First measurement of $\rm \Omega_c^0$ production in pp collisions at $\sqrt{s}=13$ TeV

The inclusive production of the charm-strange baryon $\rm \Omega_c^0$ is measured for the first time via its hadronic decay into $\rm \Omega^-\pi^+$ at midrapidity ($|y|<0.5$) in proton-proton (pp) collisions at the centre-of-mass energy $\sqrt{s}=13$ TeV with the ALICE detector at the LHC. The transverse momentum ($p_{\rm T}$) differential cross section multiplied by the branching ratio is presented in the interval $2<p_{\rm T}<12~{\rm GeV}/c$. The $p_{\rm T}$ dependence of the $\rm \Omega_c^0$-baryon production relative to the prompt $\rm D^0$-meson and to the prompt $\rm \Xi_c^0$-baryon production is compared to various models that take different hadronisation mechanisms into consideration. In the measured $p_{\rm T}$ interval, the ratio of the $p_{\rm T}$-integrated cross sections of $\rm \Omega_c^0$ and prompt $\Lambda_{\rm c}^{+}$ baryons multiplied by the $\rm \Omega^-\pi^+$ branching ratio is found to be larger by a factor of about 20 with a significance of about 4$\sigma$ when compared to $\rm e^+e^-$ collisions.

A description of the ALICE detector and its performance can be found in Refs.[29,30].The main detectors used for this measurement are the Inner Tracking System (ITS), the Time Projection Chamber (TPC), and the Time-Of-Flight detector (TOF).They are located in the central barrel, which covers the pseudorapidity interval (|η| < 0.9), and are embedded in a solenoidal magnet that provides a B = 0.5 T field parallel to the beam direction.The ITS is used for tracking, vertex reconstruction, and trigger purposes.The TPC is the main tracking detector in the central barrel and is also used for particle identification (PID) via the measurement of the particle specific energy loss (dE/dx).The TOF provides PID information via the measurement of the particle time-of-flight relative to the time of the collision [31].The analysed data sample consists of pp collisions at √ s = 13 TeV recorded with a minimum-bias (MB) trigger based on coincident signals in the two scintillator arrays (V0) located on both sides of the nominal interaction point along the beam direction.Offline selection criteria, based on the signals from the V0 and the Silicon Pixel Detector, which constitutes the two innermost ITS layers, were applied to remove background due to the interaction between one of the beams and the residual gas present in the beam vacuum tube as well as other machine-induced backgrounds [32].Events with multiple reconstructed primary vertices, which amount to 1% of the total event sample, were rejected to reduce the contamination from the superposition of several collisions within the same colliding bunches (pile-up events).Only events with a primary vertex position within 10 cm from the nominal interaction point along the beam direction were used.After the aforementioned selections, the data sample corresponds to an integrated luminosity L int = 32.08 ± 0.51 nb −1 [33].
Ω 0 c production in pp collisions at The Ω 0 c -baryon candidates were built from Ω − π + pairs using a Kalman-Filter (KF) vertexing algorithm [34] by combining a positive charged track (π + candidate) originating from the primary vertex and a Ω − -baryon candidate.The Ω − was reconstructed from the decay chain Ω − → ΛK − , BR = (67.8± 0.7)%, followed by Λ → pπ − , BR = (63.9± 0.5)% [35].The Ω − and Λ baryons were reconstructed by exploiting their characteristic decay topologies as reported in Refs.[5,36].The tracks of the charged particles involved in the decay chain were required to be in the pseudorapidity interval |η| < 0.8, to have at least 70 out of 159 crossed TPC tracking points, and to have a fit quality χ 2 /NDF < 2 in the TPC.Moreover, primary π + candidates were required to have a minimum of four (out of six) hits in the ITS.Protons, pions, and kaons were selected by requiring compatibility within four standard deviations (4σ ) between the measured signal and that expected for the respective particle hypothesis for both the TPC dE/dx and the time-of-flight measurement.Tracks without signal in the TOF detector were identified using only the TPC information.In order to reduce the large combinatorial background, a machine-learning approach based on the adaptive Boosted Decision Tree (BDT) algorithm in the Toolkit for Multivariate Data Analysis (TMVA) [37] was used.The signal sample of Ω 0 c baryons for the BDT training was obtained from a simulation based on the PYTHIA 8.243 event generator [17].The mean proper lifetime of Ω 0 c in the simulation was set to 80 µm according to the latest LHCb measurement [38].The propagation of the generated particles through the detector was performed using the GEANT 3 package [39].The luminous region distribution and the conditions of all ALICE detectors in terms of active channels, gain, noise level, and alignment, and their evolution with time during the data taking, were taken into account in the simulations.The background candidates were taken from data by selecting candidates with invariant mass in the intervals 2.39 < M < 2.62 GeV/c 2 and 2.77 < M < 2.99 GeV/c 2 , which are outside of the expected mass peak of the Ω 0 c .Before the training, loose selections were applied on the distance, normalised to its uncertainty, between the Λ decay point and the primary vertex, and on the Λ, Ω − , and Ω 0 c χ 2 geo /NDF, which is a variable calculated by the KF Particle algorithm [34] related to the intersection probability of the daughter-particle trajectories taking their uncertainties into account.The BDT model was trained independently for each p T interval with variables related to the Ω − decay topology, such as the distance of closest approach (DCA) of the decay particles, the DCA between the primary vertex and the reconstructed Ω − candidate, the pointing angle of the reconstructed Ω − decay vertex to the reconstructed Ω 0 c decay vertex, the χ 2 geo /NDF, and the χ 2 topo /NDF.The χ 2 topo /NDF is calculated by the KF Particle [34] algorithm and characterises whether the Ω − candidate points back to the reconstructed Ω 0 c decay vertex.The output of the BDT training allows the classification of each candidate with a number related to its probability to be a Ω 0 c baryon signal or combinatorial background.The Ω 0 c raw yields were obtained from the fit to the invariant-mass distribution of the candidates as shown in the left panel of Fig. 1.The signal peak was modelled with a Gaussian function and the background was described by a linear function.
The p T and y-differential production cross section in the rapidity interval |y| < 0.5 of inclusive Ω 0 c baryons multiplied by the branching ratio into the considered hadronic decay channel was calculated from the raw yields as follows where is the raw yield in a given p T interval with width ∆p T and in the rapidity interval ∆y = 1.6 assuming that the cross section does not vary significantly from |y| < 0.5 to |y| < 0.8.To confirm that this assumption has a negligible impact on the result, it was verified that by assuming the rapidity dependence expected for charm mesons in FONLL [40,41] and for charm baryons in PYTHIA 8 [17] the cross section changes by less than 1% in the measured p T interval.Since the feed-down contribution is not subtracted, the raw yield is divided by the inclusive acceptance-times-efficiency factor, (Acc × ε) inclusive  Systematic uncertainties were estimated considering several sources.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 6% uncertainty was assigned.The systematic uncertainty on the selection efficiency derives from possible differences between the detector resolutions and alignment and their description in the simulation.This uncertainty was assessed from the comparison of the corrected yields obtained by varying the selections.In particular, the selections on the BDT outputs were varied separately in the different p T intervals, with a corresponding variation of the efficiencies ranging from 30% to 50% depending on p T .The assigned systematic uncertainty is 10%, which represents the largest contribution to the systematic uncertainty of the measurement.The systematic uncertainty due to the shape of the Ω 0 c p T spectrum used in the simulation for the calculation of the (Acc × ε) inclusive factor was estimated by modifying the weights mentioned above within their uncertainties.An uncertainty of about 4% was estimated in the p T interval 2 < p T < 4 GeV/c and a 2% uncertainty in 4 < p T < 12 GeV/c.The systematic uncertainty on the raw-yield extraction was evaluated in each p T interval by repeating the fit to the invariant-mass distributions varying the function Ω 0 c production in pp collisions at √ s = 13 TeV ALICE Collaboration used to describe the background and the fit range.In order to test the sensitivity to the line-shape of the signal, a bin-counting method was used, in which the signal yield was obtained by integrating the invariant-mass distribution after subtracting the combinatorial background.A 6% uncertainty was assigned independent of p T .The sources of systematic uncertainty are assumed to be uncorrelated among each other and the total systematic uncertainty in each p T interval is calculated by a quadratic sum of the individual contributions, resulting in a 14% systematic uncertainty in 2 < p T < 4 GeV/c and 13% in 4 < p T < 12 GeV/c.The production cross section has an additional global normalisation uncertainty of 1.6% due to the integrated luminosity determination [33].
The p T -differential production cross section of inclusive Ω 0 c baryons multiplied by the branching ratio of the Ω − π + channel measured in the rapidity interval |y| < 0.5 and the p T interval 2 < p T < 12 GeV/c are shown in Fig. 2. The feed-down contribution from Ω − b , e.g.
, is not subtracted because of the lack of knowledge of the branching ratios of b-hadron decays to Ω 0 c .Given that the efficiencies of prompt and feed-down Ω 0 c are consistent within uncertainties, the inclusive measurement presented here preserve the original relative abundances of its prompt and feed-down components.The data are compared with the inclusive Ω 0 c p T -differential cross sections expected from the PYTHIA 8.243 Monash and CR-BLC tunes (Mode 2) [9,17,19] multiplied by the branching ratio, BR(Ω 0 c → Ω − π + ) = (0.51 +2.19 −0.31 )%, obtained by considering the estimate reported in Ref. [42] for the central value, and the envelope of the values (including their uncertainties) reported in Refs.[42][43][44][45][46][47] to determine the uncertainty.In the p T interval of the measurement, the cross section from the CR-BLC tune is larger than the one from the Monash tune by factor varying between 9 and 25 depending on p T .The Monash tune and CR-BLC tune underestimate the data by more than 3.3σ and 2.7σ , respectively, when BR(Ω 0 c → Ω − π + ) = 0.51% +2.19% −0.31% is considered.The error bars and empty boxes represent the statistical and systematic uncertainties, respectively.The measurement is compared with PYTHIA 8.243 with Monash tune [19] and with CR beyond the leading-colour approximation [9], which are multiplied by a theoretical BR(Ω 0 c → Ω − π + ) = (0.51 +2.19 −0.31 )% [42][43][44][45][46][47].
The ratios of the p T -differential production cross section of inclusive Ω 0 c baryons (multiplied by the branching ratio of the Ω 0 c → Ω − π + decay channel) to the prompt D 0 -meson cross section [3] and to the Ω 0 c production in pp collisions at √ s = 13 TeV ALICE Collaboration prompt Ξ 0 c -baryon one [5] are reported in the left and right panel of Fig. 3, respectively.The systematic uncertainties on the tracking efficiency and on the luminosity were propagated as fully correlated in the ratios.The uncertainties do not allow to draw a conclusion about the possible p T dependence of the ratios.The data are compared with model expectations that were obtained by scaling the Ω 0 c /D 0 and Ω 0 c /Ξ 0 c ratios predicted by the models by the BR of the Ω 0 c → Ω − π + decay channel mentioned above.The uncertainty band of the models represents the BR uncertainty.For the Catania model only the specific uncertainty of the model itself are also included in the uncertainty band [10].In the bottom panels, the ratios of the various models and the data to the Catania prediction are shown.The expectations of the models differ significantly, even by orders of magnitude, demonstrating the sensitivity of the measured ratios to the implementation of the charm hadronisation process in the models.As visible in the left panels of Fig. 3, the Monash [19] and CR-BLC [9] tunes of PYTHIA 8, as well as the QCM [11] model underestimate the data significantly.The Monash tune expects a BR(Ω 0 c → Ω − π + ) × Ω 0 c /D 0 ratio increasing with p T from about 4 × 10 −7 to about 1 × 10 −5 .The CR-BLC model enhances the ratio by a factor of 12 to 34 with respect to the Monash tune.The prediction of the QCM is larger than that of the CR-BLC model, but it is lower than the data by more than 1.8σ .The Catania model [10] is consistent with the data.In particular, in the version in which additional charm resonance states on top of those listed in the PDG [35] are considered, the Ω 0 c /D 0 ratio is enhanced by a factor of 2, thus enlarging the range of possible BR(Ω 0 c → Ω − π + ) values that would allow the model prediction to be compatible within 1σ with the data considering only the data uncertainty.The Ω 0 c /D 0 ratio decreases with p T in the measured p T range in the CR-BLC, QCM, and Catania models, oppositely to what is expected by Monash.In the Ω 0 c /Ξ 0 c baryon-to-baryon ratio, shown in the right panel of Fig. 3, a similar hierarchy among the model predictions is present, though PYTHIA 8 with CR-BLC gives an enhancement by a factor of 4 to 5 with respect to the the Monash expectation, thus smaller than that of the Ω 0 c /D 0 ratio.Also for this ratio, the CR-BLC and QCM predictions are close to each other and higher than the Monash tune.The Catania model shows a good agreement with the data, whether the augmented set of charm resonance states is considered or not.Using the ALICE Ξ 0 c [5] and ) of the cross sections integrated in the Ω 0 c measured p T interval were obtained.They are reported in Table 1.They are compared with the values measured in e + e − collisions at √ s = 10.52 GeV by Belle, obtained from the cross sections reported in Table 1 of Ref. [28].Though the limited p T and rapidity ranges of the ALICE measurement do not allow for a direct comparison of the pp and e + e − data, the ratios observed by ALICE are larger by a factor of 8.7 ± 2.2(stat.)± 0.9(syst.)and 4.7 ± 1.3(stat.)± 0.5(syst.)for the BR(Ω 0 c → Ω − π + ) × σ (Ω 0 c )/σ (Λ + c ) and BR(Ω 0 c → Ω − π + ) × σ (Ω 0 c )/σ (Ξ 0 c ), respectively.The large BR uncertainties of the Ξ 0 c are not propagated in the computation of this factor.This difference, along with the comparison of data and models in Fig. 3, represents further evidence that the hadronisation process differs in pp and e + e − collisions and is sensitive to the density of quarks, colour charges, and on the system size.
Table 1: Ratio of the p T -integrated cross section of Ω 0 c baryon (multiplied by the branching ratio into Ω − π + ) in the interval 2 < p T < 12 GeV/c with respect to the Λ + c -and Ξ 0 c -baryon cross sections measured by the ALICE [3, 5] and Belle [28] experiments in pp collisions at √ s = 13 TeV and e + e − collisions at √ s = 10.52 GeV, respectively.The first and second uncertainties represent the statistical and systematic ones.The data include the correction for the branching ratio BR(Ω − → ΛK − , Λ → pπ − )=(43.3± 0.6)% [35].

Ratio ALICE (pp 13 TeV)
Belle (e + e − 10.52 GeV) [28] 2 < p T < 12 GeV/c visible In summary, the inclusive p T -differential production cross section of the charm-strange baryon Ω 0 c multiplied by the branching ratio of the Ω 0 c → Ω − π + decay channel was measured at midrapidity (|y| < 0.5) in pp collisions at √ s = 13 TeV.The ratio of this measurement to the production cross section of the D 0 meson provides further evidence that charm quarks hadronise to Ω 0 c baryons more frequently in pp collisions than in e + e − collisions, confirming the general trend observed from previous measurements of Λ + c , Ξ 0,+ c , and Σ 0,++ c production.The large uncertainty of the Ω 0 c → Ω − π + branching ratio limits the effectiveness of the comparison with theoretical models.However, the predictions of the available models differ by large factors indicating that future measurements of the BR, which could be performed also by the LHCb or Belle 2 collaborations, will allow to exploit these data to set stringent constraints to theoretical models and obtain deep insight into the charm hadronisation and the role of strange quarks and diquarks.Moreover, despite the large uncertainties, only the Catania model, which assumes that charm-quark hadronisation proceeds via both fragmentation and coalescence, can describe the BR(Ω 0 c → Ω − π + ) × σ (Ω 0 c )/σ (D 0 ) ratio within uncertainties.More precise measurements with the data sample collected in Run 3 of the LHC will allow us to further investigate the p T shape of the Ω 0 c /D 0 and Ω 0 c /Ξ 0 c ratios.

Figure 1 :
Figure 1: (Left panel): invariant-mass distribution of Ω 0 c → Ω − π + candidates and their charge conjugates integrated over the whole p T interval 2-12 GeV/c.The blue line shows the total fit function and the red line represents the combinatorial background fit.(Right panel): acceptance-times-efficiency for prompt, feed-down, and inclusive Ω 0 c baryons decaying into Ω − π + as a function of p T in pp collisions at √ s = 13 TeV.

Figure 3 :
Figure 3: Left, top panel: ratio of the p T -differential cross section of Ω 0 c baryons (multiplied by the branching ratio into Ω − π + ) to the D 0 -meson one [3] in |y| < 0.5 in pp collisions at √ s = 13 TeV.Right, top panel: ratio of the p T -differential cross section of Ω 0 c baryons (multiplied by the branching ratio into Ω − π + ) to the Ξ 0 c -baryon one [5] in |y| < 0.5 in pp collisions at √ s = 13 TeV.Bottom panels: ratio of the data and models to the Catania (coalescence plus fragmentation) model [10].The error bars and empty boxes represent the statistical and systematic uncertainties, respectively.The measurements are compared with model calculations (see text for details), which are multiplied by a theoretical BR(Ω 0 c → Ω − π + ) = (0.51 +2.19 −0.31 )% [42-47].