Measurement of prompt D$^{0}$, $\Lambda_{c}^{+}$, and $\Sigma_{c}^{0,++}$(2455) production in pp collisions at $\sqrt{s} = 13$ TeV

The $p_{\rm T}$-differential production cross sections of prompt D$^{0}$, $\Lambda_{\rm c}^{+}$, and $\Sigma_{\rm c}^{0,++}(2455)$ charmed hadrons are measured at midrapidity ($|y|<0.5$) in pp collisions at $\sqrt{s} = 13$ TeV. This is the first measurement of $\Sigma_{\rm c}^{0,++}$ production in hadronic collisions. Assuming the same production yield for the three $\Sigma_{\rm c}^{0,+,++}$ isospin states, the baryon-to-meson cross section ratios $\Sigma_{\rm c}^{0,+,++}/{\rm D}^{0}$ and $\Lambda_{\rm c}^{+}/{\rm D}^{0}$ are calculated in the transverse momentum ($p_{\rm T}$) intervals $2<p_{\rm T}<12$ GeV/$c$ and $1<p_{\rm T}<24$ GeV/$c$. Values significantly larger than in e$^{+}$e$^{-}$ collisions are observed, indicating for the first time that baryon enhancement in hadronic collisions also extends to the $\Sigma_{\rm c}$. The feed-down contribution to $\Lambda_{\rm c}^{+}$ production from $\Sigma_{\rm c}^{0,+,++}$ is also reported and is found to be larger than in e$^{+}$e$^{-}$ collisions. The data are compared with predictions from event generators and other phenomenological models, providing a sensitive test of the different charm-hadronisation mechanisms implemented in the models.

(2455) charmed hadrons are measured at midrapidity (|y| < 0.5) in pp collisions at √ s = 13 TeV. This is the first measurement of Σ 0,++ c production in hadronic collisions. Assuming the same production yield for the three Σ 0,+,++ c isospin states, the baryon-to-meson cross section ratios Σ 0,+,++ c /D 0 and Λ + c /D 0 are calculated in the transverse momentum (p T ) intervals 2 < p T < 12 GeV/c and 1 < p T < 24 GeV/c. Values significantly larger than in e + e − collisions are observed, indicating for the first time that baryon enhancement in hadronic collisions also extends to the Σ c . The feed-down contribution to Λ + c production from Σ 0,+,++ c is also reported and is found to be larger than in e + e − collisions. The data are compared with predictions from event generators and other phenomenological models, providing a sensitive test of the different charm-hadronisation mechanisms implemented in the models.
The formation of hadrons out of quarks ("hadronisation") represents a fundamental process in nature that can be investigated at particle colliders where, at high collision energies, quarks represent the relevant degrees of freedom for a very short time of the order of 10 −23 s. The measurement of the relative production rates of different charm hadron species allows to study how charm quarks, produced only in initial hard scatterings, combine with other quarks, which may either exist in the system before hadronisation or be produced in the strong-force potential at hadronisation time. Recent measurements of Λ + c -, Ξ 0 c -and Λ 0 b -baryon production in pp collisions at √ s = 5.02, 7, and 13 TeV [1-8] indicate that the production of charm and beauty baryons relative to that of charm and beauty mesons is enhanced in pp with respect to e + e − and ep collisions [9][10][11][12][13][14][15]. Several models tuned to reproduce the e + e − data significantly underestimate the ratios measured in pp collisions and do not describe the observed transverse-momentum (p T ) trends. These measurements also set kinematic boundaries to the validity of the assumption made in perturbative-QCD calculations like FONLL [16,17] and GM-VFNS [18][19][20][21][22][23] that fragmentation functions tuned on e + e − and ep data can be used in pp collisions.
The Σ 0,+,++ c baryon triplet is the isospin I = 1 partner of the singlet (I = 0) Λ + c baryon. All these states are composed of a charm quark and a pair of light (u, d) quarks. In e + e − collisions, while in the light-flavour sector the mass dependence of the yields of the Σ and Λ states is well described by a single exponential function, the yields of the Σ 0,+,++ c states are about a factor 4 smaller than those of the Λ + c -states [24]. In the framework of hadronisation via string fragmentation, this suppression can be ascribed to the need to form Σ 0,+,++ c via the combination of a heavy charm quark, which is always a string endpoint, and a diquark with spin S = 1 and I = 1 formed via the Schwinger tunnelling process [24,25]. The large mass of S = 1 diquarks suppresses their formation with respect to S = 0 diquarks, hence the Σ 0,+,++ c production yield is suppressed with respect to the Λ + c yield. In the models that provide a fair description of the Λ + c /D 0 ratio in pp collisions (here denoted as "CR-BLC" [25], "SHM+RQM" [26], "Catania" [27, 28], "QCM" [29]) this suppression mechanism is absent or heavily reduced, and a sizeable contribution to Λ + c production from strong decays of Σ 0,+,++ c states is expected. Therefore, the measurement of the ground-state Σ 0,+,++ c (2455) production is fundamental to understand the dynamics of heavy-flavour baryon formation, providing a key test for the different scenarios proposed in the mentioned models. Among these, the CR-BLC model is a version of PYTHIA 8 in which terms beyond the leading-colour approximation (BLC) are considered in string formation, representing more accurately the QCD SU(3) algebra and de facto enhancing effects from colour reconnection (CR). These terms cause confining potentials to also arise between quarks not produced in the same hard scattering and are relevant to hadronic collisions at high energies, where multiple-parton interactions produce an environment rich in quarks and gluons. Moreover, they give rise to "junction topologies" that favour the production of baryon states and do not penalise the formation of Σ 0,+,++ c with respect to Λ + c states. The production of Σ 0,+,++ c (2455) is expected to increase by large factors, up to 25, and become even larger than that of direct Λ + c . The SHM+RQM model predicts a large feed-down contribution to the Λ + c ground state from an enriched set of mostly unobserved excited charm-hadron states expected from the Relativistic Quark Model (RQM [30]). The branching fractions of charm quarks to the various hadron species are assumed to follow the relative thermal densities calculated with the Statistical Hadronisation Model (SHM [31]), therefore to depend only on the state mass and spin-degeneracy factor. In the Catania model charm quarks can hadronise via "vacuum"-like fragmentation as well as recombine (coalesce) with surrounding light quarks from the underlying event. The Wigner formalism is used to calculate the probability to form a baryon (meson) given the phase-space distribution of three (two) quarks. A different formalism is implemented in the QCM ("quark (re-)combination mechanism") model, in which charm quarks form hadrons by combining with equal-velocity light quarks. In this model, the relative abundances of the different baryon species are fixed by thermal weights.
In this letter, the measurement performed with the ALICE experiment of the p T -differential cross sections of prompt D 0 , Λ + c , and Σ 0,++ c (2455) in pp collisions at √ s = 13 TeV at midrapidity (|y| < 0.5) is reported. This is the first production measurement for Σ 0,++ c (2455) in hadronic collisions. The baryon-  Figure 1: Left: distribution of π + K − pπ ± to π + K − p (and charge conjugate) invariant-mass difference in 4 < p Σ c T < 6 GeV/c. Right: p T -differential cross section of prompt D 0 , Λ + c , and Σ 0,++ c in pp collisions at √ s = 13 TeV. The statistical and systematic uncertainties are shown as vertical lines and boxes, respectively. reconstructed with Λ + c → pK − π + candidates is improved by requiring |d rϕ − d verse of the quadratic sum of the relative statistical and uncorrelated systematic uncertainties as weights. The total systematic uncertainty of the averaged Σ c cross section varies from 20% at low p T to 13% at high p T . The cross-section ratios Λ + c /D 0 and Σ 0,+,++ c /D 0 are compared with model expectations in Fig. 2 (left and middle panels). In the ratios, the systematic uncertainties of the track-reconstruction efficiency and luminosity, considered as fully correlated, cancel partly and completely, respectively. The feed-down uncertainty is propagated as partially correlated, while all other uncertainties are treated as uncorrelated. The Λ + c /D 0 ratio decreases with increasing p T and is significantly larger than the ≈0.12 values observed in e + e − and ep collisions at several collision energies [12][13][14][15][45][46][47]. The values measured in pp collisions at √ s = 13 TeV are compatible, within uncertainties, with those measured at √ s = 5.02 TeV [3, 4]. As shown in Fig. 2 (middle), the Σ 0,+,++ c /D 0 ratio is close to 0.2 for 2 < p T < 6 GeV/c, and decreases with p T down to about 0.1 for 8 < p T < 12 GeV/c, though the uncertainties do not allow firm conclusions about the p T dependence to be made. From Belle measurements (Table IV in Ref. [24]), the Σ 0,+,++ c /Λ + c ratio in e + e − collisions at √ s = 10.52 GeV can be evaluated to be around 0.17 and, thus, the Σ 0,+,++ c /D 0 ratio can be estimated to be around 0.02. Therefore, a remarkable difference is present between the pp and e + e − collision systems. Although rather approximate, such comparison is corroborated by the fact that a simulation performed with the default version of PYTHIA 6.2 reasonably reproduces Belle data [24], while the default version of PYTHIA 8.243 (Monash 2013 tune) severely underpredicts ALICE data, despite the very similar modelling of charm fragmentation in the two simulations. Figure 2 (right) shows the ratio Λ + c ← Σ 0,+,++ c /Λ + c as a function of p T , which quantifies the fraction of Λ + c feed-down from Σ 0,+,++ c . In order to better exploit the cancellation of correlated uncertainties, this is calculated as the weighted average of the ratios measured separately in the Λ + c → pK − π + and Λ + c → pK 0 S decay channels. The p T -integrated value in the measured p T > 2 GeV/c interval is 0.38 ± 0.06(stat) ± 0.06(syst), significantly larger than the ratio Σ 0,+,++ c /Λ + c ∼ 0.17 from Belle data and the ∼0.13 expectation from PYTHIA 8 (Monash 2013) simulations. This indicates a larger increase for Σ 0,+,++ c /D 0 than for the direct-Λ + c /D 0 ratio from e + e − to pp collisions. The larger feed-down from Σ 0,+,++ c partially explains the difference between the Λ + c /D 0 ratios in pp and e + e − collisions. As shown in Figure 2, the CR-BLC (for which the three variations defined in Ref. [25] are considered), SHM+RQM, and Catania models describe, within uncertainties, both the Λ + c /D 0 and Σ 0,+,++ c /D 0 ratios. The QCM model uses the Λ + c /D 0 data in pp collisions at √ s = 7 TeV to set the total charm baryon-c , and Σ 0,++ c production in pp collisions at √ s = 13 TeV ALICE Collaboration to-meson ratio, but it predicts correctly the Λ + c ← Σ 0,+,++ c /Λ + c and the p T -shape of all ratios. The Λ + c ← Σ 0,+,++ c /Λ + c ratio does not show a p T trend as steep as that expected from the CR-BLC model, which significantly overestimates the Λ + c feed-down from Σ 0,+,++ c at low p T . Therefore, the data suggest that further tuning of the model parameters involving the reconnection of quarks via junction topologies is needed to possibly validate this as the mechanism reducing the assumed suppression of Σ 0,+,++ c formation in e + e − collisions [24,25]. In the Catania, QCM, and SHM+RQM models, no specific penalty factor affects the formation of Σ c states. The fact that the SHM+RQM model reproduces both the Λ + c /D 0 ratio and the fraction of Λ + c feed-down from Σ 0,+,++ c may suggest that yet-unobserved higher-mass charmbaryon states exist and are formed more frequently in pp collisions than in e + e − and ep collisions. Similarly, the success of the Catania and QCM models in reproducing the data may indicate that charm hadronisation in pp collisions involves coalescence of charm quark with light quarks.
The p T -differential cross section of Σ 0,++ c has been measured in pp collisions at √ s = 13 TeV in the range 2 < p T < 12 GeV/c, the first measurement in hadron-hadron collisions, together with the Λ + c and D 0 cross sections in the range 1 < p T < 24 GeV/c. The charm baryon-to-meson cross section ratios were found to be larger than expectations based on e + e − measurements. The reported results confirm previous observations at √ s = 5.02 TeV and √ s = 7 TeV for the Λ + c and show for the first time that the effect also extends to the Σ 0,++ c . The feed-down from Σ 0,+,++ c decays to Λ + c production amounts to 0.38 ± 0.06(stat) ± 0.06(syst) in the range 2 < p T < 12 GeV/c, which is significantly larger than measurements in e + e − collisions. The results presented provide important constraints on models aiming at explaining the observed increase of charm baryons in a parton-rich environment, either increasing baryon-formation probability via enhanced colour reconnection or coalescence mechanisms, or assuming feed-down from yet-unobserved higher-mass baryon states.         [41] T. Sjöstrand, S. Mrenna, and P. Z. Skands, "PYTHIA 6.4 Physics and Manual", JHEP 05 (2006) 026, arXiv:hep-ph/0603175.