Study of ﬂavor dependence of the baryon-to-meson ratio in proton–proton collisions at √ s = 13 TeV √ s = 13 TeV √ s = 13 TeV

The production cross sections of D 0 and Λ + c hadrons originating from beauty-hadrondecays (i.e. non-prompt) were measured for the ﬁrst time at midrapidity ( | y | < 0 . 5) by the ALICE Collaboration in proton–proton collisions at a center-of-mass energy √ s = 13 TeV. They are described within uncertainties by perturbative QCD calculations employing the fragmentation fractions of beauty quarks to baryons measured at forward rapidity by the LHCb Collaboration. The bb production cross section per unit of rapidity at midrapidity, estimated from these measurements, is d σ bb / d y | | y | < 0 . 5 = 83 . 1 ± 3 . 5 ( stat ) ± 5 . 4 ( syst ) + 12 . 3 − 3 . 2 ( extrap ) µ b. The baryon-to-meson ratios are computed to investigate the hadronization mechanism of beauty quarks. The non-prompt Λ + c / D 0 production ratio has a similar trend to the one measured for the promptly produced charmed particles and to the p / π + and Λ / K 0S ratios, suggesting a similar baryon-formation mechanism among light, strange, charm, and beauty hadrons. The p T -integrated non-prompt Λ + c / D 0 ratio is found to be signiﬁcantly higher than the one measured in e + e − collisions.

Recent measurements of charm baryon-to-meson production ratios and fragmentation fractions (i.e. the probability of charm quark to fragment into a specific hadron) at midrapidity in pp collisions at LHC energies showed significant deviations from the values measured at e + e − and ep colliders [24][25][26][27][28][29][30][31][32], demonstrating that the assumption of universality of the hadronization process across the collision systems has to be reconsidered.As reported in Ref. [30], the observed baryon-to-meson enhancement also leads to an increase of the derived cc production cross section at midrapidity compared to previous measurements, where prompt D-meson cross sections and fragmentation fractions from e + e − were used.Models based on the hadronization via coalescence, i.e. recombination of heavy and light quarks close in space and with similar velocity, are able to reproduce the magnitude as well as the p T dependence of the measured Λ + c /D 0 ratio [33,34].An alternative explanation is provided by statistical hadronization models, if an augmented set of yet unobserved charm-baryon states predicted by the relativistic-quark model [35] and lattice QCD [36] is considered.Moreover, string fragmentation models including colorreconnection mechanisms beyond the leading-color (CLR-BLC) approximation introduce new topologies through the contributions of "junctions" that fragment into baryons, thus providing an augmented baryon production [37].In the beauty sector, the measurements of Λ 0 b -baryon production relative to that of B mesons at forward rapidity by the LHCb Collaboration show a modification of the fragmentation fractions among collision systems similar to that observed for charm quarks at midrapidity [38,39].However, the rapidity-dependent baryon-to-meson enhancement with respect to values measured at e + e − and ep colliders is still not fully understood and explored.Different enhancement was observed for the charm baryon-to-meson ratio between midrapidity and forward rapidity for p T < 8 GeV/c and for different colliding systems (i.e.pp, p-Pb) [27,40,41].Beauty measurements at midrapidity are available only at high transverse momentum (p T > 7 GeV/c) [5,[42][43][44][45][46][47][48], hence a firm conclusion cannot be drawn.
Flavor dependence of the baryon-to-meson ratio in pp at √ s = 13 TeV ALICE Collaboration prompt were optimized to obtain a high non-prompt D 0 and Λ + c fractions (i.e.≥ 60% in each p T interval) while maintaining a reliable signal extraction.The sample of candidates passing the BDT selection is denoted in the following as non-prompt enhanced sample.Based on the selections on the BDT outputs, samples dominated by non-prompt (prompt) candidates were selected by requiring low BDT probability for a candidate to be combinatorial background and a high BDT probability to be non-prompt (prompt).
The D 0 -meson and Λ + c -baryon raw yields were extracted via binned maximum-likelihood fits to the candidate invariant-mass distributions.The fitting function was composed of a Gaussian term to model the signal and an exponential or polynomial function to model the background.In the case of D 0 mesons, an additional term was added for the contribution of signal candidates with the wrong K-π mass assignment (reflections), parameterized from simulated candidates [1].To improve the stability of the fits, the widths of the signal peaks were fixed to the values extracted from the fits of the invariant-mass distributions in the prompt enhanced sample, given the naturally larger abundance of prompt compared to non-prompt candidates.Examples of invariant-mass fits with different contributions of signal from beauty-hadron decays in the 2 < p T < 4 GeV/c interval are shown in Fig. 1 for D 0 (top row), Λ + c → pK 0 S (middle row), and Λ + c → pK − π + (bottom row).The blue solid curves show the total fit function, the red dashed curves show the combinatorial-background contribution, and the green solid lines represent the reflection contribution only for D 0 .The fits to the invariant-mass distributions of non-prompt (prompt) enhanced samples are shown in each right (left) panel, indicating the corresponding selection applied on the BDT output score related to the probability to be a non-prompt (prompt) charm hadron.

Yield corrections and non-prompt fraction estimate
The non-prompt D 0 and Λ + c p T -differential cross sections were obtained in the rapidity interval |y| < 0.5 as where N raw is the raw yield (sum of particles and antiparticles), c ∆y (p T ) and ∆p T represent the width of the rapidity and transverse momentum intervals respectively, BR is the branching ratio of the considered decay mode, the factor of 2 is introduced to obtain the average of particle and antiparticle yields, f non-prompt is the fraction of non-prompt hadrons in the raw yield, (Acc × ε) non-prompt is the product of the geometrical acceptance and the reconstruction and selection efficiency for non-prompt hadrons, which increases with p T from 5% to 25% depending on the BDT selections and decay channel for Λ + c (5% to 40% for D 0 ), and L int is the integrated luminosity.The correction factors (Acc × ε) for the detector acceptance and the signal reconstruction and selection efficiency were determined using the aforementioned MC simulations.
A data-driven procedure based on the construction of data samples with different abundances of prompt and non-prompt candidates was used to estimate the fraction f non-prompt of non-prompt D 0 and nonprompt Λ + c hadrons.A set of raw yields (Y i ) can be obtained by varying the selection on the BDT output, which is related to the candidate's probability to be a non-prompt D 0 meson or a non-prompt Λ + c baryon.These raw yields are sensitive to the corresponding (Acc × ε) of prompt and non-prompt D 0 or Λ + c hadrons as follows where δ i represents a residual that accounts for the equation not holding exactly due to the uncertainties of Y i , (Acc × ε)  based on Eq. 2, which can be minimized to obtain the corrected yields of prompt (N prompt ) and nonprompt (N non-prompt ) Λ + c (D 0 ) hadrons as explained in Ref. [2].One of the n sets with a high non- Flavor dependence of the baryon-to-meson ratio in pp at √ s = 13 TeV ALICE Collaboration prompt component (larger than 50%) was selected as a working point (default), and the corresponding f non-prompt,default fraction (more details in Ref. [2]) can be calculated as Figure 2 shows an example of raw-yield distribution as a function of the BDT-based selection employed in the minimization procedure for D 0 in 2 < p T < 4 GeV/c (top left panel), Λ + c → pK − π + in 4 < p T < 6 GeV/c (top right panel), and Λ + c → pK 0 S in 6 < p T < 8 GeV/c (bottom left panel).The black markers are the measured raw yields corresponding to a selection on the BDT output related to the candidate's probability of being a non-prompt D 0 (Λ + c ) meson (baryon).The leftmost data point of each distribution corresponds to the loosest applied selection, while the rightmost one corresponds to the tightest selection, which preferentially selects non-prompt candidates.The prompt and non-prompt components, obtained for each BDT-based selection from the minimization procedure as are represented by the red and blue filled histograms, respectively, while their sum is reported by the green histogram.The f non-prompt fractions obtained for D 0 , Λ + c → pK − π + , and Λ + c → pK 0 S , computed for the default selections with the formula in Eq. 3 are reported as a function of p T in the bottom right panel of Fig. 2.

Systematic uncertainties
The systematic uncertainties of the non-prompt Λ + c and D 0 cross sections were studied for the different decay channels, which depend on p T .The contributions from the raw-yield extraction were evaluated by repeating the invariant-mass fits, varying the fit interval, the functional form of the background fit function, and the width of the Gaussian function used to model the signal peaks.The latter was varied within the uncertainties obtained from the fits of the invariant-mass distributions of the prompt enhanced sample.The relative uncertainty from this contribution varies in the range 1-3% for D 0 and 4-11% for Λ + c .The uncertainties of the track reconstruction efficiency were estimated by considering the uncertainty due to track quality selections and the uncertainty due to the TPC-ITS track matching efficiency as discussed in Ref. [2].It ranges from 3.5% to 5% for D 0 and from 4% to 7% for Λ + c .The systematic uncertainties of the non-prompt fractions were evaluated by varying the configuration and the number of BDT selections employed in the data-driven method and amounts to 2-3% for D 0 and 5-9% for Λ + c .The selection efficiency uncertainties, ranging from 2% to 4% for D 0 and 4% to 10% for Λ + c , were studied by repeating the analyses using different BDT working points.The systematic uncertainties of the PID selection efficiency were found to be negligible, similar to what observed for prompt charm hadrons [60].The systematic effects due to a possible difference between the real and simulated charm and beauty hadron p T spectra, were estimated by evaluating the selection efficiency after reweighting the p T shape from the PYTHIA 8.243 event generator to match the one from FONLL calculations [13][14][15] for prompt and non-prompt D 0 .For the Λ + c the reweighting was defined to match the p T shape of D 0 and B mesons from FONLL multiplied by the Λ + c /D 0 yield ratio from ALICE [27] and the Λ 0 b /B yield ratio from LHCb [39], respectively.The weights were applied to the p T distributions for prompt hadrons and to the mother beauty-hadron particles in the case of non-prompt hadrons.The systematic uncertainty from this contribution varies in the range 1-4% for D 0 and 4-5% for Λ + c .In addition, the imperfect apparatus material budget description in the MC simulation, particularly relevant for the effects of the absorption of protons, might result in a bias in the estimation of the Λ + c efficiencies.It was evaluated by comparing the corrected yields of charged pions, kaons, and protons using a standard MC production and one with the material budget increased artificially by 10%.The assigned systematic uncertainty is 2%.Further p T -independent uncertainties from the BR [61] and the luminosity [53] were considered.The total uncertainties, 5-8% for D 0 and 12-17% for Λ + c , were calculated as the quadratic sum of the contributions of the different sources.c → pK 0 S in 6 < p T < 8 GeV/c (bottom left panel).Bottom right panel: f non-prompt fraction as function as p T obtained for the set of selection criteria adopted in the analysis of for non-prompt D 0 , Λ + c → pK − π + , and Λ + c → pK 0 S hadrons.

Production cross sections
The p T -differential production cross sections of non-prompt Λ + c baryons and D 0 mesons are shown in Fig. 3.The non-prompt Λ + c cross section was obtained by computing a weighted average of the results from the analyses of the Λ + c → pK 0 S and Λ + c → pK − π + decay channels, using the inverse of the quadratic sum of the relative statistical and uncorrelated systematic uncertainties as weights.The systematic uncertainties related to the tracking, luminosity, and generated p T spectrum in the MC simulations are treated as correlated between the two decay channels, the uncertainty of the branching ratios as partially correlated as described in Ref. [54], while all the other sources of systematic uncertainties are considered uncorrelated.The data points are compared with theoretical models based on the B-meson cross section predicted by FONLL calculations in the left panel and to the TAMU statistical hadronization model [49] in the right panel.In the FONLL-based predictions, the beauty-quark fragmentation fraction to B mesons, f (b → B), was taken from e + e − collisions [54]. ) from e + e − collisions enlarges the total beauty production cross section compared to the one predicted by FONLL calculations.In the TAMU model instead, the branching fractions of beauty quarks to the different hadron species are assumed to follow the relative thermal densities calculated with the statistical hadronization model and an enriched set of heavy-flavor hadron states is obtained from the relativistic-quark model [35].The p T distribution is obtained from the one of beauty quarks, convoluted to the fragmentation functions as implemented in FONLL calculations.In this case, the bb production cross section at midrapidity is a parameter of the model, fixed to dσ bb /dy| y=0 = 85.3 µb.
The resulting beauty-hadron cross sections of both models were then folded with the h b → h c + X decay kinematics (where h c and h b denote a generic hadron species containing either a charm or beauty quark) and branching ratios provided by the PYTHIA 8 decayer, in order to obtain the non-prompt D 0 and Λ + c cross sections.In the left panel, the uncertainties in the model are those of the FONLL calculation, which arise from the choice of the normalization and factorization scales, and the mass of the beauty quark, combined with the uncertainties of the CTEQ6.6PDFs.The non-prompt D 0 cross section is in agreement with FONLL + PYTHIA 8 and TAMU + PYTHIA 8 predictions over the whole p T range, while the non-prompt Λ + c cross section shows a hint of underestimation at low p T (2 < p T < 4 GeV/c) by both models.
The measured visible cross sections of non-prompt Λ + c and D 0 hadrons were computed by integrating the measured p T -differential cross sections in the measured p T range.All the systematic uncertainties Flavor dependence of the baryon-to-meson ratio in pp at √ s = 13 TeV ALICE Collaboration were propagated as fully correlated among the measured p T intervals, except for the raw-yield extraction uncertainty.As the p T -differential cross sections predicted by FONLL + PYTHIA 8 were found to be compatible with the measurements, they were assumed to provide an accurate description of the p T shape also outside of the measured p T range.Therefore, the visible cross section was then extrapolated to the full p T range, using an extrapolation factor computed as the ratio of the p T -integrated cross sections predicted by FONLL + PYTHIA 8 integrated over p T > 0 and that in the measured p T interval.The systematic uncertainty of the extrapolation factors was computed considering (i) the FONLL uncertainties, (ii) the f (b → h b ) fragmentation fractions uncertainties, and (iii) the branching ratios uncertainties of the h b → h c + X decays.The second source was estimated by using different sets of beauty fragmentation fractions (from e + e − , pp collisions [54], or those measured by LHCb [39]), while for the third one the branching ratios implemented in PYTHIA 8 were reweighted in order to reproduce the measured values reported in Ref [54].The resulting extrapolation factors are α D 0 extrap = 1.241Similarly, the bb production cross section per unit of rapidity at midrapidity was obtained summing the visible cross sections previously computed and then using an extrapolation factor to account for the unmeasured p T regions and hadrons.This factor was computed as the ratio of the beauty cross section and the visible cross section of a non-prompt charm hadron, estimated with FONLL + PYTHIA 8 as follows The extrapolation factor for the D 0 meson was found to be α bb, D 0 extrap = 2.106 +0.366 −0.014 , while the one for Λ + c baryons α bb, Λ + c extrap = 10.98 +0.87 −1.34 .The systematic uncertainty of the extrapolation factor includes the same sources considered for the extrapolation of the single-hadron production cross sections.In addition, a correction due to the difference between the rapidity distributions of beauty quarks and beauty hadrons, and between the bb pairs and beauty quarks was applied.The first factor was evaluated to be unity in the relevant rapidity range based on FONLL calculations with 1% uncertainties evaluated from the difference between FONLL and PYTHIA 8.The second correction factor is the ratio (dσ bb /dy)/(dσ b /dy) = 1.06 ± 0.01 in |y| < 0.5, which was estimated from POWHEG simulations [62].The uncertainty was assigned by varying the factorization and renormalization scales in the POWHEG calculation and using the CT10NLO [63] and CT14NLO [64] PDFs, alternatively to the default one (CTEQ6.6).The dσ bb /dy was computed separately from the measurements of non-prompt D 0 and Λ + c hadrons were then averaged using the inverse of the quadratic sum of the absolute statistical and uncorrelated systematic uncertainties as weights.The systematic uncertainties related to the tracking uncertainty and the extrapolation uncertainties related to FONLL and the beauty fragmentation fractions were treated as fully correlated among the two hadron species, while all the other sources as uncorrelated.The resulting bb production cross section per unit of rapidity at midrapidity is compatible with the predictions from FONLL and NNLO   [22] predictions.The average dσ bb /dy of the estimates from the D 0 and Λ + c hadrons is also reported.
calculations, as reported in Table 1.The NNLO predictions are however closer to the measurement and have smaller uncertainties than the FONLL ones, as expected by the higher perturbative accuracy.The measurement is also compatible with previous estimates based on the measurements of dielectrons [65, 66] and non-prompt J/ψ mesons [3].
Figure 4 shows the bb production cross section per unit rapidity at midrapidity estimated from the production cross sections of non-prompt D 0 and Λ + c hadrons in pp collisions at √ s = 13 TeV compared to the previous values based on dielectron and non-prompt J/ψ-meson measurements.The experimental results are also compared with the predictions provided by FONLL and NNLO perturbative QCD calculations.

Baryon-to-meson ratios
The ratio of the p T -differential production cross sections of non-prompt Λ + c and D 0 hadrons is shown in Fig. 5.In the left panel, the data are compared with theoretical predictions obtained with FONLL calculations [13][14][15] and PYTHIA 8 [50,58] for the description of the decay kinematics and branching ratios.They are obtained using fragmentation fractions from e + e − collisions [61] for the B mesons and the f (b → Λ 0 b )/ f (b → B) fragmentation fraction ratio measured by the LHCb Collaboration [39].The contributions of non-prompt Λ + c baryons originating from B mesons and Λ 0 b baryons are reported separately to show that the largest contribution is represented by the beauty baryons, while the B mesons contribute only marginally to the non-prompt Λ + c production cross section.Hence, it is possible to inquire the hadronization of beauty quarks into Λ 0 b baryons through the non-prompt Λ + c .In the right panel of the same figure the data are compared with the p T -differential ratio between prompt Λ + c and D 0 hadrons.The two measurements are compatible in their common p T range, with a tension of less than two standard deviations in 2 < p T < 4 GeV/c, where the ratio of non-prompt hadrons is higher than the one of promptly produced hadrons.The experimental data are also compared to the predictions obtained  c -and D 0 -hadron cross sections compared with predictions obtained with FONLL calculations [13][14][15] and PYTHIA 8 [50,58] for the h b → h c + X decay kinematics.The contributions from beauty mesons and from the Λ 0 b baryon are depicted separately.Right: p T -differential ratios of prompt [27] and non-prompt Λ + c -and D 0 -hadron cross sections compared with predictions obtained with the TAMU model [36,49] and PYTHIA 8 for the h b → h c + X decay kinematics.
with the TAMU model combined with PYTHIA 8 to describe the h b → h c + X decay kinematics, in the case of non-prompt production.The prediction for prompt charm hadrons has an error band representing the uncertainty on the BR of excited charm baryons decaying into Λ + c , not included in the one for nonprompt hadrons.The measured non-prompt Λ + c /D 0 ratio is rather well described for p T > 4 GeV/c given the current uncertainties, while it is underestimated for 2 < p T < 4 GeV/c.The prompt charm and beauty ratios are described by the TAMU calculations within the uncertainties for the whole measured p T interval.
Figure 6 shows the p T -differential non-prompt Λ + c /D 0 yield ratio at midrapidity (|y| < 0.5) in pp collisions at √ s = 13 TeV compared with the measurements of prompt Λ + c /D 0 [27], Λ/K 0 S [67], and p/π + [67] ratios at the same energy and rapidity interval, and with the Λ 0 b /(B 0 +B + ) yield ratio measured by LHCb at forward rapidity (2.5 < y < 4).The Λ 0 b /(B 0 + B + ) ratio is a bit lower than the one between non-prompt Λ + c and D 0 mesons, however it has to be considered that the normalization is slightly different.In the LHCb result the production cross sections of B 0 and B + mesons, i.e. the total yield of non-strange B mesons is used, while the non-prompt D 0 , used in this ratio, accounts for about 70% of the non-strange D mesons.Also the fraction of B 0 and B + mesons decaying to Λ + c and D + s , as well as the Λ 0 b and B 0 s hadrons decaying to D 0 mesons influence the ratio.In addition, in the non-prompt Λ + c /D 0 ratio, the h b → h c + X decay kinematics is expected to slightly modify the p T dependence compared to the one of the ratio between beauty hadrons.Interestingly, all the measurements for beauty, charm, and strange hadrons show a similar trend as a function of p T and are compatible within the uncertainties.The p/π + production ratio also features a similar p T dependence, however it is lower in absolute terms.The experimental values are compared with the corresponding predictions obtained with PYTHIA 8 simulations, using different tunes and the same rapidity ranges of the experimental results.In the top-left panel, the results obtained with the Monash 2013 tune [58], which implements a fragmentation process tuned to reproduce the measurements in e + e − collisions, is reported.Here, all the baryon-to-meson ratios are underestimated by PYTHIA 8 except for the p/π + ratio for which the model prediction is rather good at low p T .A better agreement is instead obtained with the CLR-BLC tunes (i.e.Mode 0, 2, and 3), shown ) ratio measured by the LHCb Collaboration at forward rapidity (2.5 < y < 4) [39] and with predictions obtained with the PYTHIA 8 MC generator with the Monash 2013 tune [50,58] and the CLR-BLC modes 0, 2, and 3 [37] in the corresponding rapidity range with respect to data. in the other three panels of Fig. 6.These three tunes are characterized by different constraints on the time dilation and causality, as defined in Ref. [37].The time parameters are relevant in this model, because two strings can reconnect if they are able to resolve each other during the time between their formation and hadronization, taking also into account time-dilation effects caused by relative boosts.The Mode 0 and 2 settings, reported in the top-right and bottom-left panels of Fig. 6 respectively, predict a similar baryon-to-meson ratio for the strange, charm, and beauty flavors for p T > 2 GeV/c and a significantly higher ratio for heavy-flavor hadrons than strange hadrons for lower p T (e.g., a factor three is predicted at p T ≈ 400 MeV/c).Despite the agreement with the data is significantly improved compared to the Monash tune, the measurements of beauty hadrons are overestimated for p T 10 GeV/c.Instead, the Mode 3 (bottom-right panel of Fig. 6) underestimates the ratio for charm hadrons for p T 12 GeV/c and overestimates that of beauty hadrons in the same p T interval, quantitatively more than the other two CLR-BLC modes.The features, observed in all comparisons with PYTHIA 8 tunes, indicate that more precise Flavor dependence of the baryon-to-meson ratio in pp at √ s = 13 TeV ALICE Collaboration  1.All the systematic uncertainties, except for those related to the tracking efficiency, were propagated as uncorrelated in the ratio.The resulting value is compatible with the one measured for promptly produced particles and significantly higher than that measured in e + e − collisions at LEP [68].All the values are reported in Table 2.

Conclusions
In summary, the p T -differential and p T -integrated production cross sections of non-prompt Λ + c and D 0 hadrons were measured for the first time at midrapidity in pp collisions at √ s = 13 TeV.The results are compatible with the theoretical models based on FONLL calculations with the f (b → Λ 0 b ) and f (b → B) fragmentation fractions measured by LHCb and at e + e − , respectively, suggesting a similar beauty-baryon enhancement at forward and midrapidity in pp collisions.Furthermore, the results are in agreement with the TAMU statistical hadronization model for the relative abundances of different beauty hadron species.The extrapolated bb production cross section at midrapidity per unit of rapidity is found to be compatible with pQCD calculations with FONLL and NNLO accuracy.The measured baryon-to-meson ratios of light flavor, strange, charm, and beauty hadrons show a similar p T trend.In addition, all ratios, except the p/π + , are significantly higher than the values measured in e + e − collisions.The p T -differential baryonto-meson ratios have been compared to predictions of the TAMU statistical hadronization model and to the PYTHIA 8 simulations, that include the color-reconnection mechanism in the string fragmentation and indicate that all the flavors have to be considered simultaneously in order to obtain the best tuning of the model parameters involving the reconnection of quarks via junction topologies.This feature asks for more precise results, including a direct measurement of beauty hadrons especially in the same p T and rapidity range and the p T < 4 GeV/c region, which can be reached with the data collected in the LHC Run 3 data taking period.

Figure 1 :
Figure 1: Invariant-mass distributions of the D 0 -and Λ + c -hadron candidates and their charge conjugates produced in pp collisions at √ s = 13 TeV and reconstructed at midrapidity, shown in a selected p T range.The values for the Gaussian mean µ, width σ , and raw yield S are reported.Top row: D 0 → K − π + meson candidates measured in the 2 < p T < 4 GeV/c interval.Middle row: Λ + c → pK 0 S baryon candidates measured in the 2 < p T < 4 GeV/c interval.Bottom row: Λ + c → pK − π + baryon candidates measured in the 2 < p T < 4 GeV/c interval.The corresponding BDT probability minimum threshold for the candidate selection is reported.The left (right) column corresponds to the prompt (non-prompt) D 0 -and Λ + c -hadron candidates enriched sample.

FlavorFigure 2 :
Figure2: Raw-yield distribution as a function of the BDT-based selection employed in the χ 2 -minimization procedure adopted for the determination of f non-prompt of D 0 in 2 < p T < 4 GeV/c (top left panel), Λ + c → pK − π + in 4 < p T < 6 GeV/c (top right panel), and Λ + c → pK 0 S in 6 < p T < 8 GeV/c (bottom left panel).Bottom right panel: f non-prompt fraction as function as p T obtained for the set of selection criteria adopted in the analysis of for non-prompt D 0 , Λ + c → pK − π + , and Λ + c → pK 0 S hadrons.

Figure 3 :
Figure 3: p T -differential production cross sections of non-prompt D 0 and Λ + c hadrons in pp collisions at √ s = 13 TeV compared with predictions obtained with FONLL calculations [13-15] adopting f (b → B) and f (b → Λ 0 b) fragmentation fractions measured in e + e − collisions[61] and LHCb Collaboration[39] (left panel) and the TAMU model[49] (right panel) combined with PYTHIA 8[50,58] for the h b → h c + X decay kinematics.

Flavor
dependence of the baryon-to-meson ratio in pp at √ s

Figure 5 :
Figure 5: Left: p T -differential ratios of non-prompt Λ +c -and D 0 -hadron cross sections compared with predictions obtained with FONLL calculations[13][14][15] and PYTHIA 8[50,58] for the h b → h c + X decay kinematics.The contributions from beauty mesons and from the Λ 0 b baryon are depicted separately.Right: p T -differential ratios of prompt [27] and non-prompt Λ + c -and D 0 -hadron cross sections compared with predictions obtained with the TAMU model[36,49] and PYTHIA 8 for the h b → h c + X decay kinematics.
The p T -integrated cross sections are reported in Table 1 and compared to FONLL + PYTHIA 8 calculations, which describe the measurements within the uncertainties.

Table 1 :
Production cross sections at midrapidity per unit of rapidity (dσ /dy) |y|<0.5 in pp collisions at

Table 2 :
p T -integrated Λ + c /D 0 production ratio measured at midrapidity (|y| < 0.5) in pp collisions at √ s = 13 TeV and in e + e − collisions at LEP [68] for prompt and non-prompt production.T (p T < 2 GeV/c) are crucial for tuning the model parameters involving the reconnection of quarks via junction topologies and to possibly validate this as the mechanism responsible of the baryon enhancement observed in hadron collisions compared to e + e − collisions.It is worth pointing out that other theoretical models are proposed to describe the enhancement, based on different hadronization mechanisms (e.g.recombination).The p T -integrated non-prompt Λ + c /D 0 ratio was computed by dividing the p T -integrated cross sections reported in Table Austrian Academy of Sciences, Austrian Science Fund (FWF): [M 2467-N36] and Nationalstiftung für Forschung, Technologie und Entwicklung, Austria; Ministry of Communications and High Technologies, National Nuclear Research Center, Azerbaijan; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Financiadora de Estudos e Projetos (Finep), Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) and Universidade Federal do Rio Grande do Sul (UFRGS), Brazil; Bulgarian Ministry of Education and Science, within the National Roadmap for Research Infrastructures 2020-2027 (object CERN), Bulgaria; Ministry of Education of China (MOEC) , Ministry of Science & Technology of China (MSTC) and National Natural Science Foundation of China (NSFC), China; Ministry of Science and Education and Croatian Science Foundation, Croatia; Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Cubaenergía, Cuba; Ministry of Education, Youth and Sports of the Czech Republic, Czech Republic; The Danish Council for Independent Re-NN =5.02 TeV", Phys.Rev. C 104 (2021) 054905, arXiv:2011.06079[nucl-ex].