Measurement of $\Xi_{c}^{+}$ production in $p$Pb collisions at $\sqrt{s_{NN}}=8.16$ TeV at LHCb

A study of prompt $\Xi_{c}^{+}$ production in proton-lead collisions is performed with the LHCb experiment at a centre-of-mass energy per nucleon pair of 8.16 TeV in 2016 in $p$Pb and Pb$p$ collisions with an estimated integrated luminosity of approximately 12.5 and 17.4 nb$^{-1}$, respectively. The $\Xi_{c}^{+}$ production cross-section, as well as the $\Xi_{c}^{+}$ to $\Lambda_{c}^{+}$ production cross-section ratio, are measured as a function of the transverse momentum and rapidity and compared to latest theory predictions. The forward-backward asymmetry is also measured as a function of the $\Xi_{c}^{+}$ transverse momentum.


Introduction
In hadronic collisions, heavy quarks are produced in hard scattering processes with large momentum transfer.Theoretical predictions based on perturbative quantum chromodynamics (pQCD) describe reasonably well the transverse momentum (p T ) differential charm production cross sections in proton-proton (pp) collisions at different energies [1].The heavy-flavor hadron cross sections are usually computed using the factorization approach as a convolution of three terms [2]: the parton distribution functions of the colliding particles, the hard-scattering cross section, and the fragmentation function (FF) of heavy quarks into a given heavy-flavor hadron.It is assumed that the FFs are universal between collision systems and energies.At the CERN Large Hadron Collider (LHC), the FFs used to describe the measurements of heavy-flavor hadron production in pp collisions at different center-of-mass energies are tuned on e + e − collision data within the framework of pQCD over a wide p T range.However, evidence of nonuniversal FFs was observed by the LHCb collaboration in a study of the Λ 0 b baryon to B − and B0 meson production ratio in pp collisions [3].Multiple measurements of the relative production of different heavy-flavor hadron species have been made, as they are sensitive probes of FFs.
The measurements of heavy-flavored hadron ratios in hadronic collisions, such as the Λ + c /D 0 cross-section ratio, in pp collisions at √ s = 5, 7 and 13 TeV and in proton-lead (pPb) collisions at √ s = 5 TeV [4][5][6], show an enhancement with respect to predictions from pQCD calculations with charm fragmentation based on e + e − [7, 8] and e − p [9-11] measurements.Similar observations were made in the measurement of the Ξ 0 c (Ξ + c )/D 0 cross section ratio in pp collisions at √ s = 7 and 13 TeV [12,13].Multiple models explain the ratio enhancement.For example, color reconnection [14] could be stronger in pp collisions than in e + e − collisions, resulting in an enhanced production of baryons relative to mesons.Other models predicts that hadronization via coalescence [15] will take place.
This paper presents a study of the ratio of production of the Ξ + c particle, a charmstrange baryon, to the production of the Λ + c baryon in pPb collisions at the LHCb experiment.This measurement has the potential to shed light on the mechanism of hadronization and its universality as it is the first one to be performed in proton-nucleus collisions, considered the best environment to study the so-called cold nuclear matter (CNM) effects, such as shadowing [16][17][18], energy loss [19] and nuclear break-up [20].In nucleus-nucleus collisions, in addition to CNM effects, experimental results indicate the formation of a high-density color-deconfined medium, the quark-gluon plasma (QGP), a state of matter with asymptotically free partons, which is expected to exist at extremely high temperature and density.The presence of QGP can be determined by observing the change in behavior of the particles as they traverse the nuclear medium with respect to their behavior in the absence of QGP [21].In pPb collisions the energy density is not expected to be sufficient to produce a QGP medium; however, some theoretical models predict the formation of "QGP droplets" [22], which could partially induce in pPb the same behavior, albeit less pronounced, as in PbPb collisions.Moreover, several QGP models predict that strange (s) quark production is enhanced in heavy-ion collisions, as first reported in Ref. [23]; thus, strangeness enhancement and strange antibaryon abundance are considered signatures for QGP formation [24][25][26], mainly due to the predominance of the gluonic production mechanism gg → ss.Strangeness enhancement is investigated at accelerators by studying the ratio of production rates of hadrons containing a strange quark to those without, as done, by experiments at CERN [27] and BNL Relativistic c quarks.The detector includes a high-precision tracking system consisting of a siliconstrip vertex detector surrounding the pp interaction region [34], a large-area silicon-strip detector located upstream of a dipole magnet with a bending power of about 4 Tm, and three stations of silicon-strip detectors and straw drift tubes [35] placed downstream of the magnet.The tracking system provides a measurement of the momentum, p, of charged particles with a relative uncertainty that varies from 0.5% at low momentum to 1.0% at 200 GeV/c.The minimum distance of a track to a primary pp collision vertex (PV), the impact parameter (IP), is measured with a resolution of (15 + 29/p T ) µm, where p T is the component of the momentum transverse to the beam, in GeV/c.The different types of charged hadrons, such as the kaons and pions used in this analysis, are distinguished using information from two ring-imaging Cherenkov detectors [36].Photons, electrons and hadrons are identified by a calorimeter system consisting of scintillating-pad and preshower detectors, an electromagnetic and a hadronic calorimeter.Muons are identified by a system composed of alternating layers of iron and multiwire proportional chambers [37].The online event selection is performed by a trigger [38], which consists of a hardware stage, based on information from the calorimeter and muon systems, followed by a software stage, which applies a full event reconstruction.
Simulation is used to model the reconstruction efficiency and the effects of the selection requirements.Charmed baryons are generated in pp collisions at √ s = 8.16 TeV using the Pythia [39] generator and are embedded into the EPOS [40] generator, which simulates the environment of the proton-lead collision.Particle decays are described by EvtGen [41], while the interaction of particles with the detector, and its response in simulation, are implemented using the Geant4 toolkit [42,43].

Candidate selection
The online event selection is performed by a trigger, which consists of a hardware stage followed by a two-level software stage.In between the two software stages, an alignment and calibration of the detector is performed in near real-time and their results are used in the trigger [44].The same alignment and calibration information is propagated to the offline reconstruction, ensuring consistent and high-quality particle identification (PID) information between the trigger and offline software.The identical performance of the online and offline reconstruction offers the opportunity to perform physics analyses directly using candidates reconstructed in the trigger [38,45] which the present analysis exploits.The Ξ + c and Λ + c baryons are reconstructed by combining three tracks identified as proton, kaon and pion candidates.All the charged tracks are required to be well reconstructed and to have transverse momentum p T > 400 MeV/c and be incompatible with originating at the PV.The tracks must also be within the LHCb acceptance 2.0 < η < 5.0 and in the kinematic range 3.2 < p < 100.0 GeV/c.The Ξ + c and Λ + c candidates are required to have a good quality secondary vertex and a reconstructed decay time between 0.1 and 10 ps.The angle between the reconstructed candidate momentum and the vector pointing from the PV to the secondary vertex is required to be close to zero.The pK − π + invariant mass is required to be within ±70 MeV/c 2 of the known Ξ + c (Λ + c ) mass [31].The invariant mass resolution for the reconstructed candidates is around 10 MeV/c 2 .

Determination of signal yields and efficiency
The signal yields are determined using a maximum-likelihood fit to the pK − π + invariant mass distributions, which were verified to be independent of the other kinematic variables.The signal component of the fit model is represented by a sum of a Crystal Ball function [46] and a Gaussian function, which share a common mean value.The background component is described by a linear function.The results of the invariant mass fits for Ξ + c and Λ + c in pPb and Pbp data samples are shown in Fig. 1.
The obtained signal yields are about 13.3 × 10 3 (12.6 × 10 3 ) Ξ + c decays and 119.2 × 10 3 (104.4× 10 3 ) Λ + c decays in the pPb (Pbp) sample after background subtraction, achieved using the sPlot technique [47] with the pK − π + invariant mass as the discriminating variable.The extracted signal contains promptly produced baryons and nonprompt signal from the decay of b hadrons.To extract the prompt component, the method developed in Ref.
[6] is used, with the variable χ 2 IP discriminating between prompt and nonprompt production.The χ 2 IP variable is defined as the difference in the vertex-fit χ 2 of a given PV reconstructed with and without the Ξ + c (Λ + c ) candidate under consideration.The prompt and nonprompt components are modelled with a Bukin function [48].The asymmetry parameters of the Bukin function describing the prompt component are fixed using results   Simulated data are used to determine the total efficiency, defined as the product of the geometrical acceptance of the detector, and the reconstruction, selection, PID and trigger efficiencies.The samples are weighted to match the background-subtracted data using the distributions of p T , y * , the number of VELO clusters and the invariant mass of the pK − and K − π + combinations.The PID efficiency is also measured with dedicated calibration data samples [49].

Systematic uncertainties
Several sources of systematic uncertainty are studied.A systematic uncertainty in the signal yield determination is evaluated by changing the function used in the fit for the nonprompt component, switching from a Bukin function to a Gaussian.The difference in the signal yields obtained with the two fits is taken as a systematic uncertainty.The systematic uncertainty associated to the background determination, which is dominant, is  0.4-1.5 % 0.5-3.0 % 0.2-2.3% 0.4-3.8% ε trg/sel 0.4-0.5 % 0.4-0.6 % 0.4-0.5 % 0.4-1.2% Total 1.6-6.4% 2.7-27.8% 4.1-9.9% 1.8-17.9% evaluated by using a sideband subtraction technique, instead of the sPlot method.The uncertainties in reconstruction, selection, and PID efficiencies are evaluated by varying the reweighting procedure by excluding the distributions of the invariant mass of the pK − and K − π + combinations.The uncertainties in the branching fractions are accounted for.Summaries of the systematic uncertainties in the Ξ + c and Λ + c cross sections can be found in Tables 1, 2, and 3.

Results
In this section the different measurements performed are discussed.More results can be found in the Appendix.

Double-differential cross section
The double-differential cross sections of prompt Ξ + c production times B(Ξ + c → pK − π + ) in proton-lead collisions at √ s N N = 8. 16 TeV are measured as a function of p T integrated over y * in the regions 1.5 < y * < 4.0 and −5.0 < y * < −2.5, and as a function of y * integrated over the p T range between 2.0 and 12.0 GeV/c.The double-differential cross sections of prompt Ξ + c production are shown in Fig. 3.The data are compared with theoretical predictions [50][51][52] from the HELAC-Onia method [53,54] called EPPS16 [55] with three factorization scale choices.The data agree with the predictions and appear to be best described using the scale 0.5µ 0 .For the forward and backward regions, the integrated cross sections are where the first uncertainty is statistical, the second is the uncorrelated systematic uncertainty and the third is the systematic uncertainty fully correlated among bins.

Forward-backward asymmetry
The forward-backward ratio R FB , defined in Eq. ( 3) and measured as a function of p T , is shown in Fig. 4. The ratio is independent of p T and agrees with the theoretical prediction within one standard deviation.

Differential ratio of Ξ
The differential ratio of Ξ + c to Λ + c production is measured as a function of the number of clusters reconstructed in the VELO (N VELO clusters ) and given in Fig. 5.The ratios are constant as a function of N VELO clusters , similarly for the pPb and Pbp data, and the results show no indication of strangeness enhancement.
Since LHCb has already measured the D 0 production cross section in pPb collisions at √ s = 8.16 TeV [56], it is also possible to compute the Ξ + c /D 0 production ratio.The differential ratios of Ξ + c to Λ + c production and Ξ + c to D 0 production are shown in Fig. 6 as a function of p T .Both the Ξ + c /Λ + c and Ξ + c /D 0 ratios show no significant p T dependence, similarly for the pPb and Pbp data samples.This result provides a strong indication   that the same processes govern hadronization in pPb and Pbp collisions.This is the first time they are measured in this system.The data are compared with EPPS16 nPDF predictions [55], which uses the cross section measured in pp collisions by ALICE [13] as input for their calculation.The EPPS16 model shows a similar trend as the data, but significantly overestimates it.The measurements are also compared with results from the Pythia 8.3 event generator with a tune that implements color reconnection (CR) beyond the leading-color approximation [14] and the computation obtained with EPOS4HQ, the heavy quark extension of the new EPOS4 framework [4].Both computations are based on results in pp collisions.The Ξ + c /Λ + c cross section ratio is best described by the EPOS4HQ model within uncertainties, despite showing a different trend, especially at low p T .This behavior is even more pronounced in the Ξ + c /D 0 cross section ratio.The Ξ + c to D 0 production ratio is also compared with the result of ALICE at √ s = 13 TeV at |y| <0.5 in pp collisions [13].The ALICE result is generally higher, but the two measurements agree within the uncertainties.

Summary
In summary, the prompt Ξ + c production cross section in pPb and Pbp collisions at a centerof-mass energy of √ s N N = 8. 16 TeV at the LHCb experiment is measured differentially for the first time as a function of p T and y * .The cross section measurement provides new constraints for nPDF calculations, especially at low p T , where the uncertainty on the factorisation scale is the largest.The forward-backward ratio R FB is measured and found to be well described by nuclear shadowing calculations showing that there are no major final-state effects involved, in contrast to what has been observed in D 0 production studies in the same kinematic range at the same energy [56].Prompt Ξ + c production is compared to prompt Λ + c production in the same kinematic region and their ratio is found to be constant within the uncertainties as a function of p T and multiplicity, which is an indication that similar effects govern both Ξ + c and Λ + c production.The ratio of Ξ + c to D 0 production is also measured as a function of p T .Both ratios are found to be similar in pPb and Pbp collisions but they show different trends compared to pp theory calculations.Therefore, our results show that hadronization in pPb is not well understood and provides clear input for the hadronization studies in pPb collisions.

A Additional plots
The differential ratios of Ξ + c to Λ + c and to D 0 production multiplied by B(Ξ + c → pK − π + ) are shown in Figs. 7, 8, 9 and 10 as a function of p T and y * .o Università di Padova, Padova, Italy p Università di Perugia, Perugia, Italy q Scuola Normale Superiore, Pisa, Italy r Università di Pisa, Pisa, Italy s Università della Basilicata, Potenza, Italy t Università di Roma Tor Vergata, Roma, Italy u Università di Urbino, Urbino, Italy v Universidad de Alcalá, Alcalá de Henares , Spain † Deceased

Figure 1 :
Figure 1: Invariant mass distributions for (a) Ξ + c candidates in pPb data, (b) Ξ + c candidates in Pbp data, (c) Λ + c candidates in pPb data, and (d) Λ + c candidates in Pbp data.The results of the fit are overlaid.

Figure 2 :
Figure 2: Background-subtracted log 10 (χ 2 IP ) distributions of (a) Ξ + c and (b) Λ + c candidates in (left) pPb and (right) Pbp data.The results of the fit are overlaid.

Figure 3 :
Figure 3: Double-differential cross section of the prompt Ξ + c baryon times B(Ξ + c → pK − π + ) in proton-lead collisions as a function of (a) p T and (b) y * in pPb (red triangles) and Pbp (blue triangles) collisions.The error bars represent the statistical uncertainties, while the black squares represent the total systematic uncertainties which include correlations among bins.

Figure 4 :Figure 5 :
Figure 4: Forward-backward ratio of Ξ + c production as a function of p T .The error bars represent the statistical uncertainties, while the boxes indicate the systematic uncertainty.

Figure 6 :
Figure 6: Ratio of (left) prompt Ξ + c to Λ + c production and (right) Ξ + c to D 0 production in the pPb (red triangles) and Pbp (blue triangles) data samples as a function of p T .The error bars represent the statistical uncertainties, while the empty rectangles indicate the systematic uncertainty.Shaded rectangles denote the branching ratio uncertainty.

Figure 7 :
Figure 7: Production ratio of prompt Ξ + c to Λ + c baryons multiplied by B(Ξ + c → pK − π + ) in pPb (red triangles) and Pbp (blue triangles) data samples as a function of p T .The error bars represent the statistical uncertainties while the squares indicate the systematic uncertainty.

Figure 8 :
Figure 8: Production ratio of prompt Ξ + c to Λ + c baryons multiplied by B(Ξ + c → pK − π + ) in pPb (red triangles) Pbp (blue triangles) data samples as a function of y * .The error bars represent the statistical uncertainties while the squares indicate the systematic uncertainty.

Figure 9 :
Figure 9: Production ratio of prompt Ξ + c to D 0 baryons multiplied by B(Ξ + c → pK − π + ) in pPb (red triangles) and Pbp (blue triangles) data samples as a function of p T .The error bars represent the statistical uncertainties while the squares indicate the systematic uncertainty.

Figure 10 :
Figure 10: Production ratio of prompt Ξ + c to D 0 baryons multiplied by B(Ξ + c → pK − π + ) in pPb (red triangles) and Pbp (blue triangles) data samples as a function of y * .The error bars represent the statistical uncertainties while the squares indicate the systematic uncertainty.

Table 1 :
Summary of systematic uncertainties on the Ξ + c and Λ + c cross sections in p T bins in the pPb and Pbp samples.The range of uncertainties correspond to the values obtained for different bins of p T .

Table 2 :
Summary of systematic uncertainties on the Ξ + c and Λ + c cross sections in y * bins in the pPb and Pbp samples.The range of uncertainties correspond to the values obtained for different bins of y * .

Table 3 :
Summary of systematic uncertainties correlated among bins on the Ξ + c and Λ + c cross sections in the pPb and Pbp samples.