measurements.The Monash tune significantly underestimates the data by a factor of 23-43 in the low-p T region and by a factor of about 5 in the highest p T interval.All three CR modes give a similar magnitude and p T -dependence of Ξ c /D 0 , and although they predict a larger baryon-to-meson ratio with respect to the Monash tune, they still underestimate the measured Ξ c /D 0 ratio by a factor 4-9 for p T < 4 GeV/c.The measured Ξ c /D 0 ratio was also compared to a SHM[23] that includes additional excited charm-baryon states not yet observed but predicted by the RQM[24] and by lattice QCD[25].While this model describes the Λ + c /D 0 and Σ 0,+,++

Figure 2 :
Figure 2: Left panel: Ξ 0 c /D 0 and Ξ + c /D 0 ratios as a function of p T in pp collisions at √ s = 13 TeV.Right panel: