Abstract
The ratios of yields of antibaryons to baryons probes the mechanisms of baryonnumber transport. Results for \(\overline{\mathrm {p}}/{\mathrm{p}}\), \(\overline{\Lambda}/{\Lambda}\), \({{\overline{\Xi}}^{+}}/{\Xi ^{}}\) and \({{\overline{\Omega}}^{+}}/{\Omega^{}}\) in pp collisions at \(\sqrt{s} = 0.9,\ 2.76\mbox{ and }7\mbox{ TeV}\), measured with the ALICE detector at the LHC, are reported. Within the experimental uncertainties and ranges covered by our measurement, these ratios are independent of rapidity, transverse momentum and multiplicity for all measured energies. The results are compared to expectations from event generators, such as PYTHIA and HIJING/B, that are used to model the particle production in pp collisions. The energy dependence of \(\overline{\mathrm{p}}/{\mathrm{p}}\), \(\overline {\Lambda}/{\Lambda}\), \({{\overline{\Xi}}^{+}}/{\Xi^{}}\) and \({{\overline{\Omega}}^{+}}/{\Omega^{}}\), reaching values compatible with unity for \(\sqrt{s} = 7\mbox{ TeV}\), complement the earlier \(\overline{\mathrm{p}}/{\mathrm{p}}\) measurement of ALICE. These dependencies can be described by exchanges with the Reggetrajectory intercept of \(\alpha_{\rm{J}} \approx0.5\), which are suppressed with increasing rapidity interval Δy. Any significant contribution of an exchange not suppressed at large Δy (reached at LHC energies) is disfavoured.
Introduction
Particle production at high transverse momentum (p _{T}) is well described by processes involving hard scattering between partons within the framework of perturbative Quantum Chromodynamics (pQCD) [1, 2]. In the lowp _{T} region, though, where soft processes dominate, QCD inspired phenomenological models are commonly used. Studying the production of these soft particles, should then, shed light on the basic mechanisms responsible for particle production in this regime.
In particular, the baryon production still lacks a complete QCD description. We do not have a clear view of whether the baryon number of a hadron should be associated with its valence quarks (as naively expected via analogy with the electric charge) or with its gluonic field. The gaugeinvariant state operator representing the baryon in QCD can be interpreted as a configuration where the three (valence) quarks are connected with three strings (gluons), meeting at one point, called the string junction [3–6]. In this representation, the baryon number is associated with the gluonic field of the baryon, namely with the string junction itself: baryon–antibaryon pair production from vacuum occurs by string junction and antistring junction pair production accompanied by a combination of sea quarks and antiquarks. This should be the mechanism for antibaryon production in baryon–baryon collisions. The baryons, however, may also contain one of the valence quarks, diquarks or the string junction (or a combination of the three) of the incoming baryon(s). If any of these constituents undergo a significant diffusion over large rapidity intervals, the spectrum of baryons can differ from the spectrum of antibaryons at midrapidity. These problems have been debated in various theoretical papers for some time [3–17].
In Regge field theory [18], the probability of finding the string junction of the beam baryon at relatively large rapidity distance Δy is given by \(\exp [ (\alpha_{\rm{J}}1 )\Delta y ]\) [3], where \(\Delta y = y_{\rm beam}  y\), and \(y_{\rm beam}=\ln{(\sqrt{s}/m_{\rm B})}\), is the rapidity of the incoming baryon, y is the rapidity of the string junction and \({\alpha}_{\rm J}\) is the intercept of stringjunction trajectory. Since the string junction is a nonperturbative QCD object, it is not possible, at present, to determine theoretically its intercept \(\alpha_{\rm{J}}\). Depending on the value of the stringjunction intercept, one expects a difference in the spectra of antibaryons and baryons at midrapidity. In particular, if \(\alpha_{\rm J} \approx1\), as proposed in [9–11], then even at very high Δy values, one would expect a rapidity independent distribution of the incoming baryon string junction. However, if \(\alpha_{\rm{J}} \approx0.5\) as considered in [3], the stringjunction transport will approach zero with increasing Δy.
Another source of the difference between the spectra of particles and antiparticles are Reggeon exchanges with negative Cparity [18]. One of the well known Regge poles is the \(\rm\omega\) reggeon with intercept \(\alpha_{\rm{\omega}} \approx0.5\). The \(\rm \omega\)reggeon exchange is also considered to be the main source of the difference between particle and antiparticle interaction total cross sections for low energy interactions. Since \(\alpha_{\rm{\omega }} < 1\), its contribution at midrapidity decreases with increasing collision energy. However, if there exists a Regge pole with negative signature and α≈1, it may also be a source of a difference between particle and antiparticle yields in the central region. In this case, both the inclusive cross sections of particles and antiparticles and the interaction cross sections at asymptotically high collision energies may be different.
One can gather information about the contribution of various mechanisms of baryon production from the spectra of baryons and antibaryons in proton–proton collisions. In particular, one of the most direct ways to find constraints on different baryon production mechanisms is to measure the ratio of spectra of antibaryons and baryons \(\overline {\rm {B}}/\rm{B}\) with various (valence) quark content e.g. p, Λ, charged Ξ and Ω and at different collision energies. For instance, by increasing the strangeness of the observable, one reduces the contribution of the process related to the stopping of different constituents of beam particle. This would have a consequence of \(\overline{\rm{B}}/\rm{B}\) ratio being closer to unity for higher strangeness.
The first results from the ALICE collaboration for the \(\overline {\mathrm{p}}/{\mathrm{p}}\) ratio in pp collisions at \(\sqrt{s} = 0.9\mbox{ and }7\mbox{ TeV}\), reporting the measured ratio of the yields of antiprotons to protons at midrapidity as compatible with unity at \(\sqrt{s} = 7\mbox{ TeV}\), have set stringent limits on the mechanisms of baryon production at LHC energies [19]. In this article we complement these studies in pp collisions, by reporting the production ratio of \(\overline{\mathrm {p}}/{\mathrm{p}}\) at \(\sqrt{s} = 2.76\mbox{ TeV}\) and of baryons containing strange quarks \(\overline{\Lambda }/{\Lambda}\), \({{\overline{\Xi}}^{+}}/{\Xi^{}}\) and \({{\overline{\Omega}}^{+}}/{\Omega^{}}\) at \(\sqrt{s} = 0.9,\ 2.76\mbox{ and }7\mbox{ TeV}\). The results are presented as a function of the particle’s rapidity defined as y=0.5ln[(E+p _{ z })/(E−p _{ z })] and transverse momentum defined as \(p_{\rm T}=\sqrt{p_{x}^{2} + p_{y}^{2}}\). We also present the rapidity and transverse momentum integrated ratios as a function of the multiplicity (the definition of multiplicity will be given in Sect. 6). ALICE results at midrapidity are compared with lower energy data and with LHCb data at forward rapidities.
Experimental setup
ALICE [20], the dedicated heavyion experiment at the LHC, was designed to cope with the high chargedparticle densities measured in central Pb–Pb collisions [21]. ALICE also provides excellent performance for proton–proton interactions [22, 23]. The experiment consists of a large number of detector subsystems [20] inside a solenoidal magnet (0.5 T). These subsystems are optimised to provide highmomentum resolution as well as excellent particle identification (PID) over a broad range in momentum.
Collisions take place at the centre of the ALICE detector, inside a beryllium vacuum beam pipe (3 cm in radius and 800 μm thick). The tracking system in the ALICE central barrel covers the full azimuthal range in the pseudorapidity window η<0.9. For more details on the ALICE experimental setup, see [20]. The following detector subsystems were used in this analysis:

The Inner Tracking System (ITS) [24–26], the innermost detector of ALICE, consisting of six layers of silicon detectors. The two layers closest to the beam pipe are made of Silicon Pixel Detectors (SPD) and are used for the determination of the primary vertex as well as for track reconstruction. The next two layers are made of Silicon Drift Detectors (SDD), followed by two layers of doublesided Silicon Strip Detectors (SSD). Both detectors contribute to the tracking while providing particle identification for lowp _{T} particles. The ITS covers the range η<0.9.

The Time Projection Chamber (TPC) [27] is the main tracking detector of the central barrel, providing, together with the other centralbarrel detectors, chargedparticle momentum measurements with good twotrack separation, particle identification, and vertex determination. The phase space covered by the TPC in pseudorapidity is η<0.9 for tracks of full radial track length, whereas for reduced track length (and reduced momentum resolution), an acceptance up to about η=1.5 is accessible. The TPC covers the full azimuth, with the exception of the dead zones between its sectors (in about 10 % of the azimuthal angle the detector is nonsensitive).

The VZERO detector [20], used in the trigger system, consists of two arrays of 32 scintillators each, placed around the beam pipe on both sides of the interaction region: one (VZEROA) at z=3.3 m, covering 2.8<η<5.1, and the other (VZEROC) at z=0.9 m, covering −3.7<η<−1.7. The time resolution of this detector is better than 1 ns. Its response is recorded in a time window of ±25 ns around the nominal beam crossing time.
Data analysis
Event sample and selection
Data recorded during the 2010 and 2011 LHC pp runs at \(\sqrt{s} = 0.9,\ 2.76\mbox{ and }7\mbox{ TeV}\) were used for this analysis. The trigger required a hit in one of the VZERO counters or in the SPD detector [24–26], in coincidence with the signals from two beam pickup counters, one on each side of the interaction region, indicating the presence of passing bunches.
The luminosity at the ALICE interaction point was restricted between 0.6 and 1.2×10^{29} cm^{−2} s^{−1} for all the data used in this analysis. This ensures a collision pileup rate of 4 % or lower, in each bunch crossing. Beaminduced background was reduced to a negligible level (<0.1 %) [28–30] with the help of the timing information from the VZERO counters. In addition, in order to minimise acceptance and efficiency biases for tracks at the edge of the TPC detection volume, events are selected by requiring that the distance between the position of the primary vertex and the geometrical centre of the apparatus along the beam axis (z position) is less than 10 cm. The final number of analysed events for each energy is summarised in Table 1.
Selection of protons
Protons and antiprotons are reconstructed and identified by the TPC, which measures the ionisation in the TPC gas and the particle trajectory with up to 159 space points. Several selection criteria were imposed to ensure the quality of accepted tracks. The minimum number of associated TPC clusters (space points) per track was set to 80. In addition, the χ ^{2} per TPC cluster of the momentum fit did not exceed the value of 2 per degree of freedom. A key element of the analysis was the reduction of the contamination of the track sample from background (i.e. particles originating from the interaction of a particle with the material) and secondary (i.e. protons and antiprotons originating from the weak decays of Λ and \(\overline{\Lambda}\), respectively) particles. To reduce the contamination from background, selected tracks were required to have at least two associated ITS clusters. Furthermore, a track must have at least one associated ITS cluster on either of the SPD layers. Finally, to further reduce the contamination from background and secondary tracks, a cut on the distance of closest approach (DCA) of the track to the primary vertex on the xy plane was set to 0.2 cm (of the order of the primary vertex resolution in x and y directions). The residual contamination is corrected by a datadriven method described in Sect. 4. Figure 1 presents the DCA distributions for p and \(\overline{p}\) with full and open circles respectively, for the lowest (\(0.45 < p_{\rm{T}} < 0.55~\mathrm{GeV}/c\)—top plot) and highest (\(0.95 < p_{\rm{T}} < 1.05~\mathrm{GeV}/c\)—bottom plot) p _{T} bins (intervals) used in this analysis. The distinct feature of the distribution of protons are long tails at large values of DCA that come predominantly from background protons. The effect is more pronounced for low p _{T} values. On the other hand, the corresponding distribution of antiprotons is background free, with the main source of contamination being the weak decay of \(\overline{\Lambda}\).
Particle identification was achieved by correlating the particle momenta as measured at the inner radius of the TPC and the specific ionisation (dE/dx) in the TPC gas [27]. The dE/dx resolution of the TPC is about 5 %, depending on the number of TPC clusters and the track inclination angle. For this analysis, (anti)protons were selected by defining a band with a 3σ width with respect to the theoretical Bethe–Bloch parametrisation, similar to the procedure followed in [19].
The phase space used for (anti)protons was limited to y<0.5 and \(0.45 < p_{\rm{T}} < 1.05~\mathrm{GeV}/c\). The lower limit of the p _{T} value is driven by the systematic uncertainties that will be described later in this article, while the upper limit is chosen based on the increased contamination from the identification procedure due to the overlapping particle bands in the correlation between the dE/dx and the momentum. The resulting contamination from other particle species in this p _{T} region is negligible (<0.1 %), compatible with the observation in [19].
Topological reconstruction of Λ, charged Ξ and Ω
Baryons and their antiparticles containing strange quarks (i.e. Λ, charged Ξ and Ω), the hyperons, are reconstructed via their weak decay topologies in the charged decay channels as summarised in Table 2. The measurement of Λ and \(\overline{\Lambda}\) is based on the reconstruction of their decay vertexes which exhibits a characteristic Vshape, called V0, defined by the trajectories of the decay products. The corresponding measurement of Ξ and Ω is performed based on the cascade topology of the decay, consisting of the aforementioned Vshape structure of the Λdecay and a charged bachelor particle (i.e. π and K for the case of Ξ and Ω, respectively). The selection of Λ, Ξ and Ω is performed by applying criteria on both the quality of the candidates and on the decay products (i.e. the daughter candidates). These criteria, which are analysis and energy dependent, are described below and are also summarised in Table 3.
For all three hyperons, the V0 daughter candidates are required to have a minimum DCA to the primary vertex, enhancing the probability that they are not primary particles. In addition, a maximum DCA between the daughter candidates at the point of the V0 decay was required to ensure that they are products of the same decay. To reduce the contamination from secondary and background strange baryons, a minimum value of the cosine of the pointing angle is required. The pointing angle is defined as an angle between the momentum vector of the V0 candidate and the vector connecting the primary vertex and the production vertex of the V0. Figure 2 presents the relevant distributions for Λ and \(\overline{\Lambda}\) candidates for pp collisions at \(\sqrt{s} = 7\mbox{ TeV}\), for two p _{T} regions. These distributions at the highest measured energy are also representative of those measured at lower collision energies. It is seen that for low values of p _{T}, there is a pronounced tail in the distribution of Λ originating from background particles. Finally, V0 candidates are required to have a transverse distance between the primary and the production vertex (V0 transverse decay radius) larger than a minimum value. All these cut parameters are listed in Table 3.
Additional selection criteria are applied for the multistrange baryons (i.e. Ξ and Ω). In particular, the bachelor track is required to have a minimum DCA value to the primary vertex, increasing the probability that it is not a primary particle. A similar cut is applied to the DCA value of the V0 candidate relative to the primary vertex. Furthermore, a maximum value for the DCA between the V0 candidate and the bachelor track at the point of the cascade decay is also required. As in the case of the V0, to reduce the contamination from background particles, a minimum cut on the cosine of the pointing angle is applied. The cascade candidates are selected if the transverse distance between the primary and the decay vertex (cascade transverse decay radius) is larger than a minimum value. Also in this case, the cut parameters are listed in Table 3.
Particle identification of the daughter candidates helps to substantially decrease the background, especially in the low \(p_{\rm{T}}\)–high y regions. Particles are identified using the energy loss signal in the TPC. The selection is done within a 3σ band around the expected dE/dx value for each particle type.
In addition, for the case of Λ and Ω, we have excluded candidates falling into ±10 MeV/c ^{2} the mass window of the \(\rm{K}_{s}^{0}\) (in case of Λ) or Ξ (in case of Ω) nominal mass. The result is an improvement of the S/B ratio by a factor of ≈1.5.
Finally, the phase space used for each of the analysed baryons is summarised in Table 4. The lower limits are chosen based on the low signal to background ratio, while the upper values are driven by the limited statistics.
The resulting invariant mass distributions for Λ, Ξ and Ω candidates in pp collisions at \(\sqrt{s} = 7\mbox{ TeV}\) are presented in Fig. 3 in the top, middle and bottom plots, respectively. The raw particle yields are extracted from these distributions divided in different p _{T} bins by subtracting the contribution of the background (blue areas) from the peak regions (green areas), where both signal and background are located. Both areas are defined by first fitting the peak region with a Gaussian function and extracting the mean (μ) and the width (σ). The sum of the signal and background (S+B) is sampled in the region defined by μ±4σ [32, 33], while the background is sampled on each side of the peak region using the areas that are more than 6σ [32, 33] away from the Gaussian mean.
The background is estimated by either simultaneously fitting both sides with a polynomial function or by simply counting the number of entries, the socalled “bincounting” method. Both methods give similar results, however the first method is used as the default one. The S/B is analysis and p _{T} dependent and is summarised in Table 5.
Corrections
The TPC [27] is symmetric around midrapidity and has full azimuthal coverage, hence many detector effects are the same for particles and antiparticles and thus cancel out in the ratio. However, there are mechanisms that affect the two particle types differently and need to be accounted for by applying the relevant corrections. These corrections are extracted from a detailed Monte Carlo simulation based on the GEANT3 transport code [34, 35] and from data driven methods. The effects considered in this analysis are:

the difference in the interactions of baryons and antibaryons with the material of the detector, resulting in larger absorption of the latter particle type,

the inelastic cross section of \(\overline{\rm p}\)–A and K^{−}–A interactions accounting for the wrong parametrisation that GEANT3 employs [19],

the difference in the elastic cross section for p–A and \(\overline{\rm p}\)–A, resulting in differences in the cut efficiency,

the contamination from background particles (mainly \(\rm p\) and Λ) originating from the interaction of other particles with the material,

finally, the feeddown from secondary (anti) baryons e.g. \(\mathrm{p}(\overline{\rm p})\) originating from the weak decay of a \(\Lambda(\overline{\Lambda})\).
Each one of these corrections is described separately in the following paragraphs.
Absorption correction
The inelastic p–A cross section is measured to be significantly different than for \(\overline{\rm p}\)–A [36, 37]. As a result, different fractions of p and \(\overline{\rm p}\) are absorbed when interacting with the detectors’ material. Similar assumption could be made for the hyperons, however, the corresponding cross section values have not been measured experimentally. The absorption correction factors rely on the proper description of the inelastic cross sections of p and \(\overline{\rm p}\) used as input by the transport model (GEANT3) and on the accurate description of the material budget in the simulation.
In [19] it was pointed out that GEANT3 uses an incorrect parametrisation of the inelastic cross section for \(\overline{\rm p}\)–A interactions. In particular, GEANT3 overestimates the experimentally measured cross sections [36, 37] by a factor of two for p≈1 GeV/c, a value that represents the mean \(\overline{\rm p}\) momentum. This factor increases for lower momentum values. Also in [19], it was reported that FLUKA [38–40] describes the data very well. In addition, it was found that a small difference between the input GEANT3 parametrisation and the experimentally measured values exists also for the case of K^{−}–A interactions. The latter is important if one considers the decay mode of the Ω.
To account for these differences, a full detector Monte Carlo simulation with FLUKA as a transport code was used. This simulation was used to scale the absorption correction extracted from GEANT3 to match the correct (i.e. FLUKA) cross section parametrisation. The ratio of the detection efficiency calculated using GEANT3 as a transport code (\(\rm\varepsilon_{GEANT3}\)) to the one using FLUKA (\(\rm\varepsilon_{FLUKA}\)) as a function of the p _{T} is presented in Fig. 4. The two curves represent the parametrisation of the ratio
used to extrapolate the differences to higher values of p _{T}. The solid line corresponds to \(\overline{\rm p}\) [n=0.2 in Eq. (1)] while K^{−} [n=0.15 in Eq. (1)] is represented by the dashed line. It is seen that for both hadrons the curves exhibit a significant p _{T} dependence, which is more pronounced for the case of \(\overline{\rm p}\). The resulting correction is of the order of 8 % for the lowp _{T} region (at \(p_{\rm{T}} = 0.45~\mathrm{GeV}/c\)) for \(\overline{\rm p}\), decreasing with increasing p _{T}. For the case of the K^{−}, the corresponding correction is smaller (≈2 % for \(p_{\rm {T}} > 0.4~\mathrm{GeV}/c\))).
The amount of material in the central part of ALICE is corresponding to about 10 % of a radiation length on average between the vertex and the active volume of the TPC. It has been studied with collision data and adjusted in the simulation based on the analysis of photon conversions. The current simulation reproduces the amount and spatial distribution of reconstructed conversion points in great detail, with a relative accuracy of a few percent.
The p _{T} dependence of the correction due to absorption for p, \(\overline {\rm p}\), and charged kaons is presented in Fig. 5. The aforementioned scaling for the corrections of \(\overline{\rm p}\) and K^{−}, is already applied. The resulting correction factors vary from ≈12 % at lowp _{T} to ≈6 % at highp _{T} for the case of \(\overline{\rm p}\), while for p it is ≈3 %, independently of p _{T}. The corresponding values for K^{±} also vary from ≈17 % to ≈5 %, depending on p _{T}. The difference in the absorption of the positive and negative π was found to be negligible.
Similar corrections were also applied to the hyperons. The correction factors are on the order of ≈1 %. Due to the lack of experimental values of the corresponding inelastic cross sections we rely on the input parametrisation of GEANT3.
Finally, we also considered the absorption of the daughter candidates for the hyperon decays, and in particular the (anti)proton daughter, while for the case of the \({{\overline{\Omega}}^{+}}/{\Omega ^{}}\) ratio the absorption of the kaon bachelor particle was also considered. This was done using the aforementioned correction factors.
Correction for cut efficiency
In addition to the previous effect on baryons and antibaryons induced by absorption, it was reported in [19], that a relevant correction is needed to account for the differences in the cut efficiencies between p and \(\overline{\rm p}\). The reason for the observed charge asymmetry is that particles undergoing elastic scattering in the inner detectors can still be reconstructed in the TPC but the corresponding ITS hits will in general not be associated to the track if the scattering angle is large. This in turns results from the corresponding differences in the elastic cross sections for p and \(\overline{\rm p}\).
For the elastic cross section a limited set of experimentally measured values is available. It was found that GEANT3 cross sections are about 25 % above FLUKA, the latter being again closer to the measurements. Hence, we used the FLUKA results to account for the difference of \(\rm {p}\) and \(\overline{\rm{p}}\) cross sections. The resulting correction was estimated to be ≈3.5 % [19].
Correction for secondary and background particles
In order to distinguish between primary, secondary (i.e. products of the weak decay of particles) and background (i.e. particles emitted from the interaction of other particles with the material of the detectors) particles, we employ a data driven method based on distributions where these three categories of particles exhibit distinct differences.
Primary protons can be distinguished from secondary and background particles using the DCA distribution. The same distribution can be used for the case of \(\overline{\rm p}\) for which the contribution from background particles (i.e. \(\overline{\rm p}\) originating from the material) is negligible. Primary particles point to the primary vertex in contrast to the majority of the background, which can be removed by applying a DCA cut (described in the previous section). Secondary (anti)protons point to the primary vertex with a DCA distribution that is wider than that of primaries. To account for the residual contamination from both sources, we determine the shape of the DCA distributions from Monte Carlo simulations, adjusting the amount to the data at large DCA values. The correction is calculated and applied differentially as a function of y and p _{T}, and varies between 9 % for the lowest and less than 0.5 % for the highest p _{T} bins for the background. For the feeddown corrections, the relevant values are 20 % and 17 % for the lowest and highest p _{T} bins, respectively.
A similar procedure was applied for the case of Λ and \(\overline{\Lambda}\), using the information of the cosine of the pointing angle. These secondaries are mainly produced by primary \(\mathrm{K}^{0}_{L}\) and charged kaons. The procedure resulted in a correction that varies between 8 % for the lowest and less than 0.5 % for the highest p _{T} bins for the background.
The contamination of the Ξ^{±} sample from background particles was found to be negligible (<0.5 %), based on Monte Carlo studies.
For the feeddown correction of Λ from Ξ decays, we rely on Monte Carlo simulations. The ratio r _{feeddown} of the reconstructed Ξ candidates to the number of reconstructed Λ candidates from Ξ decays is
Assuming that this ratio is the same in both Monte Carlo and data, the whole feeddown contribution to the spectra is estimated by dividing the number of reconstructed Ξ in data by the ratio extracted from Monte Carlo.
The overall fractions of Λ and \(\overline{\Lambda}\) coming from the Ξ decays for different \(\sqrt{s}\) are summarised in Table 6. The uncertainty of the \(\overline{\Lambda}/{\Lambda}\) ratio resulting from the feeddown correction is based on our measurement of \({{\overline{\Xi}}^{+}}/{\Xi^{}}\) ratio and is described in Sect. 5.
The contribution from Ω decays was found to be negligible. It should be noted that since Λ (\(\overline{\Lambda}\)) from electromagnetic \(\rm\Sigma^{0}\) (\(\overline{\rm\Sigma^{0}}\)) decays cannot be distinguished from the primary ones, the identified Λ (\(\overline{\Lambda}\)) also include these contributions.
The feeddown contamination of the Ξ sample from decays \(\rm \Omega^{\pm} \rightarrow\Xi^{\pm} + \pi^{0}\) considering the branching ratio for this decay and the Ω/Ξ ratio reported in [32, 33] is <1 % and thus negligible.
Systematic uncertainties
Although the dominant sources of systematic uncertainties in this analysis are due to the corrections employed, uncertainties in the analysis procedure also contribute. Uncertainties arising from the correction procedures for elastic and inelastic crosssection parametrisation and for secondary particles produced in the beam pipe and detector material have been found to be very small. We have identified and estimated systematic uncertainties from the following sources:

the amount of material of the central barrel;

the experimental values of the elastic and inelastic cross section implemented in the transport code (FLUKA);

the applied corrections for background and secondary particles;

the track and topological selections;

the hyperon signal extraction procedure.
These are discussed in more detail in the following and the final uncertainty estimates are present in Tables 7 and 8 for protons and hyperons, respectively.
Systematic uncertainties due to material budget, inelastic and elastic cross sections
The amount of material in the central part of the detector is known, based on studies with γ conversions, with a precision of 7 % [19]. Dedicated simulations varying the material budget by this amount were used to determine the uncertainty from this source. The absorption corrections were recomputed using the output of these simulations and an uncertainty of 0.5 % was found in the final ratios, calculated as half of the difference between the highest and the lowest values of each ratio.
In addition, the experimental \(\overline{\rm p}\)–A inelastic cross sections are measured with an accuracy typically better than 5 % [36, 37]. We assign an uncertainty of 10 % to the absorption cross section calculated with FLUKA, resulting into an uncertainty of 0.8 % on the final measured ratio.
The inelastic hyperon–A cross sections have not been measured experimentally, so absorption corrections for predecay hyperons must rely on the cross section parametrisation implemented in GEANT3. Assuming that these have an uncertainty of 100 %, we find an error of 0.5 % on the \(\overline{\Lambda}/{\Lambda}\) ratio and 1 % on the \({{\overline{\Xi}}^{+}}/{\Xi^{}}\) and \({{\overline{\Omega }}^{+}}/{\Omega^{}}\).
By comparing GEANT3 and FLUKA with the experimentally measured elastic cross section, the corresponding uncertainty on \(\overline{\mathrm {p}}/{\mathrm{p}}\) ratio was estimated to be 0.8 %, which corresponds to the difference between the correction factors calculated with the two models.
Systematic uncertainties due to corrections for secondary and background particles
The uncertainty resulting from the subtraction of secondary protons and from the feeddown corrections was estimated to be 0.6 % by using various functional forms for the background subtraction and for the contributions of the weak decay products. The uncertainty resulting from the subtraction of secondary \(\rm \Lambda \) was estimated to be 0.4 % by using various methods for the background subtraction. The feeddown fractions of Λ and \(\overline {\Lambda}\) were estimated to be ≈0.2 (see Table 6). The total uncertainties of the measured \({{\overline {\Xi}}^{+}}/{\Xi^{}}\) ratios were propagated into \(\overline{\Lambda}/{\Lambda}\) systematic uncertainty using this fraction, resulting in an uncertainty of 1 % at \(\sqrt{s}=0.9\mbox{ TeV}\) and 0.4 % for higher energies.
Systematic uncertainties due to track and topological selections
The systematic effects of the track quality criteria and the topological selections used in the hyperon reconstruction, the “tightness” of the PID cut, and ranges of additional cuts have been investigated. The selections were varied onebyone using reasonably looser and tighter values for each parameter. The final systematic uncertainty was calculated as half of the difference between the highest and the lowest values. The final estimated systematic error presented in Tables 7 and 8 is the quadratic sum of the contributions from the variation of

the width of Nσ area used for the particle identification (±1σ);

the minimum number of TPC clusters (±10 clusters);

the topological selections used in the reconstruction of the V0 and cascade vertexes;

the width of the mass window around \(\rm{{K}_{s}^{0}}\) or \(\rm \Xi \) nominal mass in case of Λ and Ω (±2 MeV/c).
Systematic uncertainties due to signal extraction
Two methods for signal extraction have been presented in Sect. 3. The final ratios differ by ≈0.4 % depending on the method used. This difference is due to the approximation of the background using different functions and is included here as a systematic uncertainty. The difference of the ratios due to the change of the fit range and width of the considered signal area by ±1σ was found to be negligible.
Results
Rapidity and transverse momentum dependence
Antibaryon to baryon spectra ratios were measured as a function of rapidity and transverse momentum. We report results for the rapidity intervals y<0.8 in the case of hyperons and y<0.5 for \(\overline{\rm p}/{\rm p}\). The available data were not statistically sufficient to determine the \({{\overline{\Omega}}^{+}}/{\Omega ^{}}\) ratio at 0.9 TeV. For the same reason, the ratios were integrated over rapidity for \({{\overline {\Omega}}^{+}}/{\Omega^{}}\) at all remaining energies, for \({{\overline{\Xi}}^{+}}/{\Xi^{}}\) at 0.9 and 2.76 TeV and for \(\overline{\Lambda}/{\Lambda}\) at 7 TeV for p _{T}>5.5 GeV/c (i.e. rapidity dependence on Fig. 9, bottom, is for p _{T}<5.5 GeV/c).
As can be seen in Fig. 6, there is no observed dependence on either rapidity or transverse momentum in the measured \(\overline{\mathrm{p}}/{\mathrm{p}}\) ratio at \(\sqrt{s} = 2.76\mbox{ TeV}\) which is consistent with previous ALICE measurements at \(\sqrt{s} = 0.9\mbox{ and }7\mbox{ TeV}\) [19]. The data are described reasonably well by PYTHIA (Perugia2011, Tune 350) [41, 42]. On the other hand, HIJING/B [16, 17] is showing a decreasing ratio with increasing \(p_{\rm T}\) (Fig. 6, left) and a slightly larger rapidity dependence than supported by the data (Fig. 6, right). Even though HIJING/B is showing different trends with p _{T} and rapidity, compared to the data, the current uncertainties do not allow for any final conclusion yet.
Figures 7, 8 and 9 show the rapidity and p _{T} independence of the \(\overline{\Lambda}/{\Lambda}\) ratios for all energies. The same measurements are shown for the \({{\overline{\Xi}}^{+}}/{\Xi^{}}\) ratios in Figs. 10, 11 and 12 and for the \({{\overline{\Omega}}^{+}}/{\Omega ^{}}\) ratios in Figs. 13 and 14. All hyperon measurements are described reasonably well by both PYTHIA (Perugia2011) and HIJING/B.