$^{3}_{\Lambda}\mathrm H$ and $^{3}_{\bar{\Lambda}} \overline{\mathrm H}$ production in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV

The production of the hypertriton nuclei $^{3}_{\Lambda}\mathrm H$ and $^{3}_{\bar{\Lambda}} \overline{\mathrm H}$ has been measured for the first time in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV with the ALICE experiment at LHC energies. The total yield, d$N$/d$y$ $\times \mathrm{B.R.}_{\left( ^{3}_{\Lambda}\mathrm H \rightarrow ^{3}\mathrm{He},\pi^{-} \right)} = \left( 3.86 \pm 0.77 (\mathrm{stat.}) \pm 0.68 (\mathrm{syst.})\right) \times 10^{-5}$ in the 0-10% most central collisions, is consistent with the predictions from a statistical thermal model using the same temperature as for the light hadrons. The coalescence parameter $B_3$ shows a dependence on the transverse momentum, similar to the $B_2$ of deuterons and the $B_3$ of $^{3}\mathrm{He}$ nuclei. The ratio of yields $S_3$ = $^{3}_{\Lambda}\mathrm H$/($^{3}\mathrm{He}$ $\times \Lambda/\mathrm{p}$) was measured to be $S_3$ = 0.60 $\pm$ 0.13 (stat.) $\pm$ 0.21 (syst.) in 0-10% centrality events; this value is compared to different theoretical models. The measured $S_3$ is fully compatible with thermal model predictions. The measured $^{3}_{\Lambda}\mathrm H$ lifetime, $ \tau = 181^{+54}_{-39} (\mathrm{stat.}) \pm 33 (\mathrm{syst.})\ \mathrm{ps}$ is compatible within 1$\sigma$ with the world average value.


Introduction and Physics Motivations
High-energy heavy-ion collisions offer a unique way to study the behaviour of nuclear matter under conditions of extreme energy densities.At LHC energies, particles carrying strangeness are abundantly produced and light clusters of nucleons and hyperons, called hypernuclei, are expected to be formed [1].Since their first observation [2], there has been a constant interest in searching for new hypernuclei as they offer an experimental way to study the hyperon-baryon (Y N) and the hyperon-hyperon (YY ) interactions, which are relevant for nuclear physics and nuclear astrophysics.For instance, the Y N interaction plays a key role in understanding the structure of neutron stars [3][4][5][6].The production of hypernuclei in heavyion collisions has been proposed and studied for a long time [7,8] and at ultrarelativistic energies it is possible to produce particles otherwise inaccessible, such as anti-hypernuclei.In fact, while many Λ-hypernuclei have been observed, the first observation of an anti-hypernucleus is rather recent and was reported from the analysis of Au-Au collisions at √ s NN = 200 GeV by the STAR Collaboration at RHIC [9].Since hypernuclei are weakly bound nuclear systems, they are sensitive probes of the final stages of the evolution of the fireball formed in the heavy-ion collisions [10].The yield of hypernuclei can distinguish between different production scenarios, usually described using two different theoretical approaches.The first one is based on a coalescence model [11], while the second one is based on the assumption that all the particle species can be described using a statistical thermal model [12].In the statistical thermal model a constant entropy over baryon ratio [13] could explain why objects with such a small binding energy (few MeV) could survive the high temperature (≈ 170 MeV) expanding fireball.
On the other hand, if hypernuclei are produced through coalescence of protons, neutrons and hyperons at freeze-out [14], they will provide a measurement of the local correlation between baryons and hyperons (strangeness) [15].This letter presents a study of hypertriton and anti-hypertriton production at √ s NN = 2.76 TeV Pb-Pb collisions by the ALICE collaboration.The paper is organised as follows.In Section 2 the ALICE detector is briefly described.The data sample, analysis details and systematic uncertainties are presented in Section 3. In Section 4 the obtained results are compared with theoretical models.Finally the conclusions are drawn in Section 5.

The ALICE detector
A detailed description of the ALICE detector can be found in [16] and references therein.For the present analysis the main sub-detectors used are the V0 detectors, the Inner Tracking System (ITS) and the Time Projection Chamber (TPC), which are located inside a 0.5 T solenoidal magnetic field.The V0 [17] detectors are placed around the beam-pipe on either side of the interaction point: one covering the pseudorapidity range 2.8 < η < 5.1 (V0-A) and the other one covering −3.7 < η < −1.7 (V0-C).The collision centrality is estimated by using the multiplicity measured in the V0 detectors along with a Glauber model simulation to describe the multiplicity distribution as a function of the impact parameter [18,19].The ITS [20] has six cylindrical layers of silicon detectors with radii between 3.9 and 43 cm from the beam axis, covering the full azimuthal angle and the pseudorapidity range of |η| < 0.9.The same pseudorapidity range is covered by the TPC [21], which is the main tracking detector.Hits in the ITS and found clusters in the TPC are used to reconstruct charged-particle tracks.These are used to determine the primary collision vertex with a resolution of about 10 µm in the direction transverse to the beams for heavy-ion collisions.The TPC is used for particle identification through the dE/dx (specific energy loss) in the TPC gas.

Analysis
The (anti-)hypertriton ( 3 ΛH) 3 Λ H is the lightest observed hypernucleus and is a bound state formed by a (anti-)proton, a (anti-)neutron and a (anti-)Λ.The 3 Λ H and 3 ΛH production yields were measured by Λ H and 3 ΛH production in Pb-Pb collisions ALICE Collaboration detecting their mesonic decay ( 3 Λ H → 3 He + π − ) and ( 3 ΛH → 3 He + π + ) via the topological identification of secondary vertices and the analysis of the invariant mass distributions of ( 3 He+π − ) and ( 3 He+ π + ) pairs.The analysis was done using Pb-Pb collisions at √ s NN = 2.76 TeV taken in 2011.The events were collected with an interaction trigger requiring a signal in both V0-A and V0-C.Only events with a primary vertex reconstructed within ±10 cm, along the beam axis, from the nominal position of the interaction point were selected.The analysed sample, collected with two different centrality trigger configurations corresponding to the 0-10% and 10-50% centrality intervals, contained approximately 20×10 6 and 17×10 6 events, respectively.The 3 Λ H can be identified via the invariant mass of its decay products and, since it has a lifetime similar to the free Λ (cτ ∼ 8 cm), in most cases it is possible to identify its decay up to a few cm away from the primary vertex.The decay vertex was determined by exploiting a set of geometrical selections: i) the distance of closest approach (DCA) between the two particle tracks identified using dE/dx in the TPC as 3 He and π, ii) the DCA of the π ± tracks from the primary vertex, iii) the cosine of the angle between the total momentum of the decay pairs at the secondary vertex and a vector connecting the primary vertex and the secondary vertex (pointing angle), and iv) a selection on the proper lifetime (cτ) of the candidate.An additional selection on the 3 Λ H ( 3 ΛH) rapidity (|y| <0.5) was applied.Figure 1 shows the invariant mass distribution of ( 3 He,π − ) on the left and ( 3 He,π + ) on the right for events with 10-50% centrality in the pair transverse momentum range 2 ≤ p T < 10 GeV/c.In order to estimate the background, for each event the π track detected at the secondary vertex was rotated 20 times by a random azimuthal angle.The shape of the corresponding ( 3 He, π) invariant mass distribution was found to reproduce the observed background outside the signal region.The data points were fitted with a function which is the sum of a Gaussian and a third degree polynomial, used to describe the signal and the background, respectively.The background was normalized to the measured values in the 3.01 -3.08 GeV/c 2 region.The fit to the background distribution was used to fix the parameters of the polynomial in the combined fit.  e,π + ) (right) for events with 10-50% centrality in the pair 2 ≤ p T < 10 GeV/c interval.The data points are shown as filled circles, while the squares represent the background distribution as described in the text.The curve represents the function used to perform the fit and used to evaluate the background and the raw signal.The significance in ±3σ around the peak is 3.5 and 3.0 for the invariant mass distribution of ( 3 He,π − ) and ( 3 He,π + ), respectively.
In the 0-10% most central collisions, a signal was extracted in three transverse momentum intervals (2 ≤ p T < 4 GeV/c, 4 ≤ p T < 6 GeV/c, 6 ≤ p T < 10 GeV/c) , for both 3  Λ H and 3 ΛH.In the 10-50% centrality class a signal both for 3 Λ H and 3 ΛH was obtained for the full p T range under study (2 ≤ p T < 10 GeV/c).From the combined fit results the mean value, the width and the yield of the signal were extracted.The mean invariant mass (µ = 2.991 ± 0.001 (stat.)± 0.003 (syst.)GeV/c 2 ) is compatible within uncertainties with the mass from the literature [22].The signal width, σ = (3.01 ± 0.24 (stat.))×10−3 GeV/c 2 obtained as the mean value of all the measured widths, is reproduced by Monte Carlo simulations and is driven by detector resolution.The raw yield of the signal was defined as the integral of the Gaussian function in a ± 3 σ region around the mean value.The significance of both matter and anti-matter signals varies in the different p T bins in the range of 3.0-3.2σ for the most central collisions (0-10%) and ranges from 3 to 3.5 σ for the semi-central ones (10-50%).A correction factor which takes into account the detector acceptance, the reconstruction efficiency, and the absorption of 3  Λ H ( 3 ΛH) by the material crossed was determined as a function of p T .Detector acceptance and reconstruction efficiency were evaluated using a dedicated HIJING Monte Carlo simulation [23], where the only allowed decay was the two-body decay to charged particles, ( 3 Λ H → 3 He + π − ) and ( 3ΛH → 3 He + π + ).The simulated particles were propagated through the detector using the GEANT3 transport code [24] and then processed with the same reconstruction chain as for the data.Since the absorption of (anti-)(hyper)nuclei is not properly implemented in GEANT3, a correction based on the p (p) absorption was applied in order to take into account the absorption of 3 Λ H ( 3 ΛH) and 3 He ( 3 He) by the material of the ALICE detector.In this approach, the 3 He and 3 Λ H were treated as states of three independent p (p).The 3 He was considered as a bound state of 3 protons because the proton absorption correction in the ALICE detector was measured [?].The direct measurement offers the advantage of having a probability density which takes into account the effective material of the detector crossed by a charged particle.The effect of using protons instead of neutrons was tested with deuterons, which were considered as a bound state of 2 protons and the absorption correction was evaluated with the same model used for 3 He.The result was compared with the one obtained with the absorption correction of GEANT3 patched with hadronic cross sections for d and d.The two calculated absorption corrections where found to be consistent within uncertainties.To take into account the small Λ separation energy (B Λ ( 3 Λ H) = 0.13 ± 0.05 MeV [25]), the absorption cross section of the 3 Λ H was increased by 50% with respect to the one of the 3 He.This choice was based on the theoretical calculation of 3 Λ H absorption cross-section [?] on 238 U and its ratio with the extrapolation of 3 He cross section on the same target [?].Using the same extrapolation it was possible to evaluate the same ratio on ALICE materials.The correction applied to the extracted yield was about 12% for 3  Λ H and about 22% for 3 ΛH.The total systematic uncertainty takes into account, as lower and upper limits of the 3 Λ H( 3 ΛH) absorption cross section, values respectively equal to or two times higher than the absorption cross section of 3 He( 3 He).This uncertainty is p T dependent, and its values are reported in Table 1.Other sources of systematic uncertainties in the yield evaluation were estimated: -The systematic uncertainty due to the single-track efficiency, and the different choices of the track quality selections was taken from [26].A 10% uncertainty is quoted for the two body decay of 3 Λ H.
-3 Λ H lifetime: since the 3 Λ H lifetime is not accurately known, the influence of varying the 3 Λ H lifetime on the efficiency was evaluated by variation of the proper lifetime of the injected 3  Λ H in the Monte Carlo simulation.The associated uncertainty was estimated using two additional dedicated Monte Carlo simulations with different lifetimes.The injected lifetime of 3  Λ H ( 3 ΛH) was varied (±1σ ) with respect to the result obtained in this analysis, leading to an uncertainty of 8.5%.
-The uncertainty related to the signal extraction procedure was evaluated by constraining fit parameters (µ and σ ) in different ways.This source led to a 9% uncertainty.
The systematic uncertainty due to the uncertainty of the ALICE detector material budget and p T distri-bution in the Monte Carlo used for the efficiency estimation led to a 1% systematic uncertainty.The 3 Λ H and 3 ΛH spectra are shown in Figure 2 (left panel), multiplied by the branching ratio (B.R.) of the 3  Λ H → 3 He + π − decay.The anti-hypertriton to hypertriton ratio as a function of p T is shown in Figure 2 (right panel).It is consistent with unity over the whole considered p T range, as expected from zero net baryon density at LHC energies.In the ratio, the common systematic uncertainties (tracking efficiency, lifetime, and signal extraction method) cancel out and have therefore been removed.In order to take into account the unmeasured p T region and to extract the particle yields integrated over the full p T range, the spectra were fitted using a blast-wave function [27] whose parameter values were taken from the deuteron analysis [28] leaving the normalization free.The function fits the data with a χ 2 /NDF of 0.92.The extrapolation in the p T < 2 GeV/c region contributes 28% to the final yield for both 3 Λ H and 3  ΛH, while the contribution for p T > 10 GeV/c is negligible.Different transverse momentum distributions were used to evaluate the systematic uncertainty related to the extrapolation, which was found to be 5%.
To determine the lifetime, the ( 3 Λ H + 3 ΛH) sample was divided into four intervals in ct = MLc/p, where M is the mass, L the decay length, c is the speed of light, and p is the total momentum.The mass was fixed to the value from the literature M = 2.991 GeV/c 2 [22].For the determination of the lifetime, both centrality classes 0-10% and 10-50% were used.The signal was extracted in the intervals: 1 ≤ ct <4 cm, 4 ≤ ct < 7 cm, 7 ≤ ct < 10 cm and 10 ≤ ct < 28 cm.To estimate the lifetime, the raw signal was corrected by the detector acceptance, the reconstruction efficiency and the absorption of 3  Λ H ( 3 ΛH) in the material.The same dedicated HIJING Monte Carlo simulation and the same procedure used to determine the p T dependence of the efficiency were used.The sources of systematic uncertainty are shown in Table 2.
An exponential fit was performed to determine the lifetime.The dN/d(ct) distribution and the exponential fit are shown in Figure 3.The vertical bars show the statistical uncertainties and the boxes  represent the systematic uncertainties.The slope of the fit results in a proper decay length of cτ = 5.4 +1.6 −1.2 (stat.)± 1.0(syst.)cm.The lifetimes of light Λ-hypernuclei (A ≤ 4) are expected to be very similar to that of the free Λ, if the Λ in the hypernucleus is weakly bound [31].The measured lifetimes of light hypernuclei such as 3  Λ H [9,[32][33][34][35][36][37][38] are not known as precisely as the Λ lifetime, and theoretical predictions [31,[39][40][41][42][43][44][45][46]   −39 (stat.)± 33(syst.)ps has been obtained.It is compared with the previously published results in Figure 4. Our result, together with the previous ones, was used to re-evaluate the world average of the existing results using the same procedure as described in [47].The obtained value, τ = 215 +18 −16 ps , is shown as a band in Figure 4.The result obtained in this analysis is compatible with the computed average.

Comparison between experimental yields and theoretical models
The product of the p T -integrated yield and the B.R. of the 3 Λ H → ( 3 He + π − ) decay for 3 Λ H and 3 ΛH for two centrality classes (0-10% and 10-50%) are reported in Table 3.The systematic uncertainties also include the contribution due to the low p T extrapolation as described in Section 3. It is possible to compare the p T -integrated 3  Λ H yield at different centralities by scaling them according to the charged-particle densities dN ch /dη .For central (0-10%) collisions dN ch /dη = 1447 ± 39, while for semi-central (10-50%) dN ch /dη = 575 ± 12.The ratio is compatible with unity within 1 σ .The 3 Λ H ( 3 ΛH) production scales with centrality like the chargedparticle production.

Comparison between thermal models and experimental yields
Since the decay branching ratio of the 3 Λ H → 3 He + π − was estimated only relative to the charged-pion channels [37], the corresponding value (B.R. = 35%) provides an upper limit for the absolute branching ratio.On the other hand, a theoretical estimation for the   [18].also takes into account decays with neutral mesons decays, gave a B.R. = 25% [31].Assuming a possible variation on the B.R. in the range 15-35%, we show in Figure 5 a comparison of our result with different theoretical model calculations [1,48,49].The measured dN/dy × B.R. is shown as a horizontal line, where the band represent statistical and systematic uncertainties added in quadrature while the different theoretical models are shown as lines.The data are compared with the following models: two versions of the statistical hadronization model [1,48] and the hybrid UrQMD model [49], which combines the hadronic transport approach with an initial hydrodynamical stage for the hot and dense phase of a heavy-ion collision.The two versions of the statistical hadronization model used are the equilibrium statistical model (GSI-Heidelberg), described in [1] and references therein, with a temperature T ch = 156 MeV and the non-equilibrium thermal model (SHARE), described in [48] and references therein, with T ch = 138.3MeV, γ q = 1.63 and γ s = 2.08, where γ q and γ s represent the quark and strangeness phase space occupancy of the system created after the collision, respectively.The non-equilibrium thermal model (SHARE) [48] overestimates the (anti-)hypertriton p T -integrated yield by a factor from 2 to 5 depending on the branching ratio (B.R.).For the branching ratio expected following [31] (B.R. = 25%) the equilibrium thermal model [1] (GSI-Heidelberg) and the hybrid UrQMD model [49] describe the data best.A fit, based on the thermal fit described in [1], was performed to the hypertriton yield and to yields from other light flavour hadrons, except K * , previously measured by our Collaboration at √ s NN = 2.76 TeV [28, Λ H and 3 ΛH production in Pb-Pb collisions ALICE Collaboration 50 -53].The inclusion of the deuteron, 3 He [28] and 3 Λ H in the thermal fit [54] in addition to lighter particles, does not change the resulting freeze-out temperature (T ch = 156 ± 2 MeV) and the measured yields of the nuclei and the hypertriton agree with the model predictions within 1 σ .The results on the hypertriton yields discussed above were also used to determine the 3 Λ H/ 3 He and 3 ΛH/ 3 He ratios, which are shown in Table .4. In order to compute the ratios, our previous measurement of 3 He and 3 He yields [28] were used.These results were compared with different theoretical models [48,55,56] and results from the STAR experiment [9] at √ s NN = 200 GeV, which use the same B.R. = 25%.The comparison is shown in Figure 6.STAR results are higher than ALICE results, but still compatible within uncertainties.[31].The results from 3 He and 3 He analysis measured by the ALICE experiment were used [28].Λ H/ 3 He and 3 ΛH/ 3 He determined by the present analysis (filled circles) for matter and antimatter compared with STAR results (squares) [9] and theoretical predictions (lines) [1,48,55,56] as described in the legend.

Data comparison to coalescence models and S 3 ratio
At the moment no prediction of the 3 Λ H and 3 ΛH yields in a non-trivial dynamical coalescence model is available at LHC energies.Nevertheless within a simple coalescence model it is possible to evaluate some parameters which are sensitive to the existence of coalescence mechanisms for hypernuclei formation.In the empirical coalescence model [11] the cross section for the production of a cluster with mass number A is related to the probability that A nucleons have relative momenta less than p 0 , which is a free parameter of the model.This provides the following relation between the production cross sections of the nuclear cluster emitted with a momentum p A and the nucleon emitted with a momentum p p where p A = Ap p .For a given nucleus, the coalescence parameter B A should not depend on the momentum since it depends only on the cluster parameters: where M and m are the nucleus and the proton mass, respectively and p 0 is the relative momentum between the constituent nucleons of the nucleus.The parameter B 3 was computed for 3 Λ H according to Equation 2 using the spectrum shown in Figure 2 and our previous measurement of the proton [50] and Λ [52] and finally In  Λ H coalescence parameter is not flat as a function of p T contrary to the prediction of the simple coalescence model [11], which does not take into account the characteristics of the emitting source.This is the same behaviour as observed for deuterons and 3 He nuclei [28].At low p T the B 2 values are compatible, suggesting that p 0 is similar for A = 2 and A = 3.Using the measured 3  Λ H yield the ratio S 3 = 3 Λ H/( 3 He×Λ/p), also known as the strangeness population factor [57], was evaluated.This ratio was first suggested by the authors of [8] in the expectation that dividing the strange to non-strange baryon yield should result in a value near unity in a simple coalescence model.According to the authors of [57], S 3 should be also a valuable tool to probe the nature of the matter created in the collision, since it is sensitive to the local baryon-strangeness correlation [58][59][60]: a value of S 3 close to unity would indicate that the phase-space populations for strange and light quarks are similar and would support the formation of high-temperature matter of deconfined quarks.In the thermal model approach the S 3 ratio does not depend on the chemical potential of particles and was found to be almost energy independent [1,61], while in a dynamical coalescence picture it increases with decreasing beam energy and is in general larger than the thermal model predictions [61].This leads to the conclusion that the information on correlations of baryon number and strangeness is lost in the thermal calculation because S 3 essentially depends only on the temperature.The Λ/p ratio used in the present analysis was taken from [50] and [52].The S 3 values obtained for particles (anti-particles) are summarised in Table 5 and the average of the two measurements is shown in the right panel of Figure 7.These values were compared with different theoretical models and to the results from experiments at BNL-AGS [8] and RHIC [9].The models used for the comparison are the statistical hadronization model [1], the hybrid UrQMD model [61] and its extension at the LHC energy [49], the DCM (Dubna Cascade Model) coalescence model (described in [61]) and two versions -default and string melting -of the AMPT (A Multi-Phase Transport Model for Relativistic Heavy Ion Collisions) [62] plus coalescence described in [57].The present result at √ s NN = 2.76 TeV is comparable to that measured at E864 experiment [8] at √ s NN ∼ 5 GeV, while it does not confirm the rising behaviour shown by STAR [9] and by the AMPT with string melting plus coalescence model [57].This result is consistent with the thermal model approach, which predicts a constant S 3 value from √ s NN above a few GeV.     .Right: S 3 ratio measured in this analysis compared with previous experimental results (E864 [8] and STAR [9] (triangle and star, respectively)) and different theoretical models as indicated in the legend.

Conclusions
Measurements of 3 Λ H and 3 ΛH in Pb-Pb collisions at √ s NN = 2.76 TeV were presented in this letter.The 3 Λ H lifetime was measured and was found to agree with previous measurements within uncertainties.The measured value was included in the computation of the world average of the 3 Λ H lifetime.Transverse momentum yields at mid-rapidity for central (0-10%) Pb-Pb collisions at √ s NN = 2.76 TeV were measured in three p T intervals.The yields of particles and anti-particles were measured in two centrality classes (0-10% and 10-50%) and compared with different theoretical models.The ratio 3 ΛH/ 3 Λ H is consistent with unity, as expected at the LHC energy.The measured yields indicate that hypernuclei in high-energy heavy-ion collisions are produced within an equilibrated thermal environment in which the temperature is the same as for the other particles produced at the LHC.The 3 Λ H/ 3 He ( 3 ΛH/ 3 He) ratio was also measured and compared with different theoretical models and results from the STAR experiment.STAR results are higher than ALICE results, but compatible within uncertainties.The 3 Λ H coalescence parameter was also evaluated.Its value increases with p T , and within the uncertainties, is consistent with those extracted for deuteron and 3 He nuclei [28].The ratio S 3 = 3 Λ H/( 3 He×Λ/p) was evaluated and compared with different theoretical models and measurements from previous experiments.The value of S 3 suggests that the production of nuclei and hypernuclei at the LHC can be described with a thermodynamic approach, and is similar to the one calculated by the Hybrid UrQMD model [49].No conclusions can be drawn about the AMPT + coalescence model [57], since no prediction of dynamical coalescence models is available at the LHC energy.The measured S 3 value excludes the rising trend in AMPT seen up to RHIC energies extends to LHC energies.The S 3 measured at AGS, RHIC and LHC are compatible within uncertainty with a value which is independent of the centre of mass energy of the collision.

2 Figure 1 :
Figure 1: Invariant mass of ( 3 He,π − ) (left) and (3He,π + ) (right) for events with 10-50% centrality in the pair 2 ≤ p T < 10 GeV/c interval.The data points are shown as filled circles, while the squares represent the background distribution as described in the text.The curve represents the function used to perform the fit and used to evaluate the background and the raw signal.The significance in ±3σ around the peak is 3.5 and 3.0 for the invariant mass distribution of ( 3 He,π − ) and ( 3 He,π + ), respectively.

Figure 2 :
Figure 2: Left: Transverse momentum spectra multiplied by the B.R. of the 3 Λ H → 3 He + π − decay for 3 Λ H (filled circles) and 3 ΛH (squares) for the most central (0-10%) Pb-Pb collisions at √ s NN = 2.76 TeV for |y| < 0.5.Symbols are displaced for better visibility.The dashed lines are the Blast-Wave curves used to extract the particle yields integrated over the full p T range.In order to take into account the large binning used in the analysis and the limited number of bins, the center of each bin was evaluated weighting the actual bin center with the Blast-Wave function.Right: 3 ΛH to 3 Λ H ratio as a function of p T .In both panels statistical uncertainties are represented by bars and systematic uncertainties are represented by open boxes.

Figure 3 :
Figure 3: Measured dN/d(ct) distribution and an exponential fit used to determine the lifetime.The bars and boxes are the statistical and systematic uncertainties, respectively.

3 ALICEFigure 5 :
Figure 5: p T -integrated 3 Λ H yield times branching ratio as a function of branching ratio (dN/dy ×B.R. vs B.R.).The horizontal line is the measured value and the band represents statistical and systematic uncertainties added in quadrature.Lines are different theoretical expectations as explained in the text.

6 .
a simple coalescence model the B A parameter for all the light nuclei should have the same behaviour.The coalescence parameter of deuteron (B d 2 ) and the coalescence parameters of 3 He and 3 Λ The comparison of the three coalescence parameters is shown in the left panel of Figure 7.The

Figure 7 : 2 d m 3
Figure 7: Left: B 2 as a function of p T /A for d (filled circles) [28], 3 He (empty circles) [28], and 3 Λ H (filled squares).The B (d, 3 Λ H) 2 and B (d, 3 He) 2 were evaluated as explained in the text.k 1 = m 2 d m 3 He m p , and k 2 = m 2 d m Λ m 2 p m 3 Λ H

Table 1 :
Summary of systematic uncertainties for the three p T intervals and in the full range (F.R.) considered.These uncertainties are the same for events with 0-10% and 10-50% centrality.For the final systematic uncertainty evaluation they were added in quadrature.

Table 2 :
Summary of systematic uncertainties for the determination of the proper lifetime of3 Λ H+ 3 ΛH.
[30]scattered over a large range, too.Recently, a statistical combination of the experimental lifetime estimations of The band represents the world average of 3 Λ H lifetime measurements τ = 215 +18 −16 ps, while the dashed line represent the lifetime of Λ as reported by the Particle Data Group[30].
Λ H lifetime (τ) measured by in this analysis (red diamond) compared with published results.

Table 3 :
p T -integrated 3 Λ H yield times the B.R. of the 3 Λ H → ( 3 He + π − ) decay, for 3 Λ H and 3 ΛH in Pb-Pb collisions at √ s NN = 2.76 TeV for different centrality classes in |y| < 0.5.For each centrality interval the average dN ch /dη is also reported

Table 5 :
S 3 for matter and anti-matter.To compute the ratio a B.R. of 25% was assumed for the 3 Λ H → 3 He+ π decay.