Measurement of Ω 0c baryon production and branching-fraction ratio BR

The inclusive production of the charm-strange baryon Ω 0c is measured for the ﬁrst time via its semileptonic decay into Ω − e + ν e at midrapidity ( | y | < 0 . 8) in proton–proton (pp) collisions at the centre-of-mass energy √ s = 13 TeV with the ALICE detector at the LHC. The transverse momentum ( p T ) differential cross section multiplied by the branching ratio is presented in the interval 2 < p T < 12 GeV / c . The branching-fraction ratio BR ( Ω 0c → Ω − e + ν e ) / BR ( Ω 0c → Ω − π + ) is measured to be 1.12 ± 0.22 (stat.) ± 0.27 (syst.). Comparisons with other experimental measurements, as well as with theoretical calculations, are presented.


Introduction
Production measurements of heavy-flavour hadrons (i.e.hadrons containing charm or beauty quarks) in high-energy proton-proton (pp) collisions provide essential tests of calculations based on the quantum chromodynamics (QCD) factorisation approach [1].These frameworks exploit the fact that the heavy-quark masses are much larger than the QCD energy scale, Λ QCD , to calculate the production of heavy-flavour hadrons as a convolution of three factors: i) the parton distribution functions (PDFs) of the incoming protons; ii) the cross section of the partonic hard scattering; and iii) the fragmentation functions that parametrise the non-perturbative evolution of a heavy quark into a given heavy-flavour hadron species.Heavy-quark hadronisation is typically studied via the measurement of hadron-to-hadron yield ratios, because the PDFs and partonic scattering cross sections are common to the charm-or beautyhadron species and, therefore, with appropriate choice of the scheme of calculation it can be cancelled out in the yield ratios.

Experimental setup and data samples
The ALICE experiment and its performance are presented in detail in Refs.[37,38].The main detectors used in this analysis are the Inner Tracking System (ITS) [39], the Time Projection Chamber (TPC) [40], and the Time-Of-Flight detector (TOF) [41] for vertexing, tracking, and particle identification (PID) purposes.They are located in the central barrel covering the pseudorapidity interval (|η| < 0.9) and lie inside a solenoidal magnet that provides a magnetic field B = 0.5 T parallel to the beam direction.The analysed data sample consists of pp collisions at √ s = 13 TeV recorded with a minimum-bias (MB) trigger.The MB trigger requires a pair of coincident signals in two scintillator arrays (V0) [42], which are located on both sides of the nominal interaction point along the beam direction.Further offline event selection was applied to remove the contamination from beam-gas collisions and other machine-related backgrounds.These criteria were based on the timing information of the two V0 arrays and a selection on the correlation between clusters and tracklets reconstructed in the two innermost layers of the ITS (Silicon Pixel Detector, SPD).Only events with a reconstructed vertex position within ±10 cm along the beam axis from the nominal interaction point were analysed, to maintain a uniform ITS acceptance in pseudorapidity.The primary-vertex position was defined using tracks reconstructed in the TPC and ITS detectors.Events with multiple reconstructed primary vertices, which amount to about 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).After the aforementioned selection criteria, the data sample corresponds to an integrated luminosity L int = (32.08 ± 0.51) nb −1 [43].

Analysis method
The Ω 0 c candidates were built by pairing an electron or positron candidate track with an Ω cascade candidate using a Kalman-Filter (KF) vertexing algorithm [44].Charge conjugate modes are included everywhere unless otherwise stated.
The Ω candidates were reconstructed via the decay chain Ω − → ΛK − (BR = (67.8± 0.7)%), followed by the decay Λ → pπ − (BR = (63.9±0.5)%)[45], exploiting the characteristic decay topology as reported in Refs.[16,46].Charged-particle tracks used in this analysis were required to be within the pseudorapidity interval |η| < 0.8 and to have a number of crossed TPC pad rows larger than 70 out of a maximum of 159.Particle identification (PID) selection was based on the differences between the measured and expected response for a given particle species hypothesis, in units of the detector resolution (nσ det ).For proton, pion, and kaon tracks, a selection on the measured specific energy loss dE/dx in the TPC of |nσ TPC | < 4 was applied for the respective particle hypothesis.An additional PID selection of |nσ TOF | < 5 was applied for the kaon candidates when information from the TOF detector was available.Tracks without TOF hits were identified using only the TPC information.
Electron candidate tracks were selected by requiring to have a minimum of three (out of a maximum of six) hits in the ITS with two in the SPD layers [47,48], at least 50 clusters in the TPC, a number of crossed TPC pad rows larger than 70, and p T > 0.5 GeV/c.These requirements help suppressing the contribution from short tracks, which are unlikely to originate from the Ω 0 c decay.The dominant source of electron background is photon conversions.They were rejected by requiring hits in the SPD layers, minimising the effective material budget.The electron candidate tracks were identified by using dE/dx and timeof-flight information in the TPC and TOF detectors, respectively.Two selection criteria on the PID of electron candidates, |nσ e TPC | < 4 and |nσ e TOF | < 5, were required.The remaining electrons steaming from photon conversion and those originating from Dalitz decays of neutral mesons were further rejected with an invariant-mass technique [49,50].The electron candidates were paired with opposite-sign tracks from Measurement of the Ω 0 c branching-fraction ratio ALICE Collaboration the same event passing loose identification criteria (|nσ e TPC | < 5 without any TOF requirement) and were rejected if they formed at least one e + e − pairs with an invariant mass smaller than 50 MeV/c 2 .
The Ω 0 c candidates were selected by requiring the cosine of the opening angle between the electron and the Ω candidate tracks to be greater than 0 for 2 < p T < 4 GeV/c, 0.25 for 4 < p T < 6 GeV/c and 0.5 for 6 < p T < 12 GeV/c.The p T dependence of this selection was chosen by looking at its correlation with the eΩ-pair mass distribution in data and Monte Carlo (MC) simulations, minimising the rejection of signal candidates in the data.
After applying the selections described above, further separation of the signal and background was based on the Boosted Decision Tree (BDT) algorithm implemented in the XGBoost library [51,52].Independent BDT models were trained for each p T interval with a sample of signal and background candidates as performed in Refs [3,11,53].For the reconstructed signal, eΩ pairs from Ω 0 c decays were obtained from simulations with the PYTHIA 8.2 event generator [54].Each PYTHIA event was required to contain a cc or bb quark pair and Ω 0 c baryons were forced to decay into the Ω − e + ν e channel.The mean proper lifetime of Ω 0 c baryons in the simulation was set to 268 fs based on the latest LHCb measurement [55].The transport of simulated particles within the detector was performed with the GEANT 3 package [56].The conditions of all the ALICE detectors in terms of active channels, gain, noise level, and alignment, as well as the evolution of the detector configurations during the data-taking period, were taken into account in the simulations.A mixed-event (ME) technique was used to increase statistics in the background sample.The ME technique exploited randomised sub-samples of the full dataset, using the same filtering selections described above, generating eΩ pairs with the opposite charge.The ME background was obtained by correlating Ω candidates in an event with electron candidate tracks from other events with similar multiplicity and primary-vertex position along the beam direction.Exploiting a background sample using the same-charge eΩ pairs in the same event (SE) was also tested.The resulting background distributions were found to be consistent with each other, and the SE pairs were used to normalise the more statistically abundant ME background sample.
The BDT training variables included topological properties of the decays and PID variables.The training variables related to the PID information were obtained by combining the ones coming from the TPC and TOF, nσ K,e combined = 1 TOF 2 , on the electron and kaon tracks, respectively.The training variables describing the Ω decay topology were the distance of the closest approach (DCA) of the charged decay particles, the pointing angle of the reconstructed Ω momentum to the primary vertex, the χ 2 topo /NDF, which, in this analysis, characterises whether the momentum vector of the Ω candidate points back to the reconstructed primary vertex of the event, and the χ 2 geo /NDF, which is related to the geometrical intersection of the daughter-particle trajectories, taking their uncertainties into account.
The training variables related to the Λ were the DCA to the primary vertex, the radial distance of the Λ decay vertex from the beam axis, and the DCA between the decay particles.The BDT model output is a single response variable related to the probability that the candidate is a signal.The selection on the BDT output was tuned in each p T interval to maximise the expected statistical significance, which was estimated using: the expected signal obtained from the Ω 0 c production cross section reported in Ref.
[16] multiplied by the BDT selection efficiency and the expected background estimated from the normalised ME.The resulting BDT output thresholds were 0.86, 0.84, and 0.81 for the three p T intervals, respectively.
The left panel of Fig. 1 shows the invariant-mass distribution of eΩ pairs in SE (same-sign and oppositesign) and ME (opposite-sign) in the interval 2 < p eΩ T < 12 GeV/c.The raw yield was obtained by subtracting the combinatorial background computed using the ME technique from the invariant-mass distribution of eΩ pairs with opposite-sign charge in the SE.The right panel of Fig. 1 shows the invariant-mass distribution of eΩ candidates, obtained after background subtraction, in comparison with eΩ oppositesign charge pairs coming from the Ω 0 c decay computed with the PYTHIA 8 event generator [54].Only Measurement of the Ω 0 c branching-fraction ratio ALICE Collaboration  eΩ pairs satisfying 1.7 < m eΩ < 2.7 GeV/c 2 were considered for further analysis.The number of reconstructed eΩ signal pairs consists of 232 ± 15 candidates.The missing momentum of the neutrino was corrected by using the Bayesian-unfolding technique [57] implemented in the RooUnfold package [58].
The response matrix, which represents the correlation between the generated Ω 0 c and reconstructed eΩ transverse momenta, used in the unfolding procedure is shown in the left panel of Fig. 2. In this analysis, the Bayesian procedure requires two iterations to converge.Additional information on the unfolding procedure is explained in Ref. [15].The response matrix was determined with the same simulation setup used for the BDT training.
The p T -differential production cross section of inclusive Ω 0 c baryons in the rapidity interval |y| < 0.8 multiplied by the BR into the considered semileptonic decay channel was calculated from the yields obtained from the unfolding procedure as follows: where raw is the raw yield (sum of particles and antiparticles) in a given p T and rapidity interval with width ∆p T and ∆y.The factor 1/2 takes into account that the raw yield includes both particles and antiparticles, while the cross section is given for particles only.The L int is the integrated luminosity.Since the feed-down contribution is not subtracted, the (A × ε) factor is the product of the acceptance and efficiency for inclusive Ω 0 c baryons, where ε accounts for the reconstruction and selection of the Ω 0 c decay-product tracks and the Ω 0 c -candidate selection.The (A × ε) correction was obtained from a simulation with the same configuration as the one used for the BDT training and the response matrix.The (A × ε) correction factors of prompt, beauty feed-down (non-prompt), and inclusive Ω 0 c as a function of p T are observed to be consistent with each other within uncertainties, because the selection variables used are not sensitive to the displacement by a few hundred micrometres of the prompt and beauty feeddown Ω 0 c decay vertices from the collision point.The Ω 0 c -baryon p T distribution from the PYTHIA 8 simulation was reweighted to match the true distribution, which was parametrised via a Tsallis fit to the differential production cross section of Ω 0 c as measured in Ref.

Systematic uncertainties
The different contributions to the total systematic uncertainty of the Ω 0 c production cross section in 2 < p T < 12 GeV/c are summarised in Table 1.The various systematic sources were defined as the RMS of the distribution of the corrected yields obtained from the reported variations, if not differently specified.
The systematic uncertainty on the raw-yield extraction was evaluated by investigating possible contaminations to eΩ pairs with the opposite charge from other decays.The contamination of different decay channels mentioned in Refs.[32,59] are the Ω 0 c → Ξ + c e − ν e , Ξ 0 c → Ω − e + ν e K 0 , Ξ + c → Ω − e + ν e K + , and Ω 0 c → Ω − e + ν e π + π − .From PYTHIA 8 simulation studies, it was found that these decays mainly con- tribute to a mass region below 2.2 GeV/c 2 .A maximum variation of 10% at the corrected yield level was c branching-fraction ratio ALICE Collaboration found by varying the lower limit of the integration mass range for the signal extraction in the eΩ mass from 1.7 to 2.2 GeV/c 2 , which was assigned as systematic uncertainty.Note that those decay channels are not experimentally observed, therefore the Belle [31] and CLEO [32] Collaborations do not correct for it in addition to not assigning a corresponding systematic uncertainty.
The systematic uncertainty on the tracking efficiency was determined by comparing the matching efficiency of prolonging a track from the TPC to the ITS in data and simulation, and by varying the track quality selection criteria.The uncertainty on the matching efficiency, defined as the relative difference in the ITS-TPC matching efficiency between the data and simulation, affected only the electron track.
For the tracks of the Ω decay particles, the prolongation to the ITS was not required.The uncertainties on electron tracks were propagated to the Ω 0 c candidates according to the decay kinematics, resulting in an uncertainty of 2%.The second contribution to the track reconstruction was estimated by varying the track quality selection criteria and 4% uncertainty was assigned.
The systematic uncertainty on the unfolding procedure was determined by considering three contributions.The first contribution was due to the regularisation procedure in the Bayesian unfolding.It was estimated by varying the iteration number between 2 and 5, and an uncertainty of 4% was assigned.The second contribution was estimated by unfolding with the singular value decomposition algorithm [60], and a 4% uncertainty was assigned, independent of Ω 0 c p T .The third source was related to the sensitivity of the unfolding to bin edge effects and was estimated by varying the p T range and the binning of the response matrix.An uncertainty of 10% was assigned in the interval 2 < p T < 6 GeV/c.At higher p T , no variations were observed when using finer p T intervals in the unfolding procedure.
The systematic uncertainty on the selection efficiency originates 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 selections on the BDT outputs, which results in modification of the efficiencies, raw yield, and background values.The systematic evaluation was extended using a BDT model with different training variables (no PID included in the training) and preselection (PID selections were varied when not included in the BDT).A value of 15% was assigned as systematic uncertainty.
The systematic uncertainty due to the difference in the shape of the true and generated Ω 0 c p T distributions was estimated by varying the Tsallis fit used to determine the p T weights within the statistical and p T uncorrelated uncertainties.The assigned uncertainty, defined as the maximum variation observed, was 10% in the interval 2 < p T < 4 GeV/c, 2% in the interval 4 < p T < 6 GeV/c, and 1% for the highest p T interval.
All systematic uncertainties are considered uncorrelated and summed in quadrature to obtain the total systematic uncertainty.The production cross section has an additional global normalisation uncertainty of 1.6% due to the uncertainties of the integrated luminosity [43].

Results
The p T -differential cross section of inclusive Ω 0 c baryon production multiplied by the branching ratio into Ω − e + ν e , in pp collision at √ s = 13 TeV, measured in rapidity interval |y| < 0.8 and the p T interval 2 < p T < 12 GeV/c, is shown in the top panel of Fig. 3.It is compared with the previously published measurements of inclusive Ω 0 c baryon production in the hadronic decay channel Ω 0 c → Ω − π + .The error bars and boxes represent the statistical and systematic uncertainty, respectively.The uncertainty of the integrated luminosity is not included in the boxes.In the bottom panel of Fig. 3 the branching-fraction ratio BR(Ω 0 c → Ω − e + ν e )/BR(Ω 0 c → Ω − π + ) is shown as function of p T .The systematic uncertainties on the branching-fraction ratio were calculated assuming all the uncertainties between the two measurements as uncorrelated, except for the ITS-TPC matching efficiency, track quality selection, and the MC p T shape.The uncertainty of the luminosity cancels in the ratio, as it is fully correlated.) between experiments and theoretical calculations [26,[31][32][33]36].
The ratio of the two measurements, shown in the bottom panel of Fig. 3, is used to calculate the p T independent branching-fraction ratio.The result was averaged over p T using the inverse uncorrelated relative uncertainties as weights [61].The weights were defined as the sum in quadrature of the relative statistical uncertainties and the p T -uncorrelated part of the systematic uncertainties.All the systematic uncertainties were considered as p T -correlated in the semileptonic decay.For the hadronic decay, all systematic uncertainties were considered as p T -correlated, except for the raw yield extraction.The p T -correlated Measurement of the Ω 0 c branching-fraction ratio ALICE Collaboration systematic uncertainties were propagated by recomputing the ratio after shifting up and down the ratios with the corresponding p T -correlated systematic uncertainties.The final systematic uncertainty on the ratio is obtained by summing the p T -correlated and uncorrelated systematic uncertainties in quadrature.
The measured ratio is BR(Ω 0 c → Ω − e + ν e )/BR(Ω 0 c → Ω − π + ) = 1.12 ± 0.22 (stat.)± 0.27 (syst.).In Fig. 4, the measured p T -independent branching-fraction ratio is compared with previous experimental measurements from the CLEO Collaboration [32] and Belle Collaboration [31], and with the theory predictions based on the light-front approach and light-cone sum rules calculations [26,33].The ALICE result is compatible within 1σ with the CLEO result and is 2.3σ lower than the one measured by the Belle Collaboration.The ALICE measurement is also consistent within 1σ with the available theoretical predictions, which showed some tensions with the Belle results.The present result is also compatible within the uncertainties with the BR(Ξ 0 c → Ξ − e + ν e )/BR(Ξ 0 c → Ξ − π + ) measured by the ALICE Col- laboration [14].The agreement between those two measurements is also predicted by the light-front approach calculations [26,62].More precise measurements are expected to be performed during Runs 3 and 4 of the LHC.In view of those future measurements, it would be beneficial to compare also with additional model calculations, like LQCD [63] and RQM [64], which already provide their prediction for the branching-fraction ratio BR(Ξ 0 c → Ξ − e + ν e )/BR(Ξ 0 c → Ξ − π + ).

Summary
The inclusive p T -differential production cross section of the charm-baryon Ω 0 c multiplied by the branching ratio BR(Ω 0 c → Ω − e + ν e ) is measured for the first time at midrapidity (|y| < 0.8), in the p T interval 2 < p T < 12 GeV/c, in pp collisions at √ s = 13 TeV.The BR(Ω 0 c → Ω − e + ν e )/BR(Ω 0 c → Ω − π + ) is measured to be 1.12 ± 0.22 (stat.)± 0.27 (syst.), using the inclusive production cross section measured in Ref. [16].The branching-fraction ratio is consistent with theory calculations and is 2.3σ lower than the value reported by the Belle Collaboration [31].

Figure 1 :
Figure 1: Left panel: invariant-mass distribution of opposite-sign pairs (black solid circle marker) and same-sign pairs (red solid square marker) in SE, and opposite-sign pairs (blue open square marker) in ME.Right panel: invariant-mass distribution of the Ω 0 c candidates obtained by subtracting the opposite-sign charge eΩ pairs in ME from the opposite-sign charge pairs in SE (black solid circle marker), and eΩ opposite-sign charge pairs coming from Ω 0 c decay from PYTHIA 8 (green open circle marker).

Figure 2 :
Figure 2: Left panel: correlation matrix between the generated Ω 0 c baryon p T and the reconstructed opposite-sign charge pairs, obtained from the simulation based on PYTHIA 8 described in Ref. [15].Right panel: product of (A × ε) for inclusive Ω 0 c baryons in pp collisions at √ s = 13 TeV as a function of p T .

Table 1 :
Contributions to the systematic uncertainty of the Ω 0 c cross section for the p T intervals 2 < p T < 4 GeV/c, 4 < p T < 6 GeV/c, and 6 < p T < 12 GeV/c.The global uncertainty on the luminosity is quoted separately and it is not added in quadrature to the other sources.