Measurement of the fraction of jet longitudinal momentum carried by c+ baryons in pp collisions

Recent measurements of charm-baryon production in hadronic collisions have questioned the universality of charm-quark fragmentation across different collision systems. In this work the fragmentation of charm quarks into charm baryons is probed, by presenting the first measurement of the longitudinal jet momentum fraction carried by Λ þ c baryons, z ch k , in hadronic collisions. The results are obtained in proton-proton ( pp ) collisions at ﬃﬃﬃ s p ¼ 13 TeV at the LHC, with Λ þ c baryons and charged (track-based) jets reconstructed in the transverse momentum intervals of 3 ≤ p Λ þ c T < 15 GeV =c and 7 ≤ p jet ch T < 15 GeV =c , respectively. The z ch k distribution is compared to a measurement of D 0 -tagged charged jets in pp collisions as well as to PYTHIA 8 simulations. The data hints that the fragmentation of charm quarks into charm baryons is softer with respect to charm mesons, in the measured kinematic interval, as predicted by hadronization models which include color correlations beyond leading-color in the string formation.

< 15 GeV/, respectively.The  ch | | distribution is compared to a measurement of D 0 -tagged charged jets in pp collisions as well as to PYTHIA 8 simulations.The data hints that the fragmentation of charm quarks into charm baryons is softer with respect to charm mesons, in the measured kinematic interval, as predicted by hadronisation models which include colour correlations beyond leading-colour in the string formation.
The study of charm-baryon production in jets can provide more differential insights into hadronisation mechanisms in pp collisions, compared to  T -differential cross sections and yield ratios of heavy-flavour hadrons, allowing for a more accurate study of the dynamical properties of baryon production.In this paper, the first measurement of the longitudinal momentum fraction of the jet carried by T < 15 GeV/.The results are then compared to PYTHIA 8 simulations [20,23], including a version where mechanisms beyond the leading-colour approximation are considered in string formation processes during hadronisation [21], and to an analogous measurement of the  ch | | distribution of D 0 mesons, performed by the ALICE Collaboration [7].A full description of the ALICE setup and apparatus can be found in Refs.24, 25.The main detectors used in this analysis are the Inner Tracking System (ITS), which is used for vertex reconstruction and tracking; the Time Projection Chamber (TPC), which is used for tracking and particle identification (PID); and the Time-Of-Flight (TOF) detector, which is used for PID.These detectors cover a pseudorapidity interval of || < 0.9.The analysis was performed on pp collisions at √  = 13 TeV, collected using a minimum-bias (MB) trigger during the years 2016, 2017, and 2018.The trigger condition required < 35 GeV/.The full jet cone was required to be within the ALICE central barrel acceptance, limiting the jet axis to the interval | jet | < 0.5.Only jets tagged via the presence of a reconstructed Λ + c candidate amongst their constituents were considered for the analysis.For events where more than one Λ + c candidate was found, the jet finding and tagging pass was performed independently for each candidate, with only the daughters of that particular candidate replaced by the corresponding Λ + c four-vector each time.In mechanisms of hadronisation that include colour correlations beyond the leading-colour approximation [21], which have been shown to be relevant in hadronic collisions at LHC energies [10], hadrons can be formed in processes that combine quarks from the parton shower with those from the underlying event [33].As such, the underlying event is not well defined with respect to the measured hadron distributions.Therefore no underlying event correction is implemented in this work.
The fragmentation of charm quarks to Λ + c baryons is probed by measuring the fraction of the jet momentum carried by the Λ + c along the direction of the jet axis,  ch | | .This is calculated for each jet using In-jet Λ + c production in pp collisions at ) distributions were extracted in the signal and sideband regions, with the sideband distribution scaled by the ratio of the background function integrals in the signal and sideband regions.The sideband distribution was then subtracted from the signal one, with the resulting distribution scaled to account for the fact that the 2 fit width of the signal region only encompasses approximately 95% of the total signal, to obtain the sideband subtracted  ), given by The  prompt ( T , ranging from about 20% at 3 < T < 24 GeV/, and was calculated using PYTHIA 8 simulations with the Monash tune containing prompt Λ + c -tagged jets, transported through the detector using GEANT 3.This efficiency does not exhibit a  jet ch T dependence.
In order to isolate the  corr ( ch | | ,  jet ch T ) distribution of prompt Λ + c -tagged jets, a feed-down subtraction was employed to remove the non-prompt (beauty-quark initiated) contribution.The non-prompt cross section was obtained from particle level POWHEG [34] + PYTHIA 6 [35] + EvtGen [36] simulations, as a function of  T range.The simulated non-prompt results were then folded to reconstructed level, using a four-dimensional response matrix generated using non-prompt Λ + c -tagged jets in PYTHIA 8 with the Monash tune, transported through a simulation of the ALICE detector using GEANT 3. The response matrix was constructed as a function of  A two-dimensional Bayesian unfolding procedure [37] was performed to correct for detector effects and obtain the  ch | | distribution for prompt Λ + c -tagged jets at particle level.A four-dimensional response matrix as a function of  jet ch T and  ch | | , at generator and reconstruction levels, was populated with prompt Λ + c -tagged jets, obtained with PYTHIA 8 simulations with the Monash tune, passed through a simulation of the ALICE detector using GEANT 3. The measured data and response matrix were provided in the intervals of 5 ≤  The systematic uncertainties affecting the measurement were evaluated, in each  ch | | interval, by modifying the strategy adopted at various steps of the analysis procedure and assessing the impact on the unfolded  ch | | distribution.The total systematic uncertainty includes contributions from multiple sources.The first considered source is the sideband subtraction procedure, whose contribution (ranging from 3.7% to 7.6% depending on the  ch | | inteval) was estimated by varying the invariant-mass fit parameters as well as the invariant-mass intervals of the signal and sideband regions.The contribution from the BDT selection of Λ + c candidates (from 7.3% to 19%) was estimated by varying the BDT probability thresholds to induce a 25% variation in the Λ + c -tagged jet reconstruction and selection efficiency.The uncertainty from the jet energy resolution (from 4.5% to 19%) was estimated by recalculating the response matrix used for unfolding with a 4% reduced tracking efficiency.The reduction in the tracking efficiency was evaluated by varying the track-selection criteria and propagating the ITS-TPC track-matching efficiency uncertainty.The uncertainty on the feed-down subtraction (< 2%) was estimated by varying the choice of POWHEG parameters considered to generate the feed-down cross section, including the factorisation and renormalisation scales, as well as the mass of the beauty quark, which were varied according to theoretical prescriptions [38].Finally the contribution from the unfolding procedure (from 1.1% to 2.7%) was estimated by altering the choice of prior, regularisation parameter, and ranges of the response matrix.For each of the aforementioned categories, several variations were made and the root-mean-square of the resulting distributions was considered.The exceptions are related to the contribution associated to the choice of parameters of the POWHEG calculations, where only the largest deviation from the central result, in each direction, was considered, as well as the uncertainty on the jet energy resolution where the variation with respect to the central result was taken as the uncertainty.All uncertainties (other than from the feed-down subtraction) were then symmetrised.The uncertainties were combined in quadrature to obtain the total systematic uncertainty on the measurement, which ranges from 13% to 28%.

The fully corrected 𝑧 ch
| | distribution of prompt Λ + c -tagged charged jets in the intervals of 7 ≤  jet ch T < 15 GeV/ and 3 ≤  Λ + c T < 15 GeV/ is presented in the left-hand panel of Fig. 1 and compared to PYTHIA 8 simulations with two different tunes.In PYTHIA 8 the Lund string model of fragmentation is employed, where endpoints are confined by linear potentials encoded in strings.For the case of heavy quarks, the Lund fragmentation function is modified to account for the slower propagation of the massive endpoints compared to their massless counterparts.The Monash tune (red-dotted line) [20], in which the charm fragmentation is tuned on e + e − measurements, predicts a harder fragmentation than the measurement.An evaluation of the  2 /ndf between the measured data points and the model was performed, combining the statistical and systematic uncertainties on the data in quadrature and assuming the uncertainties are uncorrelated across the  ch | | intervals.This exercise determines that there is a 0.4% probability that the model describes the data.A better agreement is achieved by PYTHIA 8 with the CR-BLC Mode 2 tune, which includes colour reconnection mechanisms beyond the leading-colour approximation [23] (green-dashed line).In this model, the minimisation of the string potential is implemented considering the SU(3) multiplet structure of QCD in a more realistic way than in the leading-colour approximation, allowing for the formation of "baryonic" configurations where for example two colours can combine coherently to form an anti-colour.The same  2 /ndf approach results in a 78% probability that the model describes the data.The simulation with PYTHIA 8 with the CR-BLC Mode 2 tune also provides a much more accurate description of the Λ + c /D 0 cross section ratio, previously measured in pp collisions at the LHC [11][12][13][14][15]39].
In the right-hand panel of Fig. 1, a  simulations using both the Monash and CR-BLC Mode 2 tunes.The ratio of the two distributions is also presented in the bottom panel.The uncertainty from the jet energy resolution was considered to be correlated between the Λ + c -tagged jet and D 0 -tagged jet measurements and was evaluated directly on the ratio of the distributions.The remaining uncertainties were considered uncorrelated when taking the ratio and were then combined in quadrature with the uncertainty of the jet energy resolution.The uncertainties were considered uncorrelated across the  ch | | intervals.The same  2 /ndf exercise described above determines that there is a 12% probability that the measured ratio is described by a flat distribution at unity, hinting at a softer fragmentation of charm quarks into charm baryons than charm mesons.The ratio is better described by the PYTHIA 8 simulations with the CR-BLC Mode 2 compared to the ones with the Monash tune, with the former describing the data with 88% probability compared to a 0.03% probability for the latter.
In summary the first measurement in hadronic collisions of the longitudinal momentum fraction of the charged jet carried by Λ + c baryons was presented for pp collisions at √  = 13 TeV.The result is fully corrected to particle level and obtained in the jet and Λ + c transverse-momentum intervals of 7 ≤  jet ch T < 15 GeV/ and 3 ≤  Λ + c T < 15 GeV/, respectively.The measurement presented in this paper hints that charm quarks have a softer fragmentation into Λ + c baryons compared to D 0 mesons, in the measured kinematic interval.One possible explanation is that charm-baryon production is favoured in the presence of higher particle multiplicity originating from both the jet fragmentation and the underlying event, which could be tested with future measurements of the in-jet multiplicity of Λ + c -tagged jets.The fragmentation of charm quarks into Λ + c baryons in hadronic collisions exhibits tension with simulations tuned on e + e − data that employ a leading-colour formalism of hadronisation, such as in the Monash tune of PYTHIA 8.This occurs despite their successful description of the fragmentation of charm quarks into D 0 mesons.However, the inclusion of mechanisms sensitive to the surrounding partonic density that feature colour In-jet Λ + c production in pp collisions at √  = 13 TeV ALICE Collaboration reconnection beyond the leading-colour approximation results in a better agreement with data.This result also partially explains the  T shape of the prompt Λ + c /D 0 cross section ratio [11][12][13][14][15]39], which shows a peak at low  T (≈ 3 GeV/) and is also described within uncertainties by PYTHIA 8 with the CR-BLC Mode 2 tune.The  T trend of this ratio is driven by the fact that the Λ + c baryons produced from the fragmenting charm quark carry a significantly lower fraction of the charm-quark transverse momentum than the D 0 mesons produced in a similar way.
In-jet Λ + c production in pp collisions at Λ + c baryons,  ch | | , is presented.The measurement is performed in pp collisions at √  = 13 TeV in the interval 0.4 ≤  ch | | ≤ 1.0.The  ch | | distribution, fully corrected to particle level, is presented for prompt (charm-quark initiated) Λ + c -tagged jets with 7 ≤  jet ch T < 15 GeV/ and 3 ≤  Λ + c ch | | , and was scaled according to the integrated luminosity of the analysed data sample and the branching ratio of the Λ + c → pK 0 S → pπ + π − decay channel.The resulting particlelevel yield was multiplied by the ratio of the non-prompt to prompt Λ + c -tagged jet reconstruction and selection efficiency in intervals of  Λ + c T and integrated over the  Λ + c generator and reconstruction levels.The folded results were then subtracted from the measured  corr ( ch | | ,  jet ch T ) distribution in data, removing the non-prompt contribution.The estimated fraction of Λ + c -tagged jets coming from b-quark fragmentation is found to be about 5%, with no significant  ch | |dependence.
jet ch T < 35 GeV/ and 0.4 ≤  ch | | ≤ 1.0, with the final unfolded results reported in the intervals 7 ≤  jet ch T < 15 GeV/ and 0.4 ≤  ch | | ≤ 1.0.The extended  jet ch T range includes two padding intervals for the unfolding from 5 ≤  jet ch T < 7 GeV/ and 15 ≤  jet ch T < 35 GeV/, which allow the unfolding to account for migrations in and out of the reported 7 ≤  jet ch T < 15 GeV/ interval.Corrections accounting In-jet Λ + c production in pp collisions at √  = 13 TeV ALICE Collaboration for migrating entries in and out of the response matrix ranges, as modelled by the same MC simulation, were also applied.The corrected  ch | | distribution is normalised to the total number of Λ + c -tagged jets in the reported  ch | | and  jet ch T interval.